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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 OSTI2025

FEDERATED LEARNING ON STOCHASTIC NEURAL NETWORKS

Federated learning is a machine learning paradigm that leverages edge computing on client devices to optimize models while maintaining user privacy by ensuring that local data remain on the device. However, since all data are collected by clients, federated learning is susceptible to latent noise in local datasets. Factors such as limited measurement capabilities or human errors may introduce inaccuracies in client data. To address this challenge, we propose the use of a stochastic neural network as the local model within the federated learning framework. Stochastic neural networks not only facilitate the estimation of the true underlying states of the data but also enable the quantification of latent noise. We refer to our federated learning approach, which incorporates stochastic neural networks as local models, as federated stochastic neural networks. In this work we will present numerical experiments demonstrating the performance and effectiveness of our method, particularly in handling nonindependent and identically distributed data.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A backward SDE method for uncertainty quantification in deep learning

Here, we develop a backward stochastic differential equation based probabilistic machine learning method, which formulates a class of stochastic neural networks as a stochastic optimal control problem. An efficient stochastic gradient descent algorithm is introduced with the gradient computed through a backward stochastic differential equation. Convergence analysis for stochastic gradient descent optimization and numerical experiments for applications of stochastic neural networks are carried out to validate our methodology in both theory and performance.

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 OSTI2026

Full-stack Quantification of Variability in Predicting Ion Transport Properties using Machine-learned Interatomic Potentials

Machine-learned interatomic potentials (MLIPs) have become the state-of-the-art for performing accurate, scalable molecular dynamics (MD) simulations. It is therefore crucial to understand and quantify the reliability of MLIPs for downstream property predictions. Uncertainty in predicted properties can arise from limitations in first-principles training data, intrinsic MLIP model errors in representing the data, and the statistical noise introduced during subsequent MD simulations. Using ion transport in Li7P3S11 as a case study, we systematically assess the impact of training set size and selection, neural network stochasticity, and MD sampling statistics on predicted diffusivity and activation energy. We find that when using equivariant MLIP architectures with standard MD protocols, uncertainty arising from MD sampling dominates over model-induced errors. In contrast, MLIP errors relative to the underlying first-principles data are consistently minor. Given this, there are two main routes to improving the accuracy of predictions based on MLIP potentials: adopting higher accuracy reference data generation methods, and improving the MD sampling statistics.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Improving Predictions Under Uncertainty of Material Plasma Device Operations

Understanding the properties of materials when exposed to various plasma temperatures and fluxes is essential to the building and operating of fusion reactors. The Material Plasma Exposure eXperiment (MPEX) is an instrument currently being developed by the Department of Energy (DOE) for this purpose. MPEX is expected to come online in stages over the next five years. Proto-MPEX, the predecessor to MPEX, operated from 2014 to 2021, and was designed to understand the generation of plasma temperatures and fluxes at orders of magnitude below what will be obtained by MPEX. This work uses the recently developed stochastic neural network (SNN), a machine learning technique capable of operating under uncertainty to provide a surrogate model for the Proto-MPEX device. We demonstrate that SNN outperforms Bayesian neural network (BNN), a standard in the field of machine learning with uncertainty. The development of a robust surrogate of the Proto-MPEX will aid in the commissioning and operation of the MPEX device.

Archibald, Rick↗
DOE OSTI2023

Convergence of Hyperbolic Neural Networks Under Riemannian Stochastic Gradient Descent

Abstract We prove, under mild conditions, the convergence of a Riemannian gradient descent method for a hyperbolic neural network regression model, both in batch gradient descent and stochastic gradient descent. We also discuss a Riemannian version of the Adam algorithm. We show numerical simulations of these algorithms on various benchmarks.

Whiting, Wes (ORCID:0000000247505060)↗
DOE OSTI2022

GFINNs: GENERIC formalism informed neural networks for deterministic and stochastic dynamical systems

Here we propose the GENERIC formalism informed neural networks (GFINNs) that obey the symmetric degeneracy conditions of the GENERIC formalism. GFINNs comprise two modules, each of which contains two components. We model each component using a neural network whose architecture is designed to satisfy the required conditions. The component-wise architecture design provides flexible ways of leveraging available physics information into neural networks. We prove theoretically that GFINNs are sufficiently expressive to learn the underlying equations, hence establishing the universal approximation theorem. We demonstrate the performance of GFINNs in three simulation problems: gas containers exchanging heat and volume, thermoelastic double pendulum and the Langevin dynamics. In all the examples, GFINNs outperform existing methods, hence demonstrating good accuracy in predictions for both deterministic and stochastic systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solving inverse problems in stochastic models using deep neural networks and adversarial training

Inverse problems associated with stochastic models constitute a significant portion of scientific and engineering applications. In such cases the unknown quantities are distributions. The applicability of traditional methods is limited because of their demanding assumptions or prohibitive computational consumption; for example, maximum likelihood methods require closed-form density functions, and Markov Chain Monte Carlo needs a large number of simulations. We propose a new method that estimates the unknown distribution by matching the statistical properties between observed and simulated random processes. We leverage the expressive power of neural networks to approximate the unknown distribution and use a discriminative neural network for computing the statistical discrepancies between the observed and simulated random processes. Here we demonstrated numerically that the proposed methods can estimate both the model parameters and learn complicated unknown distributions.

42 ENGINEERING↗
DOE OSTI2022

Learning stochastic dynamics with statistics-informed neural network

We introduce a machine-learning framework named statistics-informed neural network (SINN) for learning stochastic dynamics from data. This new architecture was theoretically inspired by a universal approximation theorem for stochastic systems, which we introduce in this paper, and the projection-operator formalism for stochastic modeling. Here, we devise mechanisms for training the neural network model to reproduce the correct statistical behavior of a target stochastic process. Numerical simulation results demonstrate that a well-trained SINN can reliably approximate both Markovian and non-Markovian stochastic dynamics. We demonstrate the applicability of SINN to coarse-graining problems and the modeling of transition dynamics. Furthermore, we show that the obtained reduced-order model can be trained on temporally coarse-grained data and hence is well suited for rare-event simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Distributed Stochastic Optimization of a Neural Representation Network for Time-Space Tomography Reconstruction

4D time-space reconstruction of dynamic events or deforming objects using X-ray computed tomography (CT) is an important inverse problem in non-destructive evaluation. Conventional back-projection based reconstruction methods assume that the object remains static for the duration of several tens or hundreds of X-ray projection measurement images (reconstruction of consecutive limited-angle CT scans). However, this is an unrealistic assumption for many in-situ experiments that causes spurious artifacts and inaccurate morphological reconstructions of the object. To solve this problem, we propose to perform a 4D time-space reconstruction using a distributed implicit neural representation (DINR) network that is trained using a novel distributed stochastic training algorithm. Our DINR network learns to reconstruct the object at its output by iterative optimization of its network parameters such that the measured projection images best match the output of the CT forward measurement model. Here, we use a forward measurement model that is a function of the DINR outputs at a sparsely sampled set of continuous valued 4D object coordinates. Unlike previous neural representation architectures that forward and back propagate through dense voxel grids that sample the object's entire time-space coordinates, we only propagate through the DINR at a small subset of object coordinates in each iteration resulting in an order-of-magnitude reduction in memory and compute for training. DINR leverages distributed computation across several compute nodes and GPUs to produce high-fidelity 4D time-space reconstructions. We use both simulated parallel-beam and experimental cone-beam X-ray CT datasets to demonstrate the superior performance of our approach.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Prediction of gas hydrate saturation using machine learning and optimal set of well-logs

We report resistivity and acoustic logs are widely used to estimate gas hydrate saturation in various sedimentary systems using one of the two popular methods ((1) acoustic velocity and (2) electrical resistivity), but the limitations of these two methods are often overlooked, which include (i) well-specific calibration of empirical exponents in the electrical resistivity method, (ii) assumption of known pore morphology for gas hydrates in the acoustic velocity method, and (iii) presence of unknown mineralogy and bulk modulus terms in the acoustic velocity method. NMR-density porosity-derived gas hydrate saturation based on the analysis of the transverse magnetization relaxation time (T2) is considered the most precise method, but acquisition of NMR-based logs is limited at relatively recent drilled sites; additionally, its use in conventional oil and gas reservoirs is not that common due to higher cost and operational deployment limitations associated with acquiring NMR well-logs. This study proposes a new method that predicts gas hydrate saturation (S h ) for any well using porosity, bulk density, and compressional wave (P wave) velocity well-logs with neural network (or stochastic gradient descent regression) without any well-specific calibration and/or other aforementioned shortcomings of the existing methods. The method is developed by examining the underlying dependency between S h and different combinations of well-logs, chosen from 6 routine logs, with 12 different machine learning (ML) algorithms. The accuracy of the proposed method in predicting S h is ~ 84%, which is better than the accuracy of seismic and electrical resistivity methods (≤ 75%) per the results reported by three different studies. The robustness of the method in the specific case of permafrost-associated gas hydrates is demonstrated with well-log data from two wells drilled on the Alaska North Slope.

58 GEOSCIENCES↗
DOE OSTI2025

Resimulation-based self-supervised learning for pretraining physics foundation models

Self-supervised learning (SSL) is at the core of training modern large machine learning models, providing a scheme for learning powerful representations that can be used in a variety of downstream tasks. However, SSL strategies must be adapted to the type of training data and downstream tasks required. We propose resimulation-based self-supervised representation learning (RS3L), a novel simulation-based SSL strategy that employs a method of resimulation to drive data augmentation for contrastive learning in the physical sciences, particularly, in fields that rely on stochastic simulators. By intervening in the middle of the simulation process and rerunning simulation components downstream of the intervention, we generate multiple realizations of an event, thus producing a set of augmentations covering all physics-driven variations available in the simulator. Using experiments from high-energy physics, we explore how this strategy may enable the development of a foundation model; we show how RS3L pretraining enables powerful performance in downstream tasks such as discrimination of a variety of objects and uncertainty mitigation. In addition to our results, we make the RS3L dataset publicly available for further studies on how to improve SSL strategies.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Stochasticity and robustness in spiking neural networks

Despite drawing inspiration from biological systems which are inherently noisy and variable, artificial neural networks have been shown to require precise weights to carry out the task which they are trained to accomplish. This creates a challenge when adapting these artificial networks to specialized execution platforms which may encode weights in a manner which restricts their accuracy and/or precision.Reflecting back on the non-idealities which are observed in biological systems, we investigated the effect these properties have on the robustness of spiking neural networks under perturbations to weights. First, we examined techniques extant in conventional neural networks which resemble noisy processes, and postulated they may produce similar beneficial effects in spiking neural networks. Second, we evolved a set of spiking neural networks utilizing biological non-idealities to solve a pole-balancing task, and estimated their robustness. We showed it is higher in networks using noisy neurons, and demonstrated that one of these networks can perform well under the variance expected when a hafnium-oxide based resistive memory is used to encode synaptic weights. Lastly, we trained a series of networks using a surrogate gradient method on the MNIST classification task. We confirmed that these networks demonstrate similar trends in robustness to the evolved networks. We discuss these results and argue that they display empirical evidence supporting the role of noise as a regularizer which can increase network robustness.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Analytic continuation of noisy data using Adams Bashforth residual neural network

We propose a data-driven learning framework for the analytic continuation problem in numerical quantum many-body physics. Designing an accurate and efficient framework for the analytic continuation of imaginary time using computational data is a grand challenge that has hindered meaningful links with experimental data. The standard Maximum Entropy (MaxEnt)-based method is limited by the quality of the computational data and the availability of prior information. Also, the MaxEnt is not able to solve the inversion problem under high level of noise in the data. Here we introduce a novel learning model for the analytic continuation problem using a Adams-Bashforth residual neural network (AB-ResNet). Additionally, the advantage of this deep learning network is that it is model independent and, therefore, does not require prior information concerning the quantity of interest given by the spectral function. More importantly, the ResNet-based model achieves higher accuracy than MaxEnt for data with higher level of noise. Finally, numerical examples show that the developed AB-ResNet is able to recover the spectral function with accuracy comparable to MaxEnt where the noise level is relatively small.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Stochastic Thermo-Hydro Modeling and Neural Network Surrogate Development for Thermal Resource Assessment of the Galleries-to-Calories Geobattery

The Galleries-to-Calories Geobattery concept explores the use of abandoned coal mine workings for large-scale thermal energy transport and storage. The system involves injecting waste heat from a supercomputing facility into flooded mine galleries, where groundwater flow can store and transport thermal energy for potential recovery in downgradient district heating and cooling applications. To evaluate the feasibility and performance of the Geobattery under geological and operational uncertainty, we developed a suite of stochastic thermo-hydrological (TH) simulations using Monte Carlo sampling of key uncertain parameters (e.g., permeability, porosity, thermal conductivity, specific heat capacity) and operating conditions (e.g., injection rate, injection temperature). Results identified injection rate and temperature as the most influential parameters governing thermal front propagation, while the geometry of the room-and-pillar structure played a critical role in directing the extent and orientation of thermal advancement. Optimal combinations of material properties for maximizing heat recovery were also determined. To address the high computational cost of coupled-process stochastic modeling, we trained a neural network surrogate model on 24,000 physics-based realizations, achieving an R² > 0.99 and MAE < 0.1 for temperature predictions at monitoring locations. This surrogate enabled an additional 100,000 realizations for global sensitivity analysis and probabilistic thermal resource assessment. The integrated stochastic physics–surrogate modeling framework offers a computationally efficient tool for quantifying uncertainty, identifying key drivers, and informing early-stage design decisions for Geobattery systems.

15 - GEOTHERMAL ENERGY↗
DOE OSTI2021

Tunable Stochasticity in an Artificial Spin Network

Metamaterials present the possibility of artificially generating advanced functionalities through engineering of their internal structure. Artificial spin networks, in which a large number of nanoscale magnetic elements are coupled together, are promising metamaterial candidates that enable the control of collective magnetic behavior through tuning of the local interaction between elements. In this work, the motion of magnetic domain-walls in an artificial spin network leads to a tunable stochastic response of the metamaterial, which can be tailored through an external magnetic field and local lattice modifications. This type of tunable stochastic network produces a controllable random response exploiting intrinsic stochasticity within magnetic domain-wall motion at the nanoscale. An iconic demonstration used to illustrate the control of randomness is the Galton board. In this system, multiple balls fall into an array of pegs to generate a bell-shaped curve that can be modified via the array spacing or the tilt of the board. A nanoscale recreation of this experiment using an artificial spin network is employed to demonstrate tunable stochasticity. Furthermore, this type of tunable stochastic network opens new paths toward post-Von Neumann computing architectures such as Bayesian sensing or random neural networks, in which stochasticity is harnessed to efficiently perform complex computational tasks.

Artificial spin network↗
DOE OSTI2021

Correspondence between neuroevolution and gradient descent

Abstract We show analytically that training a neural network by conditioned stochastic mutation or neuroevolution of its weights is equivalent, in the limit of small mutations, to gradient descent on the loss function in the presence of Gaussian white noise. Averaged over independent realizations of the learning process, neuroevolution is equivalent to gradient descent on the loss function. We use numerical simulation to show that this correspondence can be observed for finite mutations, for shallow and deep neural networks. Our results provide a connection between two families of neural-network training methods that are usually considered to be fundamentally different.

97 MATHEMATICS AND COMPUTING↗