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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Efficient Subset Simulation using Hamiltonian Neural Network enhanced Markov Chain Monte Carlo Methods

The Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the variance of the estimate depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. Therefore, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, such as the random walk Metropolis-Hastings algorithm. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. As a consequence, advanced Markov Chain Monte Carlo simulations have been developed. In particular, the Hamiltonian Monte Carlo method explores the target distribution rapidly. Driven by the idea of Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis. One downside of the Hamiltonian Monte Carlo method is that gradient evaluations are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. We show that integrating Hamiltonian neural networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling task. Furthermore, the enhancement of adaptive trajectory length within the Hamiltonian Monte Carlo results in the efficient proposal of the following states. Based on this recent enhancement, we provide a fast sampling strategy for subset simulations using Hamiltonian neural networks to replace the evaluation of the gradient and significantly speed up the Hamiltonian Monte Carlo simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian Inference with Latent Hamiltonian Neural Networks (L-HNNs)

When sampling for Bayesian inference, one popular approach is to use Hamiltonian Monte Carlo (HMC) and the No-U-Turn Sampler (NUTS). However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice. We propose Hamiltonian neural networks (HNNs) with HMC and NUTS for solving Bayesian inference problems [1, 2]. Once trained, HNNs do not require gradients of the target density while sampling. Moreover, they satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well suited for use within HMC and NUTS because stationarity can be shown. We also propose an HNN extension called latent HNNs (L-HNNs), which predict latent variable outputs. Compared to HNNs, L-HNNs offer improved expressivity and a reduction in integration errors. Finally, we propose employing L-HNNs in NUTS with an online error monitoring scheme to prevent degeneracy of the sampling in regions of low probability density. We demonstrate L-HNNs in NUTS with online error monitoring by using several example cases involving complex, heavy-tailed, and high local curvature probability densities. Overall, L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. Compared to traditional NUTS, L-HNNs in NUTS with online error monitoring improved the effective sample size (ESS) per gradient by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Efficient Bayesian inference with latent Hamiltonian neural networks in No-U-Turn Sampling

When sampling for Bayesian inference, one popular approach in the computational field is to use Hamiltonian Monte Carlo (HMC) and specifically the No-U-Turn Sampler (NUTS), which automatically decides the end time of the Hamiltonian trajectory. However, HMC and NUTS can require numerous numerical gradients of the target density and can prove slow in practice when relying on computationally expensive forward models. We propose Latent Hamiltonian neural networks (L-HNNs) with HMC and NUTS for solving Bayesian inference problems. Once trained, L-HNNs do not require numerical gradients of the target density during sampling, and hence numerous evaluations of the forward computational model. Moreover, L-HNNs satisfy important properties such as perfect time reversibility and Hamiltonian conservation, making them well-suited for use within HMC and NUTS because stationarity can be shown. We also propose the integration of L-HNNs in an online error monitoring scheme, in which numerical gradients of the target density are used for a few samples whenever the L-HNNs prediction errors are large. This online error monitor scheme prevents sample degeneracy in regions of low probability density and ensures robust uncertainty quantification. We demonstrate L-HNNs in NUTS with online error monitoring on several analytical examples involving complex, heavy-tailed, and high-local-curvature probability densities. We then demonstrate the applicability of L-HNNs in NUTS to two computational case studies, namely the Allen-Cahn stochastic partial differential equation and an elliptic partial differential equation with 25 and 50 inference parameters, respectively. Overall, the L-HNNs in NUTS with online error monitoring satisfactorily inferred these probability densities. In conclusion, compared to traditional NUTS, L-HNNs in NUTS with online error monitoring required 1–2 orders of magnitude fewer numerical gradients of the target density and improved the effective sample size (ESS) per gradient (which is a measure of both the sampling quality and the computational expense) by an order of magnitude.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗
DOE OSTI2025

Accelerating Hamiltonian Monte Carlo for Bayesian inference in neural networks and neural operators

Hamiltonian Monte Carlo (HMC) is a powerful and accurate method to sample from the posterior distribution in Bayesian inference. However, HMC techniques are computationally demanding for Bayesian neural networks due to the high dimensionality of the network’s parameter space and the non-convexity of their posterior distributions. Therefore, various approximation techniques, such as variational inference (VI) or stochastic gradient MCMC, are often employed to infer the posterior distribution of the network parameters. Such approximations introduce inaccuracies in the inferred distributions, resulting in unreliable uncertainty estimates. In this work, we propose a hybrid approach that combines inexpensive VI and accurate HMC methods to efficiently and accurately quantify uncertainties in neural networks and neural operators. The proposed approach leverages an initial VI training on the full network. We examine the influence of individual parameters on the prediction uncertainty, which shows that a large proportion of the parameters do not contribute substantially to uncertainty in the network predictions. This information is then used to significantly reduce the dimension of the parameter space, and HMC is performed only for the subset of network parameters that strongly influence prediction uncertainties. This yields a framework for accelerating the full batch HMC for posterior inference in neural networks. We demonstrate the efficiency and accuracy of the proposed framework on deep neural networks and operator networks, showing that inference can be performed for large networks with tens to hundreds of thousands of parameters. Finally, we show that this method can effectively learn surrogates for complex physical systems by modeling the operator that maps from upstream conditions to wall-pressure data on a cone in hypersonic flow.

Bayesian inference↗
DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗
DOE OSTI2024

Effective many-body interactions in reduced-dimensionality spaces through neural network models

Accurately describing properties of challenging problems in physical sciences often requires complex mathematical models that are unmanageable to tackle head on. Therefore, developing reduced-dimensionality representations that encapsulate complex correlation effects in many-body systems is crucial to advance the understanding of these complicated problems. However, a numerical evaluation of these predictive models can still be associated with a significant computational overhead. To address this challenge, in this paper we discuss a combined framework that integrates recent advances in the development of active-space representations of coupled cluster (CC) downfolded Hamiltonians with neural network approaches. The primary objective of this effort is to train neural networks to eliminate the computationally expensive steps required for evaluating hundreds or thousands of Hugenholtz diagrams, which correspond to multidimensional tensor contractions necessary for evaluating a many-body form of downfolded effective Hamiltonians. Using small molecular systems (the H 2 O and HF molecules) as examples, we demonstrate that training neural networks employing effective Hamiltonians for a few nuclear geometries of molecules can accurately interpolate or extrapolate their forms to other geometrical configurations characterized by different intensities of correlation effects. We also discuss differences between effective interactions that define CC downfolded Hamiltonians with those of bare Hamiltonians defined by Coulomb interactions in the active spaces. Published by the American Physical Society 2024

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

CHGNet as a pretrained universal neural network potential for charge-informed atomistic modelling

Large-scale simulations with complex electron interactions remain one of the greatest challenges for atomistic modelling. Although classical force fields often fail to describe the coupling between electronic states and ionic rearrangements, the more accurate ab initio molecular dynamics suffers from computational complexity that prevents long-time and large-scale simulations, which are essential to study technologically relevant phenomena. Here we present the Crystal Hamiltonian Graph Neural Network (CHGNet), a graph neural network-based machine-learning interatomic potential (MLIP) that models the universal potential energy surface. CHGNet is pretrained on the energies, forces, stresses and magnetic moments from the Materials Project Trajectory Dataset, which consists of over 10 years of density functional theory calculations of more than 1.5 million inorganic structures. The explicit inclusion of magnetic moments enables CHGNet to learn and accurately represent the orbital occupancy of electrons, enhancing its capability to describe both atomic and electronic degrees of freedom. We demonstrate several applications of CHGNet in solid-state materials, including charge-informed molecular dynamics in Li x MnO 2 , the finite temperature phase diagram for Li x FePO 4 and Li diffusion in garnet conductors. We highlight the significance of charge information for capturing appropriate chemistry and provide insights into ionic systems with additional electronic degrees of freedom that cannot be observed by previous MLIPs.

36 MATERIALS SCIENCE↗
DOE OSTI2025

CLPNets: Coupled Lie–Poisson neural networks for multi-part Hamiltonian systems with symmetries

To accurately compute data-based prediction of Hamiltonian systems, it is essential to utilize methods that preserve the structure of the equations over time. We consider a particularly challenging case of systems with interacting parts that do not reduce to pure momentum evolution. Such systems are essential in scientific computations, such as discretization of a continuum elastic rod, which can be viewed as the group of rotations and translations $SE(3)$. The evolution involves not only the momenta but also the relative positions and orientations of the particles. The presence of Lie group-valued elements, such as relative positions and orientations, poses a problem for applying previously derived methods for data-based computing. We develop a novel method of data-based computation and complete phase space learning of such systems. We follow the original framework of SympNets (Jin et al., 2020) and LPNets (Eldred et al., 2024), building the neural network from phase space mappings that preserve the Lie–Poisson structure. We derive a novel system of mappings that are built into neural networks describing the evolution of such systems. We call such networks Coupled Lie–Poisson Neural Networks, or CLPNets. We consider increasingly complex examples for the applications of CLPNets, starting with the rotation of two rigid bodies about a common axis, progressing to the free rotation of two rigid bodies, and finally to the evolution of two connected and interacting $SE(3)$ components, describing the discretization of an elastic rod into two elements. Our method preserves all Casimir invariants to machine precision, preserves energy to high accuracy, and shows good resistance to the curse of dimensionality, requiring only a few thousand data points for all cases studied (three to eighteen dimensions). Additionally, the method is highly economical in memory requirements, requiring only about 200 parameters for the most complex case considered.

Data-based modeling↗
DOE OSTI2023

Machine-learning Kohn–Sham potential from dynamics in time-dependent Kohn–Sham systems

Abstract The construction of a better exchange-correlation potential in time-dependent density functional theory (TDDFT) can improve the accuracy of TDDFT calculations and provide more accurate predictions of the properties of many-electron systems. Here, we propose a machine learning method to develop the energy functional and the Kohn–Sham potential of a time-dependent Kohn–Sham (TDKS) system is proposed. The method is based on the dynamics of the Kohn–Sham system and does not require any data on the exact Kohn–Sham potential for training the model. We demonstrate the results of our method with a 1D harmonic oscillator example and a 1D two-electron example. We show that the machine-learned Kohn–Sham potential matches the exact Kohn–Sham potential in the absence of memory effect. Our method can still capture the dynamics of the Kohn–Sham system in the presence of memory effects. The machine learning method developed in this article provides insight into making better approximations of the energy functional and the Kohn–Sham potential in the TDKS system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Lie–Poisson Neural Networks (LPNets): Data-based computing of Hamiltonian systems with symmetries

An accurate data-based prediction of the long-term evolution of Hamiltonian systems requires a network that preserves the appropriate structure under each time step. Every Hamiltonian system contains two essential ingredients: the Poisson bracket and the Hamiltonian. Hamiltonian systems with symmetries, whose paradigm examples are the Lie–Poisson systems, have been shown to describe a broad category of physical phenomena, from satellite motion to underwater vehicles, fluids, geophysical applications, complex fluids, and plasma physics. The Poisson bracket in these systems comes from the symmetries, while the Hamiltonian comes from the underlying physics. We view the symmetry of the system as primary, hence the Lie–Poisson bracket is known exactly, whereas the Hamiltonian is regarded as coming from physics and is considered not known, or known approximately. Using this approach, we develop a network based on transformations that exactly preserve the Poisson bracket and the special functions of the Lie–Poisson systems (Casimirs) to machine precision. We present two flavors of such systems: one, where the parameters of transformations are computed from data using a dense neural network (LPNets), and another, where the composition of transformations is used as building blocks (G-LPNets). We also show how to adapt these methods to a larger class of Poisson brackets. We apply the resulting methods to several examples, such as rigid body (satellite) motion, underwater vehicles, a particle in a magnetic field, and others. The methods developed in this paper are important for the construction of accurate data-based methods for simulating the long-term dynamics of physical systems.

Data-based modeling↗
DOE OSTI2026

Component-Level Inverse Design of Transmon Qubits Using Neural Networks

Designing a superconducting qubit to realize specific Hamiltonian parameters typically requires iterating through a time and compute-intensive forward loop in which the designer chooses a layout geometry, simulates it, extracts circuit parameters such as capacitances, and refines the geometry. We study the inverse version of this task using a neural-network workflow that maps target Hamiltonian parameters directly to component-level layout parameters, which we subsequently demonstrate on a planar transmon layout. During training, we pair the inverse model with a frozen forward surrogate model and evaluate the loss in Hamiltonian space rather than in layout-parameter space. In validation against a conventional EM solver, 97% of generated designs produce usable geometries, and the inverse-plus-surrogate pipeline reaches mean percent errors of 0.73% for qubit frequency and 1.58% for anharmonicity, comparable to or below the fabrication and simulation-to-measurement uncertainty expected for academic-process transmon devices of this type. A single pipeline query takes ~60 ms on CPU, versus ~2 min for a conventional EM capacitance extraction on the same hardware, a speedup of approximately 2,000x. Batching minimizes the AI model inference overhead, reducing the runtime to 3.1 microseconds per sample on CPU and 2.6 microseconds per sample on GPU at a batch size of 2048, resulting in speedups of 3.9 x 10^7 and 4.6 x 10^7, respectively, relative to a single conventional CPU EM extraction. Our results indicate that component-level inverse design usefully extends and complements conventional EM simulation, including for small datasets on the order of 1,000 samples.

Seidel, Olivia [Fermilab; Texas U., Arlington]↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Distilling the Essential Elements of Nuclear Binding via Neural-Network Quantum States

To distill the essential elements of nuclear binding, we seek the simplest Hamiltonian capable of modeling atomic nuclei with percent-level accuracy. A critical aspect of this endeavor consists of accurately solving the quantum many-body problem without incurring an exponential computing cost with the number of nucleons. Furthermore, we address this challenge by leveraging a variational Monte Carlo method based on a highly expressive neural-network quantum state ansatz. In addition to computing binding energies and charge radii of nuclei with up to 𝐴 = 20 nucleons, by evaluating their magnetic moments, we demonstrate that neural-network quantum states are able to correctly capture the self-emerging nuclear shell structure. To this end, we introduce a novel computational protocol based on adding an external magnetic field to the nuclear Hamiltonian, which allows the neural network to learn the preferred polarization of the nucleus within the given magnetic field.

Binding energy & masses↗
DOE OSTI2025

Optimizing temperature distributions for training neural quantum states using parallel tempering

Parametrized artificial neural networks (ANNs) can be very expressive ansatzes for variational algorithms, reaching state-of-the-art energies on many quantum many-body Hamiltonians. Nevertheless, the training of the ANN can be slow and stymied by the presence of local minima in the parameter landscape. One approach to mitigate this issue is to use parallel tempering methods, and in this work, we focus on the role played by the temperature distribution of the parallel tempering replicas. Using an adaptive method that adjusts the temperatures in order to equate the exchange probability between neighboring replicas, we show that this temperature optimization can significantly increase the success rate of the variational algorithm with negligible computational cost by eliminating bottlenecks in the replicas' random walk. Furthermore, we demonstrate this using two different neural networks, a restricted Boltzmann machine and a feedforward network, which we use to study a toy problem based on a permutation invariant Hamiltonian with a pernicious local minimum and the 𝐽 1 −𝐽 2 model on a rectangular lattice.

Neural network simulations↗
DOE OSTI2025

Symplectic neural network and its application to charged particle dynamics in electromagnetic fields

Recently, machine learning models have shown many successes in various applications in science and technology. In this work, we focus on the charged particle dynamics, with the development of a class of symplectic neural networks, including a linear version, SympMat, and a nonlinear version, HénonNet. Both are designed to preserve the structure of Hamiltonian systems. We show that they can be used to model relevant Hamiltonian systems of interest in plasma physics and astrophysics, for linear and nonlinear charged particle dynamics, with the potential to bridge multi-scale simulations. These symplectic neural networks are adapted to the applications in plasma simulations and particle-wave interaction with parametric dependence and periodicity, where we have investigated their performance and accuracy. In particular, SympMat is shown to outperform the traditional Boris particle pusher down to the sub-gyroperiod scale in the case of charged particles in uniform magnetic fields. HénonNet successfully predicts the hot electron distribution, which is validated against theoretical results. These results highlight the potential of symplectic neural networks as a trajectory integrator for particle-in-cell simulations or a fast surrogate to replace conventional numerical schemes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Variational neural network approach to QFT in the field basis

We present a variational neural network approach for solving quantum field theories in the field basis, focusing on the free Klein-Gordon model formulated in momentum space. While recent studies have explored neural-network-based variational methods for scalar field theory in position space, a systematic benchmark of the analytically solvable Klein-Gordon ground state—particularly in the momentum-space field basis—has been lacking. In this work, we represent the ground-state wavefunctional as a neural network defined on a discretized set of field configurations and train it by minimizing the Hamiltonian expectation value. This framework enables direct comparison to exact analytic results for a range of key observables, including the ground-state energy, two-point correlators, expectation value of the field, and the structure of the learned wavefunctional itself. Our results provide quantitative diagnostics of accuracy and establish a validated foundation for extending neural-network wavefunctional methods to interacting field theories and position-space formulations.

Klein-Gordon model↗