Accurate time-series forecasting for complex physical systems is the backbone of modern industrial monitoring and control, yet deep learning models often lack the physical consistency required in regulated environments. To bridge this gap, we introduce Process-Informed Forecasting (PIF) models for temperature in pharmaceutical lyophilization, embedding deterministic production recipes as macro-structural priors. We investigate classical methods (e.g., Autoregressive Integrated Moving Average (ARIMA) model) and modern deep learning architectures, including Kolmogorov-Arnold Networks (KANs). We compare three different loss function formulations that integrate a process-informed trajectory prior: a fixed-weight loss, a dynamic uncertainty-based loss, and a Residual-Based Attention (RBA) mechanism. We evaluate all models not only for accuracy and physical consistency but also for robustness to sensor noise. Furthermore, we test the practical generalizability of the best model in a transfer-learning scenario to a new process. Our results show that PIF models outperform their data-driven counterparts in terms of accuracy, physical plausibility and noise resilience, offering a scalable framework for reliable and generalizable forecasting solutions in critical manufacturing.

We investigate the learning dynamics of fully-connected neural networks through the lens of the neural gradient signal-to-noise ratio (SNR), examining the behavior of first-order optimizers in non-convex objectives. By interpreting the drift/diffusion phases as proposed in the information bottleneck theory, we identify a third phase termed "diffusion equilibrium" (DE), a stable training phase characterized by highly-ordered neural gradients across the sample space. This phase is marked by an abrupt (first-order) transition, where sample-wise gradients align (SNR increases), and stable optimizer convergence. Moreover, we find that when homogeneous residuals are also met across the sample space during the DE phase, this leads to better generalization, as the optimization steps are equally sensitive to each sample. Based on this observation, we propose a sample-wise re-weighting scheme, which considerably improves the residual homogeneity and generalization in quadratic loss functions, by targeting the problematic samples with large residuals and vanishing gradients. Finally, we explore the information compression phenomenon, pinpointing a significant saturation-induced compression of activations at the DE phase transition, driven by the sample-wise gradient directional alignment. Interestingly, it is during the saturation of activations that the model converges, with deeper layers experiencing negligible information loss. Supported by experimental examples on physics-informed neural networks (PINNs), which highlight the critical role of gradient agreement due to their inherent PDE-based interdependence of samples, our findings suggest that when both sample-wise gradients and residuals transition in an ordered state, this leads to faster convergence and better generalization. Identifying these phase transitions could improve deep learning optimization strategies, enhancing physics-informed methods and overall machine learning performance.

Neural operators have emerged as powerful surrogates for modeling complex physical problems. However, they suffer from spectral bias making them oblivious to high-frequency modes, which are present in multiscale physical systems. Therefore, they tend to produce over-smoothed solutions, which is particularly problematic in modeling turbulence and for systems with intricate patterns and sharp gradients such as multi-phase flow systems. In this work, we introduce a new approach named high-frequency scaling (HFS) to mitigate spectral bias in convolutional-based neural operators. By integrating HFS with proper variants of UNet, we demonstrate a higher prediction accuracy by mitigating spectral bias in single and two-phase flow problems. Unlike Fourier-based techniques, HFS is directly applied to the latent space, thus eliminating the computational cost associated with the Fourier transform. Additionally, we investigate alternative spectral bias mitigation through a diffusion model conditioned on neural operators. While the diffusion model integrated with the standard neural operator may still suffer from significant errors, these errors are substantially reduced when the diffusion model is integrated with a HFS-enhanced neural operator.

Spiking neural networks (SNNs) represent a promising approach in machine learning, combining the hierarchical learning capabilities of deep neural networks with the energy efficiency of spike-based computations. Traditional end-to-end training of SNNs is often based on back-propagation, where weight updates are derived from gradients computed through the chain rule. However, this method encounters challenges due to its excessive cost, limited biological plausibility, and inefficiency on neuromorphic hardware. In this study, we introduce an alternative training approach for SNNs. Instead of using back-propagation, we leverage weight perturbation methods within a forward-mode gradient framework. Specifically, we perturb the weight matrix with a small noise term and estimate gradients by observing the changes in the network output. Experimental results on regression tasks, including solving various PDEs, show that our approach achieves competitive accuracy, suggesting its suitability for neuromorphic systems and potential hardware compatibility.

Deep operator networks (DeepONets, DONs) offer a distinct advantage over traditional neural networks in their ability learn from data collected at heterogeneous resolutions. This property, known as discretization invariance , can be particularly valuable when modeling fine-scale temporal dynamics with limited high-resolution data, provided that lower-resolution data are available. Nevertheless, DeepONets alone often struggle to capture and maintain dependencies over long sequences compared to other state-of-the-art algorithms. We propose a novel framework that leverages multi-resolution data in training and provides precise models when dealing with limited high-resolution data. We achieve this through extending the DeepONet architecture with a long short-term memory network (LSTM), and training it in a three-step procedure that utilizes data of different levels of granularity. Combining these two architectures, we equip the network with explicit mechanisms to leverage multi-resolution data, as well as capture temporal dependencies in long sequences. We test our method on long-time-evolution modeling of multiple non-linear systems and show that the proposed multi-resolution DON-LSTM achieves significantly lower generalization error and requires fewer high-resolution samples compared to its vanilla counterparts.

Inspired by the Kolmogorov-Arnold representation theorem and Ku̇rková's principle of using approximate representations, we propose the Ku̇rková-Kolmogorov-Arnold Network (KKAN), a new two-block architecture that combines robust multi-layer perceptron (MLP) based inner functions with flexible linear combinations of basis functions as outer functions. We first prove that KKAN is a universal approximator, and then we demonstrate its versatility across scientific machine-learning applications, including function regression, physics-informed machine learning (PIML), and operator-learning frameworks. The benchmark results show that KKANs outperform MLPs and the original Kolmogorov-Arnold Networks (KANs) in function approximation and operator learning tasks and achieve performance comparable to fully optimized MLPs for PIML. To better understand the behavior of the new representation models, we analyze their geometric complexity and learning dynamics using information bottleneck theory, identifying three universal learning stages, fitting, transition, and diffusion, across all types of architectures. We find a strong correlation between geometric complexity and signal-to-noise ratio (SNR), with optimal generalization achieved during the diffusion stage. Additionally, we propose self-scaled residual-based attention weights to maintain high SNR dynamically, ensuring uniform convergence and prolonged learning.

We solve high-dimensional steady-state Fokker-Planck equations on the whole space by applying tensor neural networks. The tensor networks are a linear combination of tensor products of one-dimensional feedforward networks or a linear combination of several selected radial basis functions. The use of tensor feedforward networks allows us to efficiently exploit auto-differentiation (in physical variables) in major Python packages while using radial basis functions can fully avoid auto-differentiation, which is rather expensive in high dimensions. We then use the physics-informed neural networks and stochastic gradient descent methods to learn the tensor networks. One essential step is to determine a proper bounded domain or numerical support for the Fokker-Planck equation. To better train the tensor radial basis function networks, we impose some constraints on parameters, which lead to relatively high accuracy. We demonstrate numerically that the tensor neural networks in physics-informed machine learning are efficient for steady-state Fokker-Planck equations from two to ten dimensions.

Gaucher Disease (GD) is a rare genetic disorder characterized by a deficiency in the enzyme glucocerebrosidase, leading to the accumulation of glucosylceramide in various cells, including red blood cells (RBCs). This accumulation results in altered biomechanical properties and rheological behavior of RBCs, which may play an important role in blood rheology and the development of bone infarcts, avascular necrosis (AVN) and other bone diseases associated with GD. In this study, dissipative particle dynamics (DPD) simulations are employed to investigate the biomechanics and rheology of blood and RBCs in GD under various flow conditions. The model incorporates the unique characteristics of GD RBCs, such as decreased deformability and increased aggregation properties, and aims to capture the resulting changes in RBC biophysics and blood viscosity. This study is the first to explore the Young's modulus and aggregation parameters of GD RBCs by validating simulations with confocal imaging and experimental RBC disaggregation thresholds. Through in silico simulations, we examine the impact of hematocrit, RBC disaggregation threshold, and cell stiffness on blood viscosity in GD. The results reveal three distinct domains of GD blood viscosity based on shear rate: the aggregation domain, where the RBC disaggregation threshold predominantly influences blood viscosity; the transition area, where both RBC aggregation and stiffness impact on blood viscosity; and the stiffness domain, where the stiffness of RBCs emerges as the primary determinant of blood viscosity. By analyzing RBC mechanical properties and blood viscosity in relation to bone disease, we find that the RBC aggregation properties, deformability, and blood viscosity, may contribute to its onset. These findings enhance our understanding of how changes in RBC properties impact on blood viscosity and may affect bone health, offering a partial explanation for the bone complications observed in GD patients.

Thoracic aortic aneurysms (TAAs) stem from diverse mechanical and mechanobiological disruptions to the aortic wall that can also increase the risk of dissection or rupture. There is increasing evidence that dysfunctions along the aortic mechanotransduction axis, including reduced integrity of elastic fibers and loss of cell-matrix connections, are particularly capable of causing thoracic aortopathy. Because different insults can produce distinct mechanical vulnerabilities, there is a pressing need to identify interacting factors that drive progression. In this work, we employ a finite element framework to generate synthetic TAAs arising from hundreds of heterogeneous insults that span a range of compromised elastic fiber integrity and cellular mechanosensing. From these simulations, we construct localized dilatation and distensibility maps throughout the aortic domain to serve as training data for neural network models to predict the initiating combined insult. Several candidate architectures (Deep Operator Networks, UNets, and Laplace Neural Operators) and input data formats are compared to establish a standard for handling future subject-specific information. We further quantify the predictive capability when networks are trained on geometric (dilatation) information alone, which mimics current clinical guidelines, versus training on both geometric and mechanical (distensibility) information. We show that prediction errors based on dilatation data are significantly higher than those based on dilatation and distensibility across all networks considered, highlighting the benefit of obtaining local distensibility measures in TAA assessment. Additionally, we identify UNet as the best-performing architecture across all training data formats. These findings demonstrate the importance of obtaining full-field measurements of both dilatation and distensibility in the aneurysmal aorta to identify the mechanobiological insults that drive disease progression, which will advance personalized treatment strategies that target the underlying pathologic mechanisms.

In this article, we introduce the notion of safe predefined-time stability and address an optimal safe predefined-time stabilization problem. In particular, safe predefined-time stability characterizes parameter-dependent nonlinear dynamical systems whose trajectories starting in a given set of admissible states remain in the set of admissible states for all time and converge to an equilibrium point in a predefined time. Furthermore, we provide a Lyapunov theorem establishing sufficient conditions for safe predefined-time stability. We address the optimal safe predefined-time stabilization problem by synthesizing feedback controllers that guarantee closed-loop system safe predefined-time stability while optimizing a given performance measure. Specifically, safe predefined-time stability of the closed-loop system is guaranteed via a Lyapunov function satisfying a differential inequality while simultaneously serving as a solution to the steady-state Hamilton-Jacobi-Bellman (HJB) equation ensuring optimality. Given that the HJB equation is generally difficult to solve, we develop a physics-informed machine learning-based algorithm for learning the safely predefined-time stabilizing solution to the steady-state HJB equation. Several simulation results are provided to demonstrate the efficacy of the proposed approach.

Deep neural networks are an attractive alternative for simulating complex dynamical systems, as in comparison to traditional scientific computing methods, they offer reduced computational costs during inference and can be trained directly from observational data. Existing methods, however, cannot extrapolate accurately and are prone to error accumulation in long-time integration. Herein, we address this issue by combining neural operators with recurrent neural networks, learning the operator mapping, while offering a recurrent structure to capture temporal dependencies. The integrated framework is shown to stabilize the solution and reduce error accumulation for both interpolation and extrapolation of the Korteweg-de Vries equation.

The curse-of-dimensionality taxes computational resources heavily with exponentially increasing computational cost as the dimension increases. This poses great challenges in solving high-dimensional partial differential equations (PDEs), as Richard E. Bellman first pointed out over 60 years ago. While there has been some recent success in solving numerical PDEs in high dimensions, such computations are prohibitively expensive, and true scaling of general nonlinear PDEs to high dimensions has never been achieved. We develop a new method of scaling up physics-informed neural networks (PINNs) to solve arbitrary high-dimensional PDEs. The new method, called Stochastic Dimension Gradient Descent (SDGD), decomposes a gradient of PDEs' and PINNs' residual into pieces corresponding to different dimensions and randomly samples a subset of these dimensional pieces in each iteration of training PINNs. We prove theoretically the convergence and other desired properties of the proposed method. We demonstrate in various diverse tests that the proposed method can solve many notoriously hard high-dimensional PDEs, including the Hamilton-Jacobi-Bellman (HJB) and the Schrödinger equations in tens of thousands of dimensions very fast on a single GPU using the PINNs mesh-free approach. Notably, we solve nonlinear PDEs with nontrivial, anisotropic, and inseparable solutions in less than one hour for 1000 dimensions and in 12 h for 100,000 dimensions on a single GPU using SDGD with PINNs. Since SDGD is a general training methodology of PINNs, it can be applied to any current and future variants of PINNs to scale them up for arbitrary high-dimensional PDEs.

Discovering mathematical equations that govern physical and biological systems from observed data is a fundamental challenge in scientific research. We present a new physics-informed framework for parameter estimation and missing physics identification (gray-box) in the field of Systems Biology. The proposed framework-named AI-Aristotle-combines the eXtreme Theory of Functional Connections (X-TFC) domain-decomposition and Physics-Informed Neural Networks (PINNs) with symbolic regression (SR) techniques for parameter discovery and gray-box identification. We test the accuracy, speed, flexibility, and robustness of AI-Aristotle based on two benchmark problems in Systems Biology: a pharmacokinetics drug absorption model and an ultradian endocrine model for glucose-insulin interactions. We compare the two machine learning methods (X-TFC and PINNs), and moreover, we employ two different symbolic regression techniques to cross-verify our results. To test the performance of AI-Aristotle, we use sparse synthetic data perturbed by uniformly distributed noise. More broadly, our work provides insights into the accuracy, cost, scalability, and robustness of integrating neural networks with symbolic regressors, offering a comprehensive guide for researchers tackling gray-box identification challenges in complex dynamical systems in biomedicine and beyond.

Dynamic graph embedding has gained great attention recently due to its capability of learning low-dimensional and meaningful graph representations for complex temporal graphs with high accuracy. However, recent advances mostly focus on learning node embeddings as deterministic “vectors” for static graphs, hence disregarding the key graph temporal dynamics and the evolving uncertainties associated with node embedding in the latent space. In this work, we propose an efficient stochastic dynamic graph embedding method (DynG2G) that applies an inductive feedforward encoder trained with node triplet energy-based ranking loss. Every node per timestamp is encoded as a time-dependent probabilistic multivariate Gaussian distribution in the latent space, and, hence, we are able to quantify the node embedding uncertainty on-the-fly. We have considered eight different benchmarks that represent diversity in size (from 96 nodes to 87626 and from 13398 edges to 4870863) as well as diversity in dynamics, from slowly changing temporal evolution to rapidly varying multirate dynamics. We demonstrate through extensive experiments based on these eight dynamic graph benchmarks that DynG2G achieves new state-of-the-art performance in capturing the underlying temporal node embeddings. We also demonstrate that DynG2G can simultaneously predict the evolving node embedding uncertainty, which plays a crucial role in quantifying the intrinsic dimensionality of the dynamical system over time. In particular, we obtain a “universal” relation of the optimal embedding dimension,$L_{o}$, versus the effective dimensionality of uncertainty,$D_{u}$, and infer that$L_{o}=D_{u}$for all cases. This, in turn, implies that the uncertainty quantification approach we employ in the DynG2G algorithm correctly captures the intrinsic dimensionality of the dynamics of such evolving graphs despite the diverse nature and composition of the graphs at each timestamp. In addition, this$L_{0} - D_{u}$correlation provides a clear path to selecting adaptively the optimum embedding size at each timestamp by setting$L \ge D_{u}$.

Physics-Informed Neural Networks (PINNs) and extended PINNs (XPINNs) have emerged as a promising approach in computational science and engineering for solving partial differential equations (PDEs) by combining the power of artificial intelligence (AI) with the underlying physics to accurately model and predict the solutions to complex problems in science and engineering. In this work, we propose the augmented physics-informed neural network (APINN), which adopts soft and trainable domain decomposition and flexible parameter sharing to further improve the extended PINN (XPINN) as well as the vanilla PINN methods. Concretely, a trainable gate network is employed to mimic the hard decomposition of XPINN, which can be flexibly fine-tuned for discovering a potentially better partition. The gate network satisfying the partition-of-unity property, weighted averages several sub-networks as the final output. APINN does not require complex interface conditions, whose sub-nets can utilize all training samples rather than just part of the training data in their subdomains. Lastly, each sub-net shares part of the common parameters to capture the similar components in each decomposed function. Furthermore, following the PINN generalization theory (Hu et al., 2022), APINN is shown to improve generalization by proper gate network initialization and general domain & function decomposition. Extensive experiments on different partial differential equations (PDEs) demonstrate how APINN improves PINN and XPINN. Specifically, we present examples where XPINN performs similarly to or worse than PINN, so that APINN can significantly improve both. We also show cases where XPINN is already better than PINN, so APINN can still slightly improve XPINN. Furthermore, we visualize the optimized gating networks and their optimization trajectories, and connect them with their performance, which helps discover the possibly optimal decomposition. Interestingly, if initialized by different decomposition, the performances of corresponding APINNs can differ drastically. This, in turn, shows the potential to design an optimal domain decomposition for the PDE under consideration.

Being the largest lymphatic organ in the body, the spleen also constantly controls the quality of red blood cells (RBCs) in circulation through its two major filtration components, namely interendothelial slits (IES) and red pulp macrophages. In contrast to the extensive studies in understanding the filtration function of IES, fewer works investigate how the splenic macrophages retain the aged and diseased RBCs, i.e., RBCs in sickle cell disease (SCD). Herein, we perform a computational study informed by companion experiments to quantify the dynamics of RBCs captured and retained by the macrophages. We first calibrate the parameters in the computational model based on microfluidic experimental measurements for sickle RBCs under normoxia and hypoxia, as those parameters are not available in the literature. Next, we quantify the impact of key factors expected to dictate the RBC retention by the macrophages in the spleen, namely, blood flow conditions, RBC aggregation, hematocrit, RBC morphology, and oxygen levels. Our simulation results show that hypoxic conditions could enhance the adhesion between the sickle RBCs and macrophages. This, in turn, increases the retention of RBCs by as much as four-fold, which could be a possible cause of RBC congestion in the spleen of patients with SCD. Our study on the impact of RBC aggregation illustrates a 'clustering effect', where multiple RBCs in one aggregate can make contact and adhere to the macrophages, leading to a higher retention rate than that resulting from RBC-macrophage pair interactions. Our simulations of sickle RBCs flowing past macrophages for a range of blood flow velocities indicate that the increased blood velocity could quickly attenuate the function of the red pulp macrophages on detaining aged or diseased RBCs, thereby providing a possible rationale for the slow blood flow in the open circulation of the spleen. Furthermore, we quantify the impact of RBC morphology on their tendency to be retained by the macrophages. We find that the sickle and granular-shaped RBCs are more likely to be filtered by macrophages in the spleen. This finding is consistent with the observation of low percentages of these two forms of sickle RBCs in the blood smear of SCD patients. Taken together, our experimental and simulation results aid in our quantitative understanding of the function of splenic macrophages in retaining the diseased RBCs and provide an opportunity to combine such knowledge with the current knowledge of the interaction between IES and traversing RBCs to apprehend the complete filtration function of the spleen in SCD.

We propose the Poisson neural networks (PNNs) to learn Poisson systems and trajectories of autonomous systems from data. Based on the Darboux-Lie theorem, the phase flow of a Poisson system can be written as the composition of: 1) a coordinate transformation; 2) an extended symplectic map; and 3) the inverse of the transformation. In this work, we extend this result to the unknotted trajectories of autonomous systems. We employ structured neural networks with physical priors to approximate the three aforementioned maps. We demonstrate through several simulations that PNNs are capable of handling very accurately several challenging tasks, including the motion of a particle in the electromagnetic potential, the nonlinear Schrödinger equation, and pixel observations of the two-body problem.

Emerging clinical evidence suggests that thrombosis in the microvasculature of patients with Coronavirus disease 2019 (COVID-19) plays an essential role in dictating the disease progression. Because of the infectious nature of SARS-CoV-2, patients' fresh blood samples are limited to access for in vitro experimental investigations. Herein, we employ a novel multiscale and multiphysics computational framework to perform predictive modeling of the pathological thrombus formation in the microvasculature using data from patients with COVID-19. This framework seamlessly integrates the key components in the process of blood clotting, including hemodynamics, transport of coagulation factors and coagulation kinetics, blood cell mechanics and adhesive dynamics, and thus allows us to quantify the contributions of many prothrombotic factors reported in the literature, such as stasis, the derangement in blood coagulation factor levels and activities, inflammatory responses of endothelial cells and leukocytes to the microthrombus formation in COVID-19. Our simulation results show that among the coagulation factors considered, antithrombin and factor V play more prominent roles in promoting thrombosis. Our simulations also suggest that recruitment of WBCs to the endothelial cells exacerbates thrombogenesis and contributes to the blockage of the blood flow. Additionally, we show that the recent identification of flowing blood cell clusters could be a result of detachment of WBCs from thrombogenic sites, which may serve as a nidus for new clot formation. These findings point to potential targets that should be further evaluated, and prioritized in the anti-thrombotic treatment of patients with COVID-19. Altogether, our computational framework provides a powerful tool for quantitative understanding of the mechanism of pathological thrombus formation and offers insights into new therapeutic approaches for treating COVID-19 associated thrombosis.

Microaneurysms (MAs) are one of the earliest clinically visible signs of diabetic retinopathy (DR). MA leakage or rupture may precipitate local pathology in the surrounding neural retina that impacts visual function. Thrombosis in MAs may affect their turnover time, an indicator associated with visual and anatomic outcomes in the diabetic eyes. In this work, we perform computational modeling of blood flow in microchannels containing various MAs to investigate the pathologies of MAs in DR. The particle-based model employed in this study can explicitly represent red blood cells (RBCs) and platelets as well as their interaction in the blood flow, a process that is very difficult to observe in vivo. Our simulations illustrate that while the main blood flow from the parent vessels can perfuse the entire lumen of MAs with small body-to-neck ratio (BNR), it can only perfuse part of the lumen in MAs with large BNR, particularly at a low hematocrit level, leading to possible hypoxic conditions inside MAs. We also quantify the impacts of the size of MAs, blood flow velocity, hematocrit and RBC stiffness and adhesion on the likelihood of platelets entering MAs as well as their residence time inside, two factors that are thought to be associated with thrombus formation in MAs. Our results show that enlarged MA size, increased blood velocity and hematocrit in the parent vessel of MAs as well as the RBC-RBC adhesion promote the migration of platelets into MAs and also prolong their residence time, thereby increasing the propensity of thrombosis within MAs. Overall, our work suggests that computational simulations using particle-based models can help to understand the microvascular pathology pertaining to MAs in DR and provide insights to stimulate and steer new experimental and computational studies in this area.

Many genetic mutations adversely affect the structure and function of load-bearing soft tissues, with clinical sequelae often responsible for disability or death. Parallel advances in genetics and histomechanical characterization provide significant insight into these conditions, but there remains a pressing need to integrate such information. We present a novel genotype-to-biomechanical phenotype neural network (G2Φnet) for characterizing and classifying biomechanical properties of soft tissues, which serve as important functional readouts of tissue health or disease. We illustrate the utility of our approach by inferring the nonlinear, genotype-dependent constitutive behavior of the aorta for four mouse models involving defects or deficiencies in extracellular constituents. We show that G2Φnet can infer the biomechanical response while simultaneously ascribing the associated genotype by utilizing limited, noisy, and unstructured experimental data. More broadly, G2Φnet provides a powerful method and a paradigm shift for correlating genotype and biomechanical phenotype quantitatively, promising a better understanding of their interplay in biological tissues.

We propose a potential flow generator with$L_{2}$optimal transport regularity, which can be easily integrated into a wide range of generative models, including different versions of generative adversarial networks (GANs) and normalizing flow models. With only a slight augmentation to the original generator loss functions, our generator not only tries to transport the input distribution to the target one but also aims to find the one with minimum$L_{2}$transport cost. We show the effectiveness of our method in several 2-D problems and illustrate the concept of “proximity” due to the$L_{2}$optimal transport regularity. Subsequently, we demonstrate the effectiveness of the potential flow generator in image translation tasks with unpaired training data from the MNIST data set and the CelebA data set with a comparison against vanilla Wasserstein GAN with gradient penalty (WGAN-GP) and CycleGAN.

The spleen, the largest secondary lymphoid organ in humans, not only fulfils a broad range of immune functions, but also plays an important role in red blood cell's (RBC) life cycle. Although much progress has been made to elucidate the critical biological processes involved in the maturation of young RBCs (reticulocytes) as well as removal of senescent RBCs in the spleen, the underlying mechanisms driving these processes are still obscure. Herein, we perform a computational study to simulate the passage of RBCs through interendothelial slits (IES) in the spleen at different stages of their lifespan and investigate the role of the spleen in facilitating the maturation of reticulocytes and in clearing the senescent RBCs. Our simulations reveal that at the beginning of the RBC life cycle, intracellular non-deformable particles in reticulocytes can be biomechanically expelled from the cell upon passage through IES, an insightful explanation of why this peculiar "pitting" process is spleen-specific. Our results also show that immature RBCs shed surface area by releasing vesicles after crossing IES and progressively acquire the biconcave shape of mature RBCs. These findings likely explain why RBCs from splenectomized patients are significantly larger than those from nonsplenectomized subjects. Finally, we show that at the end of their life span, senescent RBCs are not only retained by IES due to reduced deformability but also become susceptible to mechanical lysis under shear stress. This finding supports the recent hypothesis that transformation into a hemolyzed ghost is a prerequisite for phagocytosis of senescent RBCs. Altogether, our computational investigation illustrates critical biological processes in the spleen that cannot be observed in vivo or in vitro and offer insights into the role of the spleen in the RBC physiology.

Epidemiological models can provide the dynamic evolution of a pandemic but they are based on many assumptions and parameters that have to be adjusted over the time the pandemic lasts. However, often the available data are not sufficient to identify the model parameters and hence infer the unobserved dynamics. Here, we develop a general framework for building a trustworthy data-driven epidemiological model, consisting of a workflow that integrates data acquisition and event timeline, model development, identifiability analysis, sensitivity analysis, model calibration, model robustness analysis, and projection with uncertainties in different scenarios. In particular, we apply this framework to propose a modified susceptible-exposed-infectious-recovered (SEIR) model, including new compartments and model vaccination in order to project the transmission dynamics of COVID-19 in New York City (NYC). We find that we can uniquely estimate the model parameters and accurately project the daily new infection cases, hospitalizations, and deaths, in agreement with the available data from NYC's government's website. In addition, we employ the calibrated data-driven model to study the effects of vaccination and timing of reopening indoor dining in NYC.

The accuracy of deep learning, i.e., deep neural networks, can be characterized by dividing the total error into three main types: approximation error, optimization error, and generalization error. Whereas there are some satisfactory answers to the problems of approximation and optimization, much less is known about the theory of generalization. Most existing theoretical works for generalization fail to explain the performance of neural networks in practice. To derive a meaningful bound, we study the generalization error of neural networks for classification problems in terms of data distribution and neural network smoothness. We introduce the cover complexity (CC) to measure the difficulty of learning a data set and the inverse of the modulus of continuity to quantify neural network smoothness. A quantitative bound for expected accuracy/error is derived by considering both the CC and neural network smoothness. Although most of the analysis is general and not specific to neural networks, we validate our theoretical assumptions and results numerically for neural networks by several data sets of images. The numerical results confirm that the expected error of trained networks scaled with the square root of the number of classes has a linear relationship with respect to the CC. We also observe a clear consistency between test loss and neural network smoothness during the training process. In addition, we demonstrate empirically that the neural network smoothness decreases when the network size increases whereas the smoothness is insensitive to training dataset size.

Mathematical models of biological reactions at the system-level lead to a set of ordinary differential equations with many unknown parameters that need to be inferred using relatively few experimental measurements. Having a reliable and robust algorithm for parameter inference and prediction of the hidden dynamics has been one of the core subjects in systems biology, and is the focus of this study. We have developed a new systems-biology-informed deep learning algorithm that incorporates the system of ordinary differential equations into the neural networks. Enforcing these equations effectively adds constraints to the optimization procedure that manifests itself as an imposed structure on the observational data. Using few scattered and noisy measurements, we are able to infer the dynamics of unobserved species, external forcing, and the unknown model parameters. We have successfully tested the algorithm for three different benchmark problems.

Mechanical interactions between flowing and coagulated blood (thrombus) are crucial in dictating the deformation and remodeling of a thrombus after its formation in hemostasis. We propose a fully-Eulerian, three-dimensional, phase-field model of thrombus that is calibrated with existing in vitro experimental data. This phase-field model considers spatial variations in permeability and material properties within a single unified mathematical framework derived from an energy perspective, thereby allowing us to study effects of thrombus microstructure and properties on its deformation and possible release of emboli under different hemodynamic conditions. Moreover, we combine this proposed thrombus model with a particle-based model which simulates the initiation of the thrombus. The volume fraction of a thrombus obtained from the particle simulation is mapped to an input variable in the proposed phase-field thrombus model. The present work is thus the first computational study to integrate the initiation of a thrombus through platelet aggregation with its subsequent viscoelastic responses to various shear flows. This framework can be informed by clinical data and potentially be used to predict the risk of diverse thromboembolic events under physiological and pathological conditions.

Sickle cell disease (SCD) is a highly complex genetic blood disorder in which red blood cells (RBC) exhibit heterogeneous morphology changes and decreased deformability.We employ a kinetic model for cell morphological sickling that invokes parameters derived from patient-specific data.This model is used to investigate the dynamics of individual sickle cells in a capillary-like microenvironment in order to address various mechanisms associated with SCD.We show that all RBCs, both hypoxia-unaffected and hypoxia-affected ones, regularly pass through microgates under oxygenated state.However, the hypoxia-affected cells undergo sickling which significantly alters cell dynamics.In particular, the dense and rigid sickle RBCs are obstructed thereby clogging blood flow while the less dense and deformable ones are capable of circumnavigating dead (trapped) cells ahead of them by choosing a serpentine path.Informed by recent experiments involving microfluidics that provide in vitro quantitative information on cell dynamics under transient hypoxia conditions, we have performed detailed computational simulations of alterations to cell behavior in response to morphological changes and membrane stiffening.Our model reveals that SCD exhibits substantial heterogeneity even within a particular density-fractionated subpopulation.These findings provide unique insights into how individual sickle cells move through capillaries under transient hypoxic conditions, and offer novel possibilities for designing effective therapeutic interventions for SCD. Author summarySickle cell disease is a genetic blood disease that causes vaso-occlusive pain crises.Here, we investigate the individual sickle cell behavior under controlled hypoxic conditions through patient-specific predictive computational simulations that are informed by companion microfluidic experiments.We identify the different dynamic behavior between individual sickle RBCs and normal ones in microfluidic flow, and analyze the hypoxia-

Sickle cell disease (SCD) is a hematological disorder leading to blood vessel occlusion accompanied by painful episodes and even death. Red blood cells (RBCs) of SCD patients have diverse shapes that reveal important biomechanical and bio-rheological characteristics, e.g. their density, fragility, adhesive properties, etc. Hence, having an objective and effective way of RBC shape quantification and classification will lead to better insights and eventual better prognosis of the disease. To this end, we have developed an automated, high-throughput, ex-vivo RBC shape classification framework that consists of three stages. First, we present an automatic hierarchical RBC extraction method to detect the RBC region (ROI) from the background, and then separate touching RBCs in the ROI images by applying an improved random walk method based on automatic seed generation. Second, we apply a mask-based RBC patch-size normalization method to normalize the variant size of segmented single RBC patches into uniform size. Third, we employ deep convolutional neural networks (CNNs) to realize RBC classification; the alternating convolution and pooling operations can deal with non-linear and complex patterns. Furthermore, we investigate the specific shape factor quantification for the classified RBC image data in order to develop a general multiscale shape analysis. We perform several experiments on raw microscopy image datasets from 8 SCD patients (over 7,000 single RBC images) through a 5-fold cross validation method both for oxygenated and deoxygenated RBCs. We demonstrate that the proposed framework can successfully classify sickle shape RBCs in an automated manner with high accuracy, and we also provide the corresponding shape factor analysis, which can be used synergistically with the CNN analysis for more robust predictions. Moreover, the trained deep CNN exhibits good performance even for a deoxygenated dataset and distinguishes the subtle differences in texture alteration inside the oxygenated and deoxygenated RBCs.

Modeling the transport, activation, and adhesion of platelets is crucial in predicting thrombus formation and growth following a thrombotic event in normal or pathological conditions. We propose a shear-dependent platelet adhesive model based on the Morse potential that is calibrated by existing in vivo and in vitro experimental data and can be used over a wide range of flow shear rates ([Formula: see text]). We introduce an Eulerian-Lagrangian model where hemodynamics is solved on a fixed Eulerian grid, while platelets are tracked using a Lagrangian framework. A force coupling method is introduced for bidirectional coupling of platelet motion with blood flow. Further, we couple the calibrated platelet aggregation model with a tissue-factor/contact pathway coagulation cascade, representing the relevant biology of thrombin generation and the subsequent fibrin deposition. The range of shear rates covered by the proposed model encompass venous and arterial thrombosis, ranging from low-shear-rate conditions in abdominal aortic aneurysms and thoracic aortic dissections to thrombosis in stenotic arteries following plaque rupture, where local shear rates are extremely high.

Healthy red blood cells (RBCs) have remarkable deformability, squeezing through narrow capillaries as small as 3 microns in diameter without any damage. However, in many hematological disorders the spectrin network and lipid bilayer of diseased RBCs may be significantly altered, leading to impaired functionality including loss of deformability. We employ a two-component whole-cell multiscale model to quantify the biomechanical characteristics of the healthy and diseased RBCs, including Plasmodium falciparum-infected RBCs (Pf-RBCs) and defective RBCs in hereditary disorders, such as spherocytosis and elliptocytosis. In particular, we develop a two-step multiscale framework based on coarse-grained molecular dynamics (CGMD) and dissipative particle dynamics (DPD) to predict the static and dynamic responses of RBCs subject to tensile forcing, using experimental information only on the structural defects in the lipid bilayer, cytoskeleton, and their interaction. We first employ CGMD on a small RBC patch to compute the shear modulus, bending stiffness, and network parameters, which are subsequently used as input to a whole-cell DPD model to predict the RBC shape and corresponding stress field. For Pf-RBCs at trophozoite and schizont stages, the presence of cytoadherent knobs elevates the shear response in the lipid bilayer and stiffens the RBC membrane. For RBCs in spherocytosis and elliptocytosis, the bilayer-cytoskeleton interaction is weakened, resulting in substantial increase of the tensile stress in the lipid bilayer. Furthermore, we investigate the transient behavior of stretching deformation and shape relaxation of the normal and defective RBCs. Different from the normal RBCs possessing high elasticity, our simulations reveal that the defective RBCs respond irreversibly, i.e., they lose their ability to recover the normal biconcave shape in successive loading cycles of stretching and relaxation. Our findings provide fundamental insights into the microstructure and biomechanics of RBCs, and demonstrate that the two-step multiscale framework presented here can be used effectively for in silico studies of hematological disorders based on first principles and patient-specific experimental input at the protein level.

We present simulations of blood and cancer cell separation in complex microfluidic channels with subcellular resolution, demonstrating unprecedented time to solution, performing at 65.5% of the available 39.4 PetaInstructions/s in the 18, 688 nodes of the Titan supercomputer.

When blood flows through a bifurcation, red blood cells (RBCs) travel into side branches at different hematocrit levels, and it is even possible that all RBCs enter into one branch only, leading to a complete separation of plasma and RBCs. To quantify this phenomenon via particle-based mesoscopic simulations, we developed a general framework for open boundary conditions in multiphase flows that is effective even for high hematocrit levels. The inflow at the inlet is duplicated from a fully developed flow generated in a pilot simulation with periodic boundary conditions. The outflow is controlled by adaptive forces to maintain the flow rate and velocity gradient at fixed values, while the particles leaving the arteriole at the outlet are removed from the system. Upon validation of this approach, we performed systematic 3D simulations to study plasma skimming in arterioles of diameters 20 to 32 microns. For a flow rate ratio 6:1 at the branches, we observed the "all-or-nothing" phenomenon with plasma only entering the low flow rate branch. We then simulated blood-plasma separation in arteriolar bifurcations with different bifurcation angles and same diameter of the daughter branches. Our simulations predict a significant increase in RBC flux through the main daughter branch as the bifurcation angle is increased. Finally, we demonstrated the effectiveness of the new methodology in simulations of blood flow in vessels with multiple inlets and outlets, constructed using an angiogenesis model.

Hierarchical uncertainty quantification can reduce the computational cost of stochastic circuit simulation by employing spectral methods at different levels. This paper presents an efficient framework to simulate hierarchically some challenging stochastic circuits/systems that include high-dimensional subsystems. Due to the high parameter dimensionality, it is challenging to both extract surrogate models at the low level of the design hierarchy and to handle them in the high-level simulation. In this paper, we develop an efficient analysis of variance-based stochastic circuit/microelectromechanical systems simulator to efficiently extract the surrogate models at the low level. In order to avoid the curse of dimensionality, we employ tensor-train decomposition at the high level to construct the basis functions and Gauss quadrature points. As a demonstration, we verify our algorithm on a stochastic oscillator with four MEMS capacitors and 184 random parameters. This challenging example is efficiently simulated by our simulator at the cost of only 10min in MATLAB on a regular personal computer.

Interfacing atomistic-based with continuum-based simulation codes is now required in many multiscale physical and biological systems. We present the computational advances that have enabled the first multiscale simulation on 190,740 processors by coupling a high-order (spectral element) Navier-Stokes solver with a stochastic (coarse-grained) Molecular Dynamics solver based on Dissipative Particle Dynamics (DPD). The key contributions are proper interface conditions for overlapped domains, topology-aware communication, SIMDization, multiscale visualization and a new domain partitioning for atomistic solvers. We study blood flow in a patient-specific cerebrovasculature with a brain aneurysm, and analyze the interaction of blood cells with the arterial walls endowed with a glycocalyx causing thrombus formation and eventual aneurysm rupture. The macro-scale dynamics (about 3 billion unknowns) are resolved by NεκTαr - a spectral element solver; the micro-scale flow and cell dynamics within the aneurysm are resolved by an in-house version of DPD-LAMMPS (for an equivalent of about 100 billions molecules).

Red blood cells (RBCs) infected by a Plasmodium parasite in malaria may lose their membrane deformability with a relative membrane stiffening more than ten-fold in comparison with healthy RBCs leading to potential capillary occlusions. Moreover, infected RBCs are able to adhere to other healthy and parasitized cells and to the vascular endothelium resulting in a substantial disruption of normal blood circulation. In the present work, we simulate infected RBCs in malaria using a multiscale RBC model based on the dissipative particle dynamics method, coupling scales at the sub-cellular level with scales at the vessel size. Our objective is to conduct a full validation of the RBC model with a diverse set of experimental data, including temperature dependence, and to identify the limitations of this purely mechanistic model. The simulated elastic deformations of parasitized RBCs match those obtained in optical-tweezers experiments for different stages of intra-erythrocytic parasite development. The rheological properties of RBCs in malaria are compared with those obtained by optical magnetic twisting cytometry and by monitoring membrane fluctuations at room, physiological, and febrile temperatures. We also study the dynamics of infected RBCs in Poiseuille flow in comparison with healthy cells and present validated bulk viscosity predictions of malaria-infected blood for a wide range of parasitemia levels (percentage of infected RBCs with respect to the total number of cells in a unit volume).

Proper orthogonal decomposition (POD), Kriging interpolation, and smoothing are applied to reconstruct gappy and noisy data of blood flow in a carotid artery. While we have applied these techniques to clinical data, in this paper in order to rigorously evaluate their effectiveness we rely on data obtained by computational fluid dynamics (CFD). Specifically, gappy data sets are generated by removing nodal values from high-resolution 3-D CFD data (at random or in a fixed area) while noisy data sets are formed by superimposing speckle noise on the CFD results. A combined POD-Kriging procedure is applied to planar data sets mimicking coarse resolution "ultrasound-like" blood flow images. A method for locating the vessel wall boundary and for calculating the wall shear stress (WSS) is also proposed. The results show good agreement with the original CFD data. The combined POD-Kriging method, enhanced by proper smoothing if needed, holds great potential in dealing effectively with gappy and noisy data reconstruction of in vivo velocity measurements based on color Doppler ultrasound (CDUS) imaging or magnetic resonance angiography (MRA).

Large-scale simulation codes typically execute for extended periods of time and often on distributed computational resources. Because these simulations can run for hours, or even days, scientists like to get feedback about the state of the computation and the validity of its results as it runs. It is also important that these capabilities be made available with little impact on the performance and stability of the simulation. Visualizing and exploring data in the early stages of the simulation can help scientists identify problems early, potentially avoiding a situation where a simulation runs for several days, only to discover that an error with an input parameter caused both time and resources to be wasted. We describe an application that aids in the monitoring and analysis of a simulation of the human arterial tree. The application provides researchers with high-level feedback about the state of the ongoing simulation and enables them to investigate particular areas of interest in greater detail. The application also offers monitoring information about the amount of data produced and data transfer performance among the various components of the application.

Computational grids and grid middleware offer unprecedented computational power and storage capacity, and thus, have opened the possibility of solving problems that was previously not possible on even the largest single computational resources. These opportunities notwithstanding, the development of grid applications that run efficiently remains a challenge due to the inherent heterogeneity of networks and system architectures inherent in such environments. We present grid solutions to two grand challenge problems in computational mechanics. To study the scalability of our solutions we implemented both as MPI applications and ran them on the TeraGrid using NEKTAR and MPICH-G2. We present the results of our study which demonstrate near linear scalability in both applications when run across multiple TeraGrid sites and at a scale of hundreds or processors

The human arterial tree consists of a complex network of branching blood vessels leading from the heart to arterioles, capillaries, and venules - comprising the microcirculation. The numerical simulation of the blood flow in a single part of the human arterial tree requires hundreds of CPUs; a full human arterial tree will require thousands of CPUs. Nowadays, we can use geographically distributed supercomputers connected by a fast network to perform large-scale simulations.Nektar-G2 is the grid-enabled version of Nektar, software developed at Brown University, that allows to solve problems on geographically distributed supercomputers. The topology-aware feature of MPICH-G2 is utilized to enforce an efficient data distribution strategy. Multi-level message passing algorithms minimizes the inter-site communication. Our ultimate goal is to model blood flow interaction of different regions of the cardiovascular system and to establish a biomechanics gateway on the TeraGrid.During poster presentation we will present results of ongoing project.

Introduction: We present visualizations that emphasize vortices in simulated airflow around a motion-captured bat model. These visualizations aim to help biologists gain understanding on the mechanics of bat flight. As suggested by our fluid dynamics collaborators, studying the formation and shedding of vortices in the flight of bats will help scientists understand the efficient mechanisms bats employ in generating lift. By understanding bat flight, we hope to make discoveries in areas such as biomechanics, aerodynamics, and evolutionary biology. This work is the time varying extension of R. Weinstein’s simulation and visualization of a still bat [7].

A hybrid two-level parallelism using MPI/OpenMP is implemented in the general-purpose spectral/hp element CFD code NekTar to take advantage of the hierarchical structures arising in deterministic and stochastic CFD problems. We take a coarse grain approach to shared-memory parallelism with OpenMP and employ a workload-splitting scheme that can reduce the OpenMP synchronizations to the minimum. The hybrid implementation shows good scalability with respect to both the problem size and the number of processors in case of a fixed problem size. With the same number of processors, the hybrid model with 2 (or 4) OpenMP threads per MPI process is observed to perform better than pure MPI and pure OpenMP on the NCSA SGI Origin 2000, while the pure MPI model performs the best on the IBM SP3 at SDSC and on the Compaq Alpha cluster at PSC. A key new result is that the use of threads facilitates effectively p-refinement, which is crucial to adaptive discretization using high-order methods.

We present an immersive system for exploring numerically simulated flow data through a model of a coronary artery graft. This tightly-coupled interdisciplinary project is aimed at understanding how to reduce the failure rate of these grafts. The visualization system provides a mechanism for exploring the effect of changes to the geometry, to the flow, and for exploring potential sources of future lesions. The system uses gestural and voice interactions exclusively, moving away from more traditional windows/icons/menus/point-and-click (WIMP) interfaces. We present an example session using the system and discuss our experiences developing, testing, and using it. We describe some of the interaction and rendering techniques that we experimented with and describe their level of success. Our experience suggests that systems like this are exciting to clinical researchers, but conclusive evidence of their value is not yet available.

Direct Numerical Simulation (DNS) of turbulence requires many CPU days and Gigabytes of memory.These requirements limit most DNS to using supercomputers, available at supercomputer centres.With the rapid development and low cost of PCs, PC clusters are evaluated as a viable low-cost option for scientific computing.Both low-end and high-end PC clusters, ranging from 2 to 128 processors, are compared to a range of existing supercomputers, such as the IBM SP nodes, Silicon Graphics Origin 2000, Fujitsu AP3000 and Cray T3E.The comparison concentrates on CPU and communication performance.At the kernel level, BLAS libraries are used for CPU performance evaluation.Regarding communication, the free implementations of MPICH and LAM are used on fast-ethernet-based systems and compared to myrinet-based and supercomputer networks.At the application level, serial and parallel simulations are performed on state of the art DNS, such as turbulent wake flows in stationary and moving computational domains.

In this paper we analyze communication patterns in the parallel three-dimensional Navier-Stokes solver Prism, and present performance results on the IBM SP2, the Cray T3D and the SGI Power Challenge XL. Prism is used for direct numerical simulation of turbulence in non-separable and multiply-connected domains. The numerical method used in the solver is based on mixed spectral element-Fourier expansions in (x-y) planes and z-direction, respectively. Each (or a group) of Fourier modes is computed on a separate processor as the linear contributions (Helmholtz solves) are completely uncoupled in the incompressible Navier-Stokes equations; coupling is obtained via the nonlinear contributions (convective terms). The transfer of data between physical and Fourier space requires a series of complete exchange operations, which dominate the communication cost for small number of processors. As the number of processors increases, global reduction and gather operations become important while complete exchange becomes more latency dominated. Predictive models for these communication operations are proposed and tested against measurements. A relatively large variation in communication timings per iteration is observed in simulations and quantified in terms of specific operations. A number of improvements are proposed that could significantly reduce the communications overhead with increasing numbers of processors, and {\em generic} predictive maps are developed for the complete exchange operation, which remains the fundamental communication in Prism. Results presented in this paper are representative of a wider class of parallel spectral and finite element codes for computational mechanics which require similar communication operations.