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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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At least 109 records · Page 6
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Combining variational autoencoders and physical bias for improved microscopy data analysis *

Electron and scanning probe microscopy produce vast amounts of data in the form of images or hyperspectral data, such as electron energy loss spectroscopy or 4D scanning transmission electron microscope, that contain information on a wide range of structural, physical, and chemical properties of materials. To extract valuable insights from these data, it is crucial to identify physically separate regions in the data, such as phases, ferroic variants, and boundaries between them. In order to derive an easily interpretable feature analysis, combining with well-defined boundaries in a principled and unsupervised manner, here we present a physics augmented machine learning method which combines the capability of variational autoencoders to disentangle factors of variability within the data and the physics driven loss function that seeks to minimize the total length of the discontinuities in images corresponding to latent representations. Our method is applied to various materials, including NiO-LSMO, BiFeO 3 , and graphene. The results demonstrate the effectiveness of our approach in extracting meaningful information from large volumes of imaging data. The customized codes of the required functions and classes to develop phyVAE is available at https://github.com/arpanbiswas52/phy-VAE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SchrödingerNet: A Universal Neural Network Solver for the Schrödinger Equation

Recent advances in machine learning have facilitated numerically accurate solution of the electronic Schrödinger equation (SE) by integrating various neural network (NN)-based wave function ansatzes with variational Monte Carlo methods. Nevertheless, such NN-based methods are all based on the Born–Oppenheimer approximation (BOA) and require computationally expensive training for each nuclear configuration. In this work, we propose a novel NN architecture, SchrödingerNet, to solve the full electronic-nuclear SE by defining a loss function designed to equalize local energies across the system. This approach is based on a translationally, rotationally and permutationally symmetry-adapted total wave function ansatz that includes both nuclear and electronic coordinates. Furthermore, this strategy not only allows for an efficient and accurate generation of a continuous potential energy surface at any geometry within the well-sampled nuclear configuration space, but also incorporates non-BOA corrections, through a single training process. Comparison with benchmarks of atomic and small molecular systems demonstrates its accuracy and efficiency.

Chemical calculations↗
DOE OSTI2024

Sparsified time-dependent Fourier neural operators for fusion simulations

This paper presents a sparsified Fourier neural operator for coupled time-dependent partial differential equations (ST-FNO) as an efficient machine learning surrogate for fluid and particle-based fusion codes such as NIMROD (Non-Ideal Magnetohydrodynamics with Rotation - Open Discussion) and GTC (Gyrokinetic Toroidal Code). ST-FNO leverages the structures in the governing equations and utilizes neural operators to represent Green's function-like numerical operators in the corresponding numerical solvers. Once trained, ST-FNO can rapidly and accurately predict dynamics in fusion devices compared with first-principle numerical algorithms. In general, ST-FNO represents an efficient and accurate machine learning surrogate for numerical simulators for multi-variable nonlinear time-dependent partial differential equations, with the proposed architectures and loss functions. The efficacy of ST-FNO has been demonstrated using quiescent H-mode simulation data from NIMROD and kink-mode simulation data from GTC. The ST-FNO H-mode results show orders of magnitude reduction in memory and central processing unit usage in comparison with the numerical solvers in NIMROD when computing fields over a selected poloidal plane. The ST-FNO kink-mode results achieve a factor of 2 reduction in the number of parameters compared to baseline FNO models without accuracy loss.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Nonlinear Matrix Approximation with Radial Basis Function Components

We introduce and investigate matrix approximation by decomposition into a sum of radial basis function (RBF) components. An RBF component is a generalization of the outer product between a pair of vectors, where an RBF function replaces the scalar multiplication between individual vector elements. Even though the RBF functions are positive definite, the summation across components is not restricted to convex combinations and allows us to compute the decomposition for any real matrix that is not necessarily symmetric or positive definite. We formulate the problem of seeking such a decomposition as an optimization problem with a nonlinear and non-convex loss function. Several modern versions of the gradient descent method, including their scalable stochastic counterparts, are used to solve this problem. We provide extensive empirical evidence of the effectiveness of the RBF decomposition and that of the gradient-based fitting algorithm. While being conceptually motivated by singular value decomposition (SVD), our proposed nonlinear counterpart outperforms SVD by drastically reducing the memory required to approximate a data matrix with the same L2 error for a wide range of matrix types. For example, it leads to 2 to 6 times memory save for Gaussian noise, graph adjacency matrices, and kernel matrices. Moreover, this proximity-based decomposition can offer additional interpretability in applications that involve, e.g., capturing the inner low-dimensional structure of the data, retaining graph connectivity structure, and preserving the acutance of images.

Rebrova, Elizaveta↗
DOE OSTI2020

Locally adaptive activation functions with slope recovery for deep and physics-informed neural networks

Here we propose two approaches of locally adaptive activation functions namely, layer-wise and neuron-wise locally adaptive activation functions, which improve the performance of deep and physics-informed neural networks. The local adaptation of activation function is achieved by introducing a scalable parameter in each layer (layer-wise) and for every neuron (neuron-wise) separately, and then optimizing it using a variant of stochastic gradient descent algorithm. In order to further increase the training speed, an activation slope-based slope recovery term is added in the loss function, which further accelerates convergence, thereby reducing the training cost. On the theoretical side, we prove that in the proposed method, the gradient descent algorithms are not attracted to sub-optimal critical points or local minima under practical conditions on the initialization and learning rate, and that the gradient dynamics of the proposed method is not achievable by base methods with any (adaptive) learning rates. We further show that the adaptive activation methods accelerate the convergence by implicitly multiplying conditioning matrices to the gradient of the base method without any explicit computation of the conditioning matrix and the matrix–vector product. The different adaptive activation functions are shown to induce different implicit conditioning matrices. Furthermore, the proposed methods with the slope recovery are shown to accelerate the training process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

PI3NN: Out-of-distribution-aware Prediction Intervals from Three Neural Networks

We propose a novel prediction interval (PI) method for uncertainty quantification, which addresses three major issues with the state-of-the-art PI methods. First, existing PI methods require retraining of neural networks (NNs) for every given confidence level and suffer from the crossing issue in calculating multiple PIs. Second, they usually rely on customized loss functions with extra sensitive hyperparameters for which fine tuning is required to achieve a well-calibrated PI. Third, they usually underestimate uncertainties of out-of-distribution (OOD) samples leading to over-confident PIs. Our PI3NN method calculates PIs from linear combinations of three NNs, each of which is independently trained using the standard mean squared error loss. The coefficients of the linear combinations are computed using root-finding algorithms to ensure tight PIs for a given confidence level. We theoretically prove that PI3NN can calculate PIs for a series of confidence levels without retraining NNs and it completely avoids the crossing issue. Additionally, PI3NN does not introduce any unusual hyperparameters resulting in a stable performance. Furthermore, we address OOD identification challenge by introducing an initialization scheme which provides reasonably larger PIs of the OOD samples than those of the in-distribution samples. Benchmark and real-world experiments show that our method outperforms several state-of-the-art approaches with respect to predictive uncertainty quality, robustness, and OOD samples identification.

Liu, Siyan↗
DOE OSTI2023

Lagrangian large eddy simulations via physics-informed machine learning

High-Reynolds number homogeneous isotropic turbulence (HIT) is fully described within the Navier–Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as large eddy simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about effects of subgrid scales on the resolved scales. Here, we take an alternative approach and design LES heuristics stated in terms of Lagrangian particles moving with the flow. Our Lagrangian LES, thus L-LES, is described by equations generalizing the weakly compressible smoothed particle hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from direct numerical simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The subgrid-scale contributions are modeled separately with physical constraints to account for the effects from unresolved scales. We build the resulting model under the differentiable programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our L-LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Code for the manuscript "Lagrangian Large Eddy Simulations vis Physics-informed Machine Learning"

We would like to disclose a code based on Python/Pytorch, in which we implement the data-driven physics-informed machine learning of Lagrangian large eddy simulation that is described in the manuscript "Lagrangian Large Eddy Simulations via Physics-Informed Machine Learning ". High-Reynolds number Homogeneous Isotropic Turbulence is fully described within the Navier-Stokes (NS) equations, which are notoriously difficult to solve numerically. Engineers, interested primarily in describing turbulence at a reduced range of resolved scales, have designed heuristics, known as Large Eddy Simulation (LES). LES is described in terms of the temporally evolving Eulerian velocity field defined over a spatial grid with the mean-spacing correspondent to the resolved scale. This classic Eulerian LES depends on assumptions about the effects of sub-grid scales on the resolved scales. Here, we take an alternative approach and design novel LES heuristics stated in terms of Lagrangian particles moving with the flow. Our \emph{Lagrangian LES}, thus L-LES, is described by equations generalizing the weakly compressible Smoothed Particle Hydrodynamics formulation with extended parametric and functional freedom, which is then resolved via Machine Learning training on Lagrangian data from Direct Numerical Simulations of the NS equations. The L-LES model includes physics-informed parameterization and functional form, by combining physics-based parameters and physics-inspired Neural Networks to describe the evolution of turbulence within the resolved range of scales. The sub-grid scale contributions are modeled separately with physical constraints to account for the effects from un-resolved scales. We build the resulting model under the Differentiable Programming framework to facilitate efficient training. We experiment with loss functions of different types, including physics-informed ones accounting for statistics of Lagrangian particles. We show that our Lagrangian LES model is capable of reproducing Eulerian and unique Lagrangian turbulence structures and statistics over a range of turbulent Mach numbers.

Tian, Yifeng↗
DOE OSTI2024

Enhancing high-fidelity neural network potentials through low-fidelity sampling

The efficacy of neural network potentials (NNPs) critically depends on the quality of the configurational datasets used for training. Prior research using empirical potentials has shown that well-selected liquid–solid transitional configurations of a metallic system can be translated to other metallic systems. This study demonstrates that such validated configurations can be relabeled using density functional theory (DFT) calculations, thereby enhancing the development of high-fidelity NNPs. Training strategies and sampling approaches are efficiently assessed using empirical potentials and subsequently relabeled via DFT in a highly parallelized fashion for high-fidelity NNP training. Our results reveal that relying solely on energy and force for NNP training is inadequate to prevent overfitting, highlighting the necessity of incorporating stress terms into the loss functions. To optimize training involving force and stress terms, we propose employing transfer learning to fine-tune the weights, ensuring that the potential surface is smooth for these quantities composed of energy derivatives. This approach markedly improves the accuracy of elastic constants derived from simulations in both empirical potential-based NNPs and relabeled DFT-based NNPs. Overall, this study offers significant insights into leveraging empirical potentials to expedite the development of reliable and robust NNPs at the DFT level.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

4D Multimodal Co-attention Fusion Network with Latent Contrastive Alignment for Alzheimer’s Diagnosis

Multimodal neuroimaging provides complementary structural and functional insights into both human brain organization and disease-related dynamics. Recent studies demonstrate enhanced diagnostic sensitivity for Alzheimer’s disease (AD) through synergistic integration of neuroimaging data (e.g., sMRI, fMRI) with tabular data (e.g., behavioral and cognitive tests). However, the intrinsic heterogeneity across modalities (e.g., 4D spatiotemporal fMRI dynamics vs. 3D anatomical sMRI structure) presents critical challenges for discriminative feature fusion, often leading to information loss or biased fusion. To bridge this gap, we propose M2M-AlignNet: a multimodal co-attention network with latent alignment for early AD diagnosis using sMRI and fMRI. At the core of our approach is a multi-patch-to-multi-patch (M2M) contrastive loss function that quantifies and reduces representational discrepancies via weighted patch correspondence, explicitly aligning fMRI components across brain regions with their sMRI structural substrates without one-to-one constraints. Additionally, we propose a latent-as-query co-attention module to autonomously discover fusion patterns, circumventing modality prioritization biases while minimizing feature redundancy. We conduct extensive experiments to confirm the effectiveness of our method and highlight the correspondence between fMRI and sMRI as AD biomarkers.

Wei, Yuxiang [Georgia Institute of Technology]↗
DOE OSTI2022

Physics-informed neural networks for identification of material properties using standing waves

A metallic structure in its initial stage of failure involves plastic deformation or environmental degradation that changes the elastic modulus and density. This work presents the detection of change in wave velocity (a function of elastic modulus and density) as a system identification problem. A physics-informed neural network (PINN) is proposed to solve the system identification problem. The PINN takes the spatial coordinates of scanning locations and time as inputs and provides the displacement and wave velocity as outputs. The governing partial differential equation of standing waves in a rod is incorporated into the neural network as physics in the form of a loss function. The wave velocity vector is randomly initiated. During the training of the network, physics is used to determine and update the wave velocity target vector from the network’s displacement predictions. The measured data, comprising sparse displacement response on the rod structure, are used to train the PINN. The wave velocity at the sparse locations on the rod is learned from the predicted displacements during the training. Using the predictions of the trained network, the response of free vibration or material property variation can be reconstructed at unscanned locations on the structure to obtain high-resolution maps for full-field imaging to detect and localize the changes caused by plastic deformation. The PINN’s sparse scanning and simultaneous prediction capability during training can lead to high scanning and data-processing speeds. This capability yields a nondestructive evaluation system that can predict the presence of degraded material locations as the structural vibrations are scanned and processed in real time.

Rathod, Vivek↗
DOE OSTI2024

Challenges in Training PINNs: A Loss Landscape Perspective

This paper explores challenges in training Physics Informed Neural Networks (PINNs), emphasizing the role of the loss landscape in the training process. We examine difficulties in minimizing the PINN loss function, particularly due to ill conditioning caused by differential operators in the residual term. We compare gradient-based optimizers Adam, L-BFGS, and their combination Adam+L-FGS, showing the superiority of Adam+L-BFGS, and introduce a novel secondorder optimizer, NysNewton-CG (NNCG), which significantly improves PINN performance. Theoretically, our work elucidates the connection between ill-conditioned differential operators and ill-conditioning in the PINN loss and shows the benefits of combining first- and second-order optimization methods. Our work presents valuable insights and more powerful optimization strategies for training PINNs, which could improve the utility of PINNs for solving difficult partial differential equations.

Rathore, Pratik↗
DOE OSTI2022

Neural conditional reweighting

There is a growing use of neural network classifiers as unbinned, high-dimensional (and variable-dimensional) reweighting functions. To date, the focus has been on marginal reweighting, where a subset of features are used for reweighting while all other features are integrated over. There are some situations, though, where it is preferable to condition on auxiliary features instead of marginalizing over them. Here, we introduce neural conditional reweighting, which extends neural marginal reweighting to the conditional case. This approach is particularly relevant in high-energy physics experiments for reweighting detector effects conditioned on particle-level truth information. Furthermore we leverage a custom loss function that not only allows us to achieve neural conditional reweighting through a single training procedure, but also yields sensible interpolation even in the presence of phase space holes. As a specific example, we apply neural conditional reweighting to the energy response of high-energy jets, which could be used to improve the modeling of physics objects in parametrized fast simulation packages.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Electronic and optical properties of plutonium metal and oxides from Reflection Electron Energy Loss Spectroscopy

Reflection Electron Energy Loss Spectra (REELS) have been acquired on plutonium δ-Pu-Ga alloys, α-Pu 2 O 3 and PuO 2 . The position of the peaks attributable to the Pu 6p excitation can be used as ‘fingerprint’ for these species. X-ray Photoelectron Spectroscopy has been used to aid interpretation of the REELS spectra. The band gap of PuO 2 was determined from the onset of the energy loss in the REELS spectrum. The REELS data have been evaluated within the dielectric response theory by means of the QUEELS-ε(k, w)-REELS software. In this work, the Energy Loss Function, dielectric function, refractive index and extinction coefficient for these materials have been determined in the ultraviolet and extreme ultraviolet range and are compared to previously reported results.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Gearbox bearing crack growth prognostics and uncertainty quantification with physics-informed machine learning

This paper introduces the extreme theory of functional connections (X-TFC), a physics-informed machine learning algorithm, and tailors it to estimate the remaining useful life (RUL) of wind turbine gearbox bearings experiencing fatigue crack growth. Unlike purely data-driven methods, X-TFC embeds a physics model, based on Head's theory in this work, into its training objective. The core of X-TFC is a random-projection single-layer neural network trained via an extreme learning machine, which requires only limited damage progression data and solves for output weights with a least-squares optimization algorithm. A composite loss function balances the network's fit to observed degradation data against the residuals of the governing crack growth differential equation, ensuring the learned damage trajectory remains physically plausible. When applied to a vibration-based health-index (HI) dataset measured during the growth of a crack on the inner ring of a high-speed bearing in a wind turbine gearbox (Bechhoefer and Dubé, 2020), X-TFC achieves near-zero prediction bias. Even when trained on only the first 10 %–20 % of the damage progression data, with sufficient physics weighting its predictions remain monotonic and smooth, delivering high prognosability and trendability. To quantify the epistemic uncertainty, we employ a Monte Carlo ensemble of independently initialized X-TFC models trained on noise-perturbed data, which yields confidence intervals around each RUL estimate and captures both model-parameter and epistemic uncertainty. In addition to a vibration-based HI, we demonstrate that the proposed framework can be directly applied to a supervisory control and data acquisition (SCADA) data-based HI (Eftekhari Milani et al., 2026) measured during similar wind turbine gearbox bearing crack faults, preserving its accuracy and interpretability. This extension shows the versatility of our approach, which is applicable to bearings of multiple gearbox manufacturers, models, and ratings using only SCADA data. By integrating domain knowledge with machine learning, X-TFC offers a rapid, reliable tool for crack prognostics. Its adaptability to other bearing failure modes, such as pitch bearing ring cracks, positions X-TFC as a powerful enabler of data-driven, physics-informed asset management in the wind energy sector and beyond.

17 WIND ENERGY↗
DOE OSTI2024

Hutchinson Trace Estimation for high-dimensional and high-order Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have proven effective in solving partial differential equations (PDEs), especially when some data are available by seamlessly blending data and physics. However, extending PINNs to high-dimensional and even high-order PDEs encounters significant challenges due to the computational cost associated with automatic differentiation in the residual loss function calculation. Herein, we address the limitations of PINNs in handling high-dimensional and high-order PDEs by introducing the Hutchinson Trace Estimation (HTE) method. Starting with the second-order high-dimensional PDEs, which are ubiquitous in scientific computing, HTE is applied to transform the calculation of the entire Hessian matrix into a Hessian vector product (HVP). This approach not only alleviates the computational bottleneck via Taylor-mode automatic differentiation but also significantly reduces memory consumption from the Hessian matrix to an HVP’s scalar output. We further showcase HTE’s convergence to the original PINN loss and its unbiased behavior under specific conditions. Comparisons with the Stochastic Dimension Gradient Descent (SDGD) highlight the distinct advantages of HTE, particularly in scenarios with significant variability and variance among dimensions. We further extend the application of HTE to higher-order and higher-dimensional PDEs, specifically addressing the biharmonic equation. By employing tensor-vector products (TVP), HTE efficiently computes the colossal tensor associated with the fourth-order high-dimensional biharmonic equation, saving memory and enabling rapid computation. The effectiveness of HTE is illustrated through experimental setups, demonstrating comparable convergence rates with SDGD under memory and speed constraints. Additionally, HTE proves valuable in accelerating the Gradient-Enhanced PINN (gPINN) version as well as the Biharmonic equation. Overall, HTE opens up a new capability in scientific machine learning for tackling high-order and high-dimensional PDEs.

Curse of dimensionality↗
DOE OSTI2021

Differentiable programming for online training of a neural artificial viscosity function within a staggered grid Lagrangian hydrodynamics scheme

Lagrangian methods to solve the inviscid Euler equations produce numerical oscillations near shock waves. A common approach to reducing these oscillations is to add artificial viscosity (AV) to the discrete equations. The AV term acts as a dissipative mechanism that attenuates oscillations by smearing the shock across a finite number of computational cells. However, AV introduces several control parameters that are not determined by the underlying physical model, and hence, in practice are tuned to the characteristics of a given problem. We seek to improve the standard quadratic-linear AV form by replacing it with a learned neural function that reduces oscillations relative to exact solutions of the Euler equations, resulting in a hybrid numerical-neural hydrodynamic solver. Because AV is an artificial construct that exists solely to improve the numerical properties of a hydrodynamic code, there is no offline ‘viscosity data’ against which a neural network can be trained before inserting into a numerical simulation, thus requiring online training. We achieve this via differentiable programming, i.e. end-to-end backpropagation or adjoint solution through both the neural and differential equation code, using automatic differentiation of the hybrid code in the Julia programming language to calculate the necessary loss function gradients. A novel offline pre-training step accelerates training by initializing the neural network to the default numerical AV scheme, which can be learned rapidly by space-filling sampling over the AV input space. We find that online training over early time steps of simulation is sufficient to learn a neural AV function that reduces numerical oscillations in long-term hydrodynamic shock simulations. These results offer an early proof-of-principle that online differentiable training of hybrid numerical schemes with novel neural network components can improve certain performance aspects existing in purely numerical schemes.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Solving Inverse Stochastic Problems from Discrete Particle Observations Using the Fokker--Planck Equation and Physics-Informed Neural Networks

The Fokker--Planck (FP) equation governing the evolution of the probability density function (PDF) is applicable to many disciplines, but it requires specification of the coefficients for each case, which can be functions of space-time and not just constants and hence require the development of a data-driven modeling approach. When the data available is directly on the PDF, there exist methods for inverse problems that can be employed to infer the coefficients and thus determine the FP equation and subsequently obtain its solution. Herein, we address a more realistic scenario, where only sparse data are given on the particles' positions at a few time instants, which are not sufficient to accurately construct directly the PDF even at those times from existing methods, e.g., kernel estimation algorithms. To this end, we develop a general framework based on physics-informed neural networks (PINNs) that introduces a new loss function using the Kullback--Leibler divergence to connect the stochastic samples with the FP equation to simultaneously learn the equation and infer the multidimensional PDF at all times. In particular, we consider two types of inverse problems, type I, where the FP equation is known but the initial PDF is unknown, and type II, in which, in addition to the unknown initial PDF, the drift and diffusion terms are also unknown. In both cases, we investigate problems with either Brownian or Lévy noise or a combination of both. Here, we demonstrate the new PINN framework in detail in the one-dimensional (1D) case, but we also provide results for up to five dimensions demonstrating that we can infer both the FP equation and dynamics simultaneously at all times with high accuracy using only very few discrete observations of the particles.

97 MATHEMATICS AND COMPUTING↗