• A novel GNN-based surrogate model predicts material deformation with high accuracy. • Recurrent structures capture temporal dynamics in large material deformations. • Graph U-Net architecture efficiently processes large and complex geometries. • New contact representation method improves efficiency in large contact interactions. • The model facilitates manufacturability assessment in material forming. In recent years, various artificial intelligence-based surrogate models have been proposed to provide rapid manufacturability predictions of material forming processes. However, traditional AI-based surrogate models, typically built with scalar or image-based neural networks, are limited in their ability to capture complex 3D spatial relationships and to operate in a permutation-invariant manner. To overcome these issues, emerging graph-based surrogate models are developed using graph neural networks. This study developed a new graph neural network surrogate model named Recurrent U Net-based Graph Neural Network (RUGNN). The RUGNN model can achieve accurate predictions of sheet material deformation fields across multiple forming timesteps. The RUGNN model incorporates Gated Recurrent Units (GRUs) to model temporal dynamics and a U-Net inspired graph-based downsample/upsample mechanism to handle spatial long-range dependencies. A novel ’node-to-surface’ contact representation method was proposed, offering significant improvements in computational efficiency for large-scale contact interactions. The RUGNN model was validated using a cold forming case study and a more complex hot forming case study using aluminium alloys. Results demonstrate that the RUGNN model provides accurate deformation predictions closely matching ground truth FE simulations and outperforming several baseline GNN architectures. Model tuning was also performed to identify suitable hyperparameters, training strategies, and input feature representations. These results demonstrate that RUGNN is a reliable approach to support sheet material forming design by enabling accurate manufacturability predictions.

Antibodies are Y-shaped proteins that protect the host by binding to specific antigens, and their binding is mainly determined by the Complementary Determining Regions (CDRs) in the antibody. Despite the great progress made in CDR design, existing computational methods still encounter several challenges: 1) poor capability of modeling complex CDRs with long sequences due to insufficient contextual information; 2) conditioned on pre-given antigenic epitopes and their static interaction with the target antibody; 3) neglect of specificity during antibody optimization leads to non-specific antibodies. In this paper, we take into account a variety of node features, edge features, and edge relations to include more contextual and geometric information. We propose a novel Relation-Aware Antibody Design (RAAD) framework, which dynamically models antigen-antibody interactions for co-designing the sequences and structures of antigen-specific CDRs. Furthermore, we propose a new evaluation metric to better measure antibody specificity and develop a contrasting specificity-enhancing constraint to optimize the specificity of antibodies. Extensive experiments have demonstrated the superior capability of RAAD in terms of antibody modeling, generation, and optimization across different CDR types, sequence lengths, pre-training strategies, and input contexts.

Motif-scaffolding is a fundamental component of protein design, which aims to construct the scaffold structure that stabilizes motifs conferring desired functions. Recent advances in generative models are promising for designing scaffolds, with two main approaches: training-based and sampling-based methods. Training-based methods are resource-heavy and slow, while training-free sampling-based methods are flexible but require numerous sampling steps and costly, unstable guidance. To speed up and improve sampling-based methods, we analyzed failure cases and found that errors stem from the trade-off between generation and guidance. Thus we proposed to exploit the spatial context and adjust the generative direction to be consistent with guidance to overcome this trade-off. Motivated by this, we formulate motif-scaffolding as a Geometric Inverse Design task inspired by the image inverse problem, and present Evolution-ViA-reconstruction (EVA), a novel sampling-based coupled flow framework on geometric manifolds, which starts with a pretrained flow-based generative model. EVA uses motif-coupled priors to leverage spatial contexts, guiding the generative process along a straighter probability path, with generative directions aligned with guidance in the early sampling steps. EVA is 70× faster than SOTA model RFDiffusion with competitive and even better performance on benchmark tests. Further experiments on real-world cases including vaccine design, multi-motif scaffolding and motif optimal placement searching demonstrate EVA's superior efficiency and effectiveness.

Semi-supervised learning (SSL) effectively leverages unlabeled data and has been proven successful across various fields. Current safe SSL methods believe that unseen classes in unlabeled data harm the performance of SSL models. However, previous methods for assessing the impact of unseen classes on SSL model performance are flawed. They fix the size of the unlabeled dataset and adjust the proportion of unseen classes within the unlabeled data to assess the impact. This process contravenes the principle of controlling variables. Adjusting the proportion of unseen classes in unlabeled data alters the proportion of seen classes, meaning the decreased classification performance of seen classes may not be due to an increase in unseen class samples in the unlabeled data, but rather a decrease in seen class samples. Thus, the prior flawed assessment standard that "unseen classes in unlabeled data can damage SSL model performance" may not always hold true. This paper strictly adheres to the principle of controlling variables, maintaining the proportion of seen classes in unlabeled data while only changing the unseen classes across five critical dimensions, to investigate their impact on SSL models from global robustness and local robustness. Experiments demonstrate that unseen classes in unlabeled data do not necessarily impair the performance of SSL models; in fact, under certain conditions, unseen classes may even enhance them.

Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these tasks due to their ability to capture long-term dependencies and model high-dimensional states. However, diffusion models typically struggle with handling system states with abrupt changes and generalizing to higher resolutions. In this work, we propose Wavelet Diffusion Neural Operator (WDNO), a novel PDE simulation and control framework that enhances the handling of these complexities. WDNO comprises two key innovations. Firstly, WDNO performs diffusion-based generative modeling in the wavelet domain for the entire trajectory to handle abrupt changes and long-term dependencies effectively. Secondly, to address the issue of poor generalization across different resolutions, which is one of the fundamental tasks in modeling physical systems, we introduce multi-resolution training. We validate WDNO on five physical systems, including 1D advection equation, three challenging physical systems with abrupt changes (1D Burgers' equation, 1D compressible Navier-Stokes equation and 2D incompressible fluid), and a real-world dataset ERA5, which demonstrates superior performance on both simulation and control tasks over state-of-the-art methods, with significant improvements in long-term and detail prediction accuracy. Remarkably, in the challenging context of the 2D high-dimensional and indirect control task aimed at reducing smoke leakage, WDNO reduces the leakage by 78% compared to the second-best baseline. The code can be found at https://github.com/AI4Science-WestlakeU/wdno.git.

The control problems of complex physical systems have broad applications in science and engineering. Previous studies have shown that generative control methods based on diffusion models offer significant advantages for solving these problems. However, existing generative control approaches face challenges in both performance and efficiency when extended to the closed-loop setting, which is essential for effective control. In this paper, we propose an efficient Closed-Loop Diffusion method for Physical systems Control (CL-DiffPhyCon). By employing an asynchronous denoising framework for different physical time steps, CL-DiffPhyCon generates control signals conditioned on real-time feedback from the system with significantly reduced computational cost during sampling. Additionally, the control process could be further accelerated by incorporating fast sampling techniques, such as DDIM. We evaluate CL-DiffPhyCon on two tasks: 1D Burgers' equation control and 2D incompressible fluid control. The results demonstrate that CL-DiffPhyCon achieves superior control performance with significant improvements in sampling efficiency. The code can be found at https://github.com/AI4Science-WestlakeU/CL_DiffPhyCon.

Multiphysics simulation, which models the interactions between multiple physical processes, and multi-component simulation of complex structures are critical in fields like nuclear and aerospace engineering. Previous studies use numerical solvers or ML-based surrogate models for these simulations. However, multiphysics simulations typically require integrating multiple specialized solvers-each for a specific physical process-into a coupled program, which introduces significant development challenges. Furthermore, existing numerical algorithms struggle with highly complex large-scale structures in multi-component simulations. Here we propose compositional Multiphysics and Multi-component PDE Simulation with Diffusion models (M2PDE) to overcome these challenges. During diffusion-based training, M2PDE learns energy functions modeling the conditional probability of one physical process/component conditioned on other processes/components. In inference, M2PDE generates coupled multiphysics and multi-component solutions by sampling from the joint probability distribution. We evaluate M2PDE on two multiphysics tasks-reaction-diffusion and nuclear thermal coupling--where it achieves more accurate predictions than surrogate models in challenging scenarios. We then apply it to a multi-component prismatic fuel element problem, demonstrating that M2PDE scales from single-component training to a 64-component structure and outperforms existing domain-decomposition and graph-based approaches. The code is available at github.com/AI4Science-WestlakeU/M2PDE.

Flow matching has shown state-of-the-art performance in various generative tasks, ranging from image generation to decision-making, where generation under energy guidance (abbreviated as guidance in the following) is pivotal. However, the guidance of flow matching is more general than and thus substantially different from that of its predecessor, diffusion models. Therefore, the challenge in guidance for general flow matching remains largely underexplored. In this paper, we propose the first framework of general guidance for flow matching. From this framework, we derive a family of guidance techniques that can be applied to general flow matching. These include a new training-free asymptotically exact guidance, novel training losses for training-based guidance, and two classes of approximate guidance that cover classical gradient guidance methods as special cases. We theoretically investigate these different methods to give a practical guideline for choosing suitable methods in different scenarios. Experiments on synthetic datasets, image inverse problems, and offline reinforcement learning demonstrate the effectiveness of our proposed guidance methods and verify the correctness of our flow matching guidance framework. Code to reproduce the experiments can be found at https://github.com/AI4Science-WestlakeU/flow_guidance.

The application of deep learning for partial differential equation (PDE)-constrained control is gaining increasing attention. However, existing methods rarely consider safety requirements crucial in real-world applications. To address this limitation, we propose Safe Diffusion Models for PDE Control (SafeDiffCon), which introduce the uncertainty quantile as model uncertainty quantification to achieve optimal control under safety constraints through both post-training and inference phases. Firstly, our approach post-trains a pre-trained diffusion model to generate control sequences that better satisfy safety constraints while achieving improved control objectives via a reweighted diffusion loss, which incorporates the uncertainty quantile estimated using conformal prediction. Secondly, during inference, the diffusion model dynamically adjusts both its generation process and parameters through iterative guidance and fine-tuning, conditioned on control targets while simultaneously integrating the estimated uncertainty quantile. We evaluate SafeDiffCon on three control tasks: 1D Burgers’ equation, 2D incompressible fluid, and controlled nuclear fusion problem. Results demonstrate that SafeDiffCon is the only method that satisfies all safety constraints, whereas other classical and deep learning baselines fail. Furthermore, while adhering to safety constraints, SafeDiffCon achieves the best control performance. The code can be found at https://github.com/AI4Science-WestlakeU/safediffcon.

Deep learning-based surrogate models have demonstrated remarkable advantages over classical solvers in terms of speed, often achieving speedups of 10 to 1000 times over traditional partial differential equation (PDE) solvers. However, a significant challenge hindering their widespread adoption in both scientific and industrial domains is the lack of understanding about their prediction uncertainties, particularly in scenarios that involve critical decision making. To address this limitation, we propose a method that integrates efficient and precise uncertainty quantification into a deep learning-based surrogate model. Our method, termed Latent Evolution of PDEs with Uncertainty Quantification (LE-PDE-UQ), endows deep learning-based surrogate models with robust and efficient uncertainty quantification capabilities for both forward and inverse problems. LE-PDE-UQ leverages latent vectors within a latent space to evolve both the system's state and its corresponding uncertainty estimation. The latent vectors are decoded to provide predictions for the system's state as well as estimates of its uncertainty. In extensive experiments, we demonstrate the accurate uncertainty quantification performance of our approach, surpassing that of strong baselines including deep ensembles, Bayesian neural network layers, and dropout. Our method excels at propagating uncertainty over extended auto-regressive rollouts, making it suitable for scenarios involving long-term predictions. Our code is available at: https://github.com/AI4Science-WestlakeU/le-pde-uq.

Elliptic partial differential equations (PDEs) are a major class of time-independent PDEs that play a key role in many scientific and engineering domains such as fluid dynamics, plasma physics, and solid mechanics. Recently, neural operators have emerged as a promising technique to solve elliptic PDEs more efficiently by directly mapping the input to solutions. However, existing networks typically neglect complex geometries and inhomogeneous boundary values present in the real world. Here we introduce Boundary-Embedded Neural Operators (BENO), a novel neural operator architecture that embeds the complex geometries and inhomogeneous boundary values into the solving of elliptic PDEs. Inspired by classical Green's function, BENO consists of two Graph Neural Networks (GNNs) for interior source term and boundary values, respectively. Furthermore, a Transformer encoder maps the global boundary geometry into a latent vector which influences each message passing layer of the GNNs. We test our model and strong baselines extensively in elliptic PDEs with complex boundary conditions. We show that all existing baseline methods fail to learn the solution operator. In contrast, our model, endowed with boundary-embedded architecture, outperforms state-of-the-art neural operators and strong baselines by an average of 60.96%.

Inverse design, where we seek to design input variables in order to optimize an underlying objective function, is an important problem that arises across fields such as mechanical engineering to aerospace engineering. Inverse design is typically formulated as an optimization problem, with recent works leveraging optimization across learned dynamics models. However, as models are optimized they tend to fall into adversarial modes, preventing effective sampling. We illustrate that by instead optimizing over the learned energy function captured by the diffusion model, we can avoid such adversarial examples and significantly improve design performance. We further illustrate how such a design system is compositional, enabling us to combine multiple different diffusion models representing subcomponents of our desired system to design systems with every specified component. In an N-body interaction task and a challenging 2D multi-airfoil design task, we demonstrate that by composing the learned diffusion model at test time, our method allows us to design initial states and boundary shapes that are more complex than those in the training data. Our method generalizes to more objects for N-body dataset and discovers formation flying to minimize drag in the multi-airfoil design task. Project website and code can be found at https://github.com/AI4Science-WestlakeU/cindm.

Controlling the evolution of complex physical systems is a fundamental task across science and engineering. Classical techniques suffer from limited applicability or huge computational costs. On the other hand, recent deep learning and reinforcement learning-based approaches often struggle to optimize long-term control sequences under the constraints of system dynamics. In this work, we introduce Diffusion Physical systems Control (DiffPhyCon), a new class of method to address the physical systems control problem. DiffPhyCon excels by simultaneously minimizing both the learned generative energy function and the predefined control objectives across the entire trajectory and control sequence. Thus, it can explore globally and plan near-optimal control sequences. Moreover, we enhance DiffPhyCon with prior reweighting, enabling the discovery of control sequences that significantly deviate from the training distribution. We test our method on three tasks: 1D Burgers' equation, 2D jellyfish movement control, and 2D high-dimensional smoke control, where our generated jellyfish dataset is released as a benchmark for complex physical system control research. Our method outperforms widely applied classical approaches and state-of-the-art deep learning and reinforcement learning methods. Notably, DiffPhyCon unveils an intriguing fast-close-slow-open pattern observed in the jellyfish, aligning with established findings in the field of fluid dynamics. The project website, jellyfish dataset, and code can be found at https://github.com/AI4Science-WestlakeU/diffphycon.

Subsurface simulations use computational models to predict the flow of fluids (e.g., oil, water, gas) through porous media. These simulations are pivotal in industrial applications such as petroleum production, where fast and accurate models are needed for high-stake decision making, for example, for well placement optimization and field development planning. Classical finite difference numerical simulators require massive computational resources to model large-scale real-world reservoirs. Alternatively, streamline simulators and data-driven surrogate models are computationally more efficient by relying on approximate physics models, however they are insufficient to model complex reservoir dynamics at scale.

Simulating the time evolution of Partial Differential Equations (PDEs) of large-scale systems is crucial in many scientific and engineering domains such as fluid dynamics, weather forecasting and their inverse optimization problems. However, both classical solvers and recent deep learning-based surrogate models are typically extremely computationally intensive, because of their local evolution: they need to update the state of each discretized cell at each time step during inference. Here we develop Latent Evolution of PDEs (LE-PDE), a simple, fast and scalable method to accelerate the simulation and inverse optimization of PDEs. LE-PDE learns a compact, global representation of the system and efficiently evolves it fully in the latent space with learned latent evolution models. LE-PDE achieves speedup by having a much smaller latent dimension to update during long rollout as compared to updating in the input space. We introduce new learning objectives to effectively learn such latent dynamics to ensure long-term stability. We further introduce techniques for speeding-up inverse optimization of boundary conditions for PDEs via backpropagation through time in latent space, and an annealing technique to address the non-differentiability and sparse interaction of boundary conditions. We test our method in a 1D benchmark of nonlinear PDEs, 2D Navier-Stokes flows into turbulent phase and an inverse optimization of boundary conditions in 2D Navier-Stokes flow. Compared to state-of-the-art deep learning-based surrogate models and other strong baselines, we demonstrate up to 128x reduction in the dimensions to update, and up to 15x improvement in speed, while achieving competitive accuracy.

Humans have the remarkable ability to recognize and acquire novel visual concepts in a zero-shot manner. Given a high-level, symbolic description of a novel concept in terms of previously learned visual concepts and their relations, humans can recognize novel concepts without seeing any examples. Moreover, they can acquire new concepts by parsing and communicating symbolic structures using learned visual concepts and relations. Endowing these capabilities in machines is pivotal in improving their generalization capability at inference time. In this work, we introduce Zero-shot Concept Recognition and Acquisition (ZeroC), a neuro-symbolic architecture that can recognize and acquire novel concepts in a zero-shot way. ZeroC represents concepts as graphs of constituent concept models (as nodes) and their relations (as edges). To allow inference time composition, we employ energy-based models (EBMs) to model concepts and relations. We design ZeroC architecture so that it allows a one-to-one mapping between a symbolic graph structure of a concept and its corresponding EBM, which for the first time, allows acquiring new concepts, communicating its graph structure, and applying it to classification and detection tasks (even across domains) at inference time. We introduce algorithms for learning and inference with ZeroC. We evaluate ZeroC on a challenging grid-world dataset which is designed to probe zero-shot concept recognition and acquisition, and demonstrate its capability.

BACKGROUND: Determining cell identity in volumetric images of tagged neuronal nuclei is an ongoing challenge in contemporary neuroscience. Frequently, cell identity is determined by aligning and matching tags to an "atlas" of labeled neuronal positions and other identifying characteristics. Previous analyses of such C. elegans datasets have been hampered by the limited accuracy of such atlases, especially for neurons present in the ventral nerve cord, and also by time-consuming manual elements of the alignment process. RESULTS: We present a novel automated alignment method for sparse and incomplete point clouds of the sort resulting from typical C. elegans fluorescence microscopy datasets. This method involves a tunable learning parameter and a kernel that enforces biologically realistic deformation. We also present a pipeline for creating alignment atlases from datasets of the recently developed NeuroPAL transgene. In combination, these advances allow us to label neurons in volumetric images with confidence much higher than previous methods. CONCLUSIONS: We release, to the best of our knowledge, the most complete full-body C. elegans 3D positional neuron atlas, incorporating positional variability derived from at least 7 animals per neuron, for the purposes of cell-type identity prediction for myriad applications (e.g., imaging neuronal activity, gene expression, and cell-fate).

The core network is the most basic facility in the entire telecommunications network, which is consists of large number of routers, switches and firewalls. Network management like re-planning routes or adjusting policies is very important to avoid failures. However, the timing of intervention is very challenging. Too early intervention will incur unnecessary overheads, and too late intervention will cause serious disaster. In this paper, we analyzed a large data set from a real-world core telecommunications network and proposed Linear Bayesian Neural Networks (LBNN)11Code available at https://github.com/YanyingLin/Lbnn to perceive the core network state changes and make decisions about network intervention. In particular, we considered three aspects of complexity, including the weight of the mutual effect between devices, the dependence on the time dimension of the network states, and the randomness of the network state changes. The entire model is extended to a probability model based on the Bayesian framework to better capture the randomness and variability of the data. Experimental results on real-world data set show that LBNN achieves very high detection accuracy, with an average of 92.1%.

We present an improved method for symbolic regression that seeks to fit data to formulas that are Pareto-optimal, in the sense of having the best accuracy for a given complexity. It improves on the previous state-of-the-art by typically being orders of magnitude more robust toward noise and bad data, and also by discovering many formulas that stumped previous methods. We develop a method for discovering generalized symmetries (arbitrary modularity in the computational graph of a formula) from gradient properties of a neural network fit. We use normalizing flows to generalize our symbolic regression method to probability distributions from which we only have samples, and employ statistical hypothesis testing to accelerate robust brute-force search.

Representation learning of graph-structured data is challenging because both graph structure and node features carry important information. Graph Neural Networks (GNNs) provide an expressive way to fuse information from network structure and node features. However, GNNs are prone to adversarial attacks. Here we introduce Graph Information Bottleneck (GIB), an information-theoretic principle that optimally balances expressiveness and robustness of the learned representation of graph-structured data. Inheriting from the general Information Bottleneck (IB), GIB aims to learn the minimal sufficient representation for a given task by maximizing the mutual information between the representation and the target, and simultaneously constraining the mutual information between the representation and the input data. Different from the general IB, GIB regularizes the structural as well as the feature information. We design two sampling algorithms for structural regularization and instantiate the GIB principle with two new models: GIB-Cat and GIB-Bern, and demonstrate the benefits by evaluating the resilience to adversarial attacks. We show that our proposed models are more robust than state-of-the-art graph defense models. GIB-based models empirically achieve up to 31% improvement with adversarial perturbation of the graph structure as well as node features.