Current state-of-the-art generative models map noise to data distributions by matching flows or scores. A key limitation of these models is their inability to readily integrate available partial observations and additional priors. In contrast, energy-based models (EBMs) address this by incorporating corresponding scalar energy terms. Here, we propose Energy Matching, a framework that endows flow-based approaches with the flexibility of EBMs. Far from the data manifold, samples move from noise to data along irrotational, optimal transport paths. As they approach the data manifold, an entropic energy term guides the system into a Boltzmann equilibrium distribution, explicitly capturing the underlying likelihood structure of the data. We parameterize these dynamics with a single time-independent scalar field, which serves as both a powerful generator and a flexible prior for effective regularization of inverse problems. The present method substantially outperforms existing EBMs on CIFAR-10 and ImageNet generation in terms of fidelity, while retaining simulation-free training of transport-based approaches away from the data manifold. Furthermore, we leverage the flexibility of the method to introduce an interaction energy that supports the exploration of diverse modes, which we demonstrate in a controlled protein generation setting. This approach learns a scalar potential energy, without time conditioning, auxiliary generators, or additional networks, marking a significant departure from recent EBM methods. We believe this simplified yet rigorous formulation significantly advances EBMs capabilities and paves the way for their wider adoption in generative modeling in diverse domains.

Physical models in the form of partial differential equations serve as important priors for many under-constrained problems. One such application is tumor treatment planning, which relies on accurately estimating the spatial distribution of tumor cells within a patient’s anatomy. While medical imaging can detect the bulk of a tumor, it cannot capture the full extent of its spread, as low-concentration tumor cells often remain undetectable, particularly in glioblastoma, the most common primary brain tumor. Machine learning approaches struggle to estimate the complete tumor cell distribution due to a lack of appropriate training data. Consequently, most existing methods rely on physics-based simulations to generate anatomically and physiologically plausible estimations. However, these approaches face challenges with complex and unknown initial conditions and are constrained by overly rigid physical models. In this work, we introduce a novel method that integrates data-driven and physics-based cost functions, akin to Physics-Informed Neural Networks (PINNs). However, our approach parametrizes the solution directly on a dynamic discrete mesh, allowing for the effective modeling of complex biomechanical behaviors. Specifically, we propose a unique discretization scheme that quantifies how well the learned spatiotemporal distributions of tumor and brain tissues adhere to their respective growth and elasticity equations. This quantification acts as a regularization term, offering greater flexibility and improved integration of patient data compared to existing models. We demonstrate enhanced coverage of tumor recurrence areas using real-world data from a patient cohort, highlighting the potential of our method to improve model-driven treatment planning for glioblastoma in clinical practice.

Experience replay (ER) is a fundamental component of off-policy deep reinforcement learning (RL). ER recalls experiences from past iterations to compute gradient estimates for the current policy, increasing data-efficiency. However, the accuracy of such updates may deteriorate when the policy diverges from past behaviors and can undermine the performance of ER. Many algorithms mitigate this issue by tuning hyper-parameters to slow down policy changes. An alternative is to actively enforce the similarity between policy and the experiences in the replay memory. We introduce Remember and Forget Experience Replay (ReF-ER), a novel method that can enhance RL algorithms with parameterized policies. ReF-ER (1) skips gradients computed from experiences that are too unlikely with the current policy and (2) regulates policy changes within a trust region of the replayed behaviors. We couple ReF-ER with Q-learning, deterministic policy gradient and off-policy gradient methods. We find that ReF-ER consistently improves the performance of continuous-action, off-policy RL on fully observable benchmarks and partially observable flow control problems.

Glioblastoma (GBM) is a highly invasive brain tumor, whose cells infiltrate surrounding normal brain tissue beyond the lesion outlines visible in the current medical scans. These infiltrative cells are treated mainly by radiotherapy. Existing radiotherapy plans for brain tumors derive from population studies and scarcely account for patient-specific conditions. Here, we provide a Bayesian machine learning framework for the rational design of improved, personalized radiotherapy plans using mathematical modeling and patient multimodal medical scans. Our method, for the first time, integrates complementary information from high-resolution MRI scans and highly specific FET-PET metabolic maps to infer tumor cell density in GBM patients. The Bayesian framework quantifies imaging and modeling uncertainties and predicts patient-specific tumor cell density with credible intervals. The proposed methodology relies only on data acquired at a single time point and, thus, is applicable to standard clinical settings. An initial clinical population study shows that the radiotherapy plans generated from the inferred tumor cell infiltration maps spare more healthy tissue thereby reducing radiation toxicity while yielding comparable accuracy with standard radiotherapy protocols. Moreover, the inferred regions of high tumor cell densities coincide with the tumor radioresistant areas, providing guidance for personalized dose-escalation. The proposed integration of multimodal scans and mathematical modeling provides a robust, non-invasive tool to assist personalized radiotherapy design.

A fundamental understanding of how various biological traits and features provide organisms with a competitive advantage can help us improve the design of several mechanical systems. Numerical optimization can be invaluable for this purpose, by allowing us to scrutinize the evolution of specific biological adaptations. Importantly, the use of numerical optimization can help us overcome limiting constraints that restrict the evolutionary capability of biological species. Thus, we couple high-fidelity simulations of self-propelled swimmers with evolutionary optimization algorithms, to examine peculiar swimming patterns observed in a number of fish species. More specifically, we investigate the intermittent form of locomotion referred to as `burst-and-coast' swimming, which involves a few quick flicks of the fish's tail followed by a prolonged unpowered glide. This mode of swimming is believed to confer energetic benefits, in addition to several other advantages. We discover a range of intermittent-swimming patterns, the most efficient of which resembles the swimming-behaviour observed in live fish. We also discover patterns which lead to a marked increase in swimming-speed, albeit with a significant increase in energy expenditure. Notably, the use of multi-objective optimization reveals locomotion patterns that strike the perfect balance between speed and efficiency, which can be invaluable for use in robotic applications. The analyses presented may also be extended for optimal design and control of airborne vehicles. As an additional goal of the paper, we highlight the ease with which disparate codes can be coupled via the software framework used, without encumbering the user with the details of efficient parallelization.

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.

We present unprecedented, high throughput simulations of cloud cavitation collapse on 1.6 million cores of Sequoia reaching 55% of its nominal peak performance, corresponding to 11 PFLOP/s. The destructive power of cavitation reduces the lifetime of energy critical systems such as internal combustion engines and hydraulic turbines, yet it has been harnessed for water purification and kidney lithotripsy. The present two-phase flow simulations enable the quantitative prediction of cavitation using 13 trillion grid points to resolve the collapse of 15'000 bubbles. We advance by one order of magnitude the current state-of-the-art in terms of time to solution, and by two orders the geometrical complexity of the flow. The software successfully addresses the challenges that hinder the effective solution of complex flows on contemporary supercomputers, such as limited memory bandwidth, I/O bandwidth and storage capacity. The present work redefines the frontier of high performance computing for fluid dynamics simulations.

We present an open source, object-oriented software for high throughput Direct Numerical Simulations of compressible, two-phase flows. The Navier-Stokes equations are discretized on uniform grids using high order finite volume methods. The software exploits recent CPU micro-architectures by explicit vectorization and adopts NUMA-aware techniques as well as data and computation reordering. We report a compressible flow solver with unprecedented fractions of peak performance: 45% of the peak for a single node (nominal performance of 840 GFLOP/s) and 30% for a cluster of 47'000 cores (nominal performance of 0.8 PFLOP/s). We suggest that the present work may serve as a performance upper bound, regarding achievable GFLOP/s, for two-phase flow solvers using adaptive mesh refinement. The software enables 3D simulations of shock-bubble interaction including, for the first time, effects of diffusion and surface tension, by efficiently employing two hundred billion computational elements.

Abstract We build wavelet‐based adaptive numerical methods for the simulation of advection‐dominated flows that develop multiple spatial scales, with an emphasis on fluid mechanics problems. Wavelet‐based adaptivity is inherently sequential and in this work we demonstrate that these numerical methods can be implemented in software that is capable of harnessing the capabilities of multi‐core architectures while maintaining their computational efficiency. Recent designs in frameworks for multi‐core software development allow us to rethink parallelism as task‐based, where parallel tasks are specified and automatically mapped onto physical threads. This way of exposing parallelism enables the parallelization of algorithms that were considered inherently sequential, such as wavelet‐based adaptive simulations. In this paper we present a framework that combines wavelet‐based adaptivity with the task‐based parallelism. We demonstrate the promising performance obtained by simulating various physical systems on different multi‐core architectures using up to 16 cores. Copyright © 2010 John Wiley & Sons, Ltd.

BACKGROUND: Despite significant progress in imaging technologies, the efficient detection of edges and elongated features in images of intracellular and multicellular structures acquired using light or electron microscopy is a challenging and time consuming task in many laboratories. RESULTS: We present a novel method, based on the discrete curvelet transform, to extract a directional field from the image that indicates the location and direction of the edges. This directional field is then processed using the non-maximal suppression and thresholding steps of the Canny algorithm to trace along the edges and mark them. Optionally, the edges may then be extended along the directions given by the curvelets to provide a more connected edge map. We compare our scheme to the Canny edge detector and an edge detector based on Gabor filters, and show that our scheme performs better in detecting larger, elongated structures possibly composed of several step or ridge edges. CONCLUSION: The proposed curvelet based edge detection is a novel and competitive approach for imaging problems. We expect that the methodology and the accompanying software will facilitate and improve edge detection in images available using light or electron microscopy.

Cytoplasmic transport of organelles, nucleic acids and proteins on microtubules is usually bidirectional with dynein and kinesin motors mediating the delivery of cargoes in the cytoplasm. Here we combine live cell microscopy, single virus tracking and trajectory segmentation to systematically identify the parameters of a stochastic computational model of cargo transport by molecular motors on microtubules. The model parameters are identified using an evolutionary optimization algorithm to minimize the Kullback-Leibler divergence between the in silico and the in vivo run length and velocity distributions of the viruses on microtubules. The present stochastic model suggests that bidirectional transport of human adenoviruses can be explained without explicit motor coordination. The model enables the prediction of the number of motors active on the viral cargo during microtubule-dependent motions as well as the number of motor binding sites, with the protein hexon as the binding site for the motors.

We present a novel method for handling uncertainty in evolutionary optimization. The method entails quantification and treatment of uncertainty and relies on the rank based selection operator of evolutionary algorithms. The proposed uncertainty handling is implemented in the context of the covariance matrix adaptation evolution strategy (CMA-ES) and verified on test functions. The present method is independent of the uncertainty distribution, prevents premature convergence of the evolution strategy and is well suited for online optimization as it requires only a small number of additional function evaluations. The algorithm is applied in an experimental setup to the online optimization of feedback controllers of thermoacoustic instabilities of gas turbine combustors. In order to mitigate these instabilities, gain-delay or model-basedHinfincontrollers sense the pressure and command secondary fuel injectors. The parameters of these controllers are usually specified via a trial and error procedure. We demonstrate that their online optimization with the proposed methodology enhances, in an automated fashion, the online performance of the controllers, even under highly unsteady operating conditions, and it also compensates for uncertainties in the model-building and design process.

We present an overview of evolutionary algorithms that use empirical models of the fitness function to accelerate convergence, distinguishing between evolution control and the surrogate approach. We describe the Gaussian process model and propose using it as an inexpensive fitness function surrogate. Implementation issues such as efficient and numerically stable computation, exploration versus exploitation, local modeling, multiple objectives and constraints, and failed evaluations are addressed. Our resulting Gaussian process optimization procedure clearly outperforms other evolutionary strategies on standard test functions as well as on a real-world problem: the optimization of stationary gas turbine compressor profiles.

Given some optimization problem and a series of typically expensive trials of solution candidates sampled from a search space, how can we efficiently select the next candidate? We address this fundamental problem by embedding simple optimization strategies in learning algorithms inspired by Kohonen's self-organizing maps and neural gas networks. Our adaptive nets or grids are used to identify and exploit search space regions that maximize the probability of generating points closer to the optima. Net nodes are attracted by candidates that lead to improved evaluations, thus, quickly biasing the active data selection process toward promising regions, without loss of ability to escape from local optima. On standard benchmark functions, our techniques perform more reliably than the widely used covariance matrix adaptation evolution strategy. The proposed algorithm is also applied to the problem of drag reduction in a flow past an actively controlled circular cylinder, leading to unprecedented drag reduction.

This paper presents a novel evolutionary optimization strategy based on the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). This new approach is intended to reduce the number of generations required for convergence to the optimum. Reducing the number of generations, i.e., the time complexity of the algorithm, is important if a large population size is desired: (1) to reduce the effect of noise; (2) to improve global search properties; and (3) to implement the algorithm on (highly) parallel machines. Our method results in a highly parallel algorithm which scales favorably with large numbers of processors. This is accomplished by efficiently incorporating the available information from a large population, thus significantly reducing the number of generations needed to adapt the covariance matrix. The original version of the CMA-ES was designed to reliably adapt the covariance matrix in small populations but it cannot exploit large populations efficiently. Our modifications scale up the efficiency to population sizes of up to 10n, where n is the problem dimension. This method has been applied to a large number of test problems, demonstrating that in many cases the CMA-ES can be advanced from quadratic to linear time complexity.

We discuss the implementation of a learning algorithm for determining adaptation parameters in evolution strategies. As an initial test case, we consider the application of reinforcement learning for determining the relationship between success rates and the adaptation of step sizes in the (1+1)-evolution strategy. The results from the new adaptive scheme when applied to several test functions are compared with those obtained from the (1+1)-evolution strategy with a priori selected parameters. Our results indicate that assigning good reward measures seems to be crucial to the performance of the combined strategy.

We present an optimization algorithm based on a model of bacterial chemotaxis. The original biological model is used to formulate a simple optimization algorithm, which is evaluated on a set of standard test problems. Based on this evaluation, several features are added to the basic algorithm using evolutionary concepts in order to obtain an improved optimization strategy, called the bacteria chemotaxis (BC) algorithm. This strategy is evaluated on a number of test functions for local and global optimization, compared with other optimization techniques, and applied to the problem of inverse airfoil design. The comparisons show that on average, BC performs similar to standard evolution strategies and worse than evolution strategies with enhanced convergence properties.

Single- and multicriteria evolution strategies are implemented to optimize micro-fluidic devices, namely the shape of a microchannel used for bioanalysls and the mixing rate in a micromixer used for medical applications. First, multimembered evolution strategies employing mutative step size adaptation are combined with the Strength Pareto approach. In order to support targetting, an extension of the Strength Pareto evolutionary algorithm is proposed. Applied on the optimization of the microchannel, these algorithms suggest a novel design with improved properties over traditional designs. A comparison with a gradient method is presented. Second, an evolution strategy with derandomized self-adaptation of the mutation distribution is used to optimize the micromixer. The results agree well with dynamical systems theory.

Rechenberg and Schwefel (Rechenberg, 1994) came up with the idea of evolution strategies for flow optimization. Since then advances in computer architectures and numerical algorithms have greatly decreased computational costs of realistic flow simulations, and today computational fluid dynamics (CFD) is complementing flow experiments as a key guiding tool for aerodynamic design. Of particular interest are designs with active devices controlling the inherently unsteady flow fields, promising potentially drastic performance leaps. We demonstrate that CFD-based design of active control strategies can benefit from evolutionary computation. We optimize the flow past an actively controlled circular cylinder, a fundamental prototypical configuration. The flow is controlled using surface-mounted vortex generators; evolutionary algorithms are used to optimize actuator placement and operating parameters. We achieve drag reduction of up to 60 percent, outperforming the best methods previously reported in the fluid dynamics literature on this benchmark problem.