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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Learning and meta-learning of stochastic advection–diffusion–reaction systems from sparse measurements

Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Crustal Scale Travel Time Prediction with the SALSA3D Framework and Machine Learning

The SALSA3D project aims to improve our models used in travel time prediction. The current version uses tomographic modeling for propagation through the Earth’s mantle because of the large number (order of millions) of observations of seismic phases which primarily traverse the Earth’s mantle and the ability to pose the travel time problem as a set of linear equations. However, all seismic rays traverse the crust to reach receivers at the surface and therefore models of propagation through the crust are required. Therefore, the primary motivation for this study is to explore how to increase the scope of the SALSA3D project to phases which travel primarily through the crust. In this report, we evaluate new, machine learning based and physics-based methods to model these travel times for integration into the SALSA3D framework. Our results suggest that using our existing physics-based travel time tomography method is a viable approach for the regional to global scale, but better predictive capabilities can be achieved through a neural network trained on the region of interest for near-regional offsets. We suggest future iterations of SALSA3D should incorporate machine learning tools such as Physics-Informed Neural Networks or Bayesian Neural Networks.

58 GEOSCIENCES↗
DOE OSTI2022

Understanding the Physics Representation of Deep Learning Models in Environmental Applications

Deep learning (DL) models have been popular in earth and environmental modeling and analysis, which exhibit huge potential in capturing and reconstructing the non-linearity of relevant environmental processes. They are extensively used as analytical tools or emulators for multiple domains (atmosphere, land surface, ocean, and biogeochemistry). Despite their success, their internal working mechanism remains largely unknown. Such a lack of knowledge hinders the identification of physically consistent models that are fully adaptive to non-stationary climate, as well as the development of physics-informed machine learning such as physics-informed neural network (PINN). To establish preliminary knowledge and framework of such physics representation evaluation, this project focuses on an improved understanding of DL models in the environmental applications. DL models are increasingly applied to environmental modeling and prediction. However, they have been evaluated mostly from a performance perspective, and there is a gap in understanding how they represent the known physics internally. Such knowledge is especially critical when applying DL models under climate change conditions, where new inputs are likely outside the ranges of the training datasets. In this project, we reveal how the known physical processes are represented within DL models from both statistical and mechanistic perspectives. Leveraging the traditional model evaluations that focus more on the accuracies of predictions, we establish a framework that examines both the accuracy and physics representation of DL models. This analysis framework can identify DL models that make the correct predictions based on correct physics, thus enhancing the existing explainable artificial intelligence (explainable-AI) portfolio. It lays a foundation for developing novel metrics to evaluate the emerging DL models in environmental applications. This knowledge also informs the development of physics-informed DL models by revealing the direct connections between the known physical processes and specific model components or structures.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2025

Constrained or unconstrained? Neural-network-based equation discovery from data

Throughout many fields, practitioners often rely on differential equations to model systems. Yet, for many applications, the theoretical derivation of such equations and/or the accurate resolution of their solutions may be intractable. Instead, recently developed methods, including those based on parameter estimation, operator subset selection, and neural networks, allow for the data-driven discovery of both ordinary and partial differential equations (PDEs), on a spectrum of interpretability. The success of these strategies is often contingent upon the correct identification of representative equations from noisy observations of state variables and, as importantly and intertwined with that, the mathematical strategies utilized to enforce those equations. Specifically, the latter has been commonly addressed via unconstrained optimization strategies. Representing the PDE as a neural network, we propose to discover the PDE (or the associated operator) by solving a constrained optimization problem and using an intermediate state representation similar to a physics-informed neural network (PINN). The objective function of this constrained optimization problem promotes matching the data, while the constraints require that the discovered PDE is satisfied at a number of spatial collocation points. We present a penalty method and a widely used trust-region barrier method to solve this constrained optimization problem, and we compare these methods on numerical examples. Our results on several example problems demonstrate that the latter constrained method outperforms the penalty method, particularly for higher noise levels or fewer collocation points. This work motivates further exploration into using sophisticated constrained optimization methods in scientific machine learning, as opposed to their commonly used, penalty-method or unconstrained counterparts. For both of these methods, we solve these discovered neural network PDEs with classical methods, such as finite difference methods, as opposed to PINNs-type methods relying on automatic differentiation. Here, we briefly highlight how simultaneously fitting the data while discovering the PDE improves the robustness to noise and other small, yet crucial, implementation details.

Data-driven discovery↗
DOE OSTI2021

Artificial intelligence velocimetry and microaneurysm-on-a-chip for three-dimensional analysis of blood flow in physiology and disease

Significance Microfluidics is an important in vitro platform to gain insights into mechanics of blood flow and mechanisms of pathophysiology of human diseases. Extraction of 3D fields in microfluidics with dense cell suspensions remains a formidable challenge. We present artificial-intelligence velocimetry (AIV) as a general platform to determine 3D flow fields and a microaneurysm-on-a-chip to simulate blood flow in microaneurysms in patients with diabetic retinopathy. AIV is built on physics-informed neural networks that integrate seamlessly 2D images from microfluidic experiments or in vivo observations with physical laws to estimate full 3D velocity and stress fields. AIV could be integrated into imaging technologies to automatically infer key hemodynamic metrics from in vivo and in vitro biomedical images.

42 ENGINEERING↗
DOE OSTI2025

PruningAMR

PruningAMR is an algorithm that reads in data stored as a neural network and outputs an adaptive mesh with values of the neural network stored at its vertices. Examples of input data include implicit neural representations (INRs) and physics-informed neural networks (PINNs). The output mesh is a grid-based adaptive mesh with larger elements for regions in which the neural network has coarse-scale variation and smaller elements for regions with fine scale variation. The goal of the software is to discretize the neural network to a mesh that faithfully captures the details encoded in the data without resorting a fine scale mesh.

Zvonek, JenniferE [Lawrence Livermore National Lab↗
DOE OSTI2023

Physics-informed machine learning of redox flow battery based on a two-dimensional unit cell model

In this paper, we present a physics-informed neural network (PINN) approach for predicting the performance of an all-vanadium redox flow battery, with its physics constraints enforced by a two-dimensional (2D) mathematical model. The 2D model, which includes 6 governing equations and 24 boundary conditions, provides a detailed representation of the electrochemical reactions, mass transport and hydrodynamics occurring inside the redox flow battery. To solve the 2D model with the PINN approach, a composite neural network is employed to approximate species concentration and potentials; the input and output are normalized according to prior knowledge of the battery system; the governing equations and boundary conditions are first scaled to an order of magnitude around 1, and then further balanced with a self-weighting method. Our numerical results show that the PINN is able to predict cell voltage correctly, but the prediction of potentials shows a constant-like shift. To fix the shift, the PINN is enhanced by further constrains derived from the current collector boundary. Finally, we show that the enhanced PINN can be even further improved if a small number of labeled data is available.

25 ENERGY STORAGE↗
DOE OSTI2024

Solving the Orszag–Tang vortex magnetohydrodynamics problem with physics-constrained convolutional neural networks

We study the 2D Orszag–Tang vortex magnetohydrodynamics (MHD) problem through the use of physics-constrained convolutional neural networks (PCNNs) for forecasting the density, ρ, and the magnetic field, B, as well as the prediction of B given the velocity field v of the fluid. In addition to translation equivariance from the convolutional architecture, other physics constraints were embedded: absence of magnetic monopoles, non-negativity of ρ, use of only relevant variables, and the periodic boundary conditions of the problem. The use of only relevant variables and the hard constraint of non-negative ρ were found to facilitate learning greatly. The divergenceless condition ∇·B=0 was implemented as a hard constraint up to machine precision through the use of a magnetic potential to define B=∇×A. Residual networks and data augmentation were also used to improve performance. This allowed for some of the residual models to function as surrogate models and provide reasonably accurate simulations. For the prediction task, the PCNNs were evaluated against a physics-informed neural network, which had the ideal MHD induction equation as a soft constraint. Several models were able to generate highly accurate fields, which are visually almost indistinguishable and have low mean squared error. Only methods with built-in hard constraints produced physical fields with ∇·B=0. The use of PCNNs for MHD has the potential to produce physically consistent real-time simulations to serve as virtual diagnostics in cases where inferences must be made with limited observables.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

An adaptive and stability-promoting layerwise training approach for sparse deep neural network architecture

This work presents a two-stage adaptive framework for progressively developing deep neural network (DNN) architectures that generalize well for a given training data set. In the first stage, a layerwise training approach is adopted where a new layer is added each time and trained independently by freezing parameters in the previous layers. We impose desirable structures on the DNN by employing manifold regularization, sparsity regularization, and physics-informed terms. We introduce a ε – δ – stability-promoting concept as a desirable property for a learning algorithm and show that employing manifold regularization yields a ε – δ stability-promoting algorithm. Further, we also derive the necessary conditions for the trainability of a newly added layer and investigate the training saturation problem. In the second stage of the algorithm (post-processing), a sequence of shallow networks is employed to extract information from the residual produced in the first stage, thereby improving the prediction accuracy. Numerical investigations on prototype regression and classification problems demonstrate that the proposed approach can outperform fully connected DNNs of the same size. Moreover, by equipping the physics-informed neural network (PINN) with the proposed adaptive architecture strategy to solve partial differential equations, we numerically show that adaptive PINNs not only are superior to standard PINNs but also produce interpretable hidden layers with provable stability. As a result, we also apply our architecture design strategy to solve inverse problems governed by elliptic partial differential equations.

42 ENGINEERING↗
DOE OSTI2024

A physics-informed deep learning description of Knudsen layer reactivity reduction

A physics-informed neural network (PINN) is used to evaluate the fast ion distribution in the hot spot of an inertial confinement fusion target. The use of tailored input and output layers to the neural network is shown to enable a PINN to learn the parametric solution to the Vlasov–Fokker–Planck equation in the absence of any synthetic or experimental data. As an explicit demonstration of the approach, the specific problem of Knudsen layer fusion yield reduction is treated. Here, the predictions from the Vlasov–Fokker–Planck PINN are used to provide a non-perturbative solution of the fast ion tail in the vicinity of the hot spot, thus allowing the spatial profile of the fusion reactivity to be evaluated for a range of collisionalities and hot spot conditions. Excellent agreement is found between the predictions of the Vlasov–Fokker–Planck PINN and the results from traditional numerical solvers with respect to both the energy and spatial distribution of fast ions and the fusion reactivity profile, demonstrating that the Vlasov–Fokker–Planck PINN provides an accurate and efficient means of determining the impact of Knudsen layer yield reduction across a broad range of plasma conditions.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2026

Precise Modeling of a Complex Solenoidal Magnetic Field Using a Combination of Analytic Functions and a PINN

We demonstrate an iterative approach to modeling a sparsely measured magnetic field in a large-bore solenoid. This approach uses a hybrid of traditional and machine learning techniques. The traditional technique is a linear least-squares fit using a series solution to Laplace's equation, while the machine learning technique involves the training of a physics-informed neural network (PINN) on the least-squares fit residuals. We use a newly defined activation function "DELTAsnake," a modification to the snake activation function proposed by Ziyin et al. that allows for stronger curvature and non-monotonicity. The combined model approximately obeys Maxwell's equations to a level sufficient for producing high quality physics simulations and analysis. Our approach is applied to a highly realistic calculation of the expected magnetic field in the Mu2e experiment's Detector Solenoid which includes a simple model for the expected statistical measurement uncertainties. Using ten toy measurement simulations, we demonstrate the capabilities of our model in comparison to the least-squares method alone; the least-squares method alone results in a reduced chi-squared statistic of ${2.15 \pm 0.01}$, while our approach improves the reduced chi-square to ${1.034 \pm 0.005}$. Furthermore, for an average toy simulation, we show that the range of the RMS of the three field component residuals reduces from ${0.07-0.37}$ Gauss to ${0.05-0.07}$ Gauss. We find that this novel method is robust against a realistic systematic uncertainty deriving from Hall probe calibration bias and can be used to significantly reduce the number of measurements required to achieve an accurate model.

Kampa, Cole [Caltech] (ORCID:0000000192972920)↗
DOE OSTI2023

Data-driven prediction of the output composition of an atmospheric pressure plasma jet

Cold atmospheric plasma (CAP) in open air hosts numerous chemical species engaged in thousands of chemical reactions. Comprehensive diagnosis of its chemical composition is important across various fields from medicine, where reactive oxygen and nitrogen play key roles, to surface modification. In applications, a centimeter-scale helium–air jet operates for minutes, featuring micrometer-sized streamers and an atmospheric pressure-induced collision frequency in the hundreds of GHz range. To address this intricate multi-scale issue, we introduce a machine learning approach: using a physics-informed neural network (PINN) to tackle the multi-scale complexities inherent in predicting the complete list of species concentrations, gas temperature, and electron temperature of a CAP jet supplied with a mixture of helium and air. Experimental measurements of O 3 , N 2 O, and NO 2 concentrations downstream of the plasma jet, combined with fundamental physics laws, the conservation of mass and charge, constrain the PINN, enabling it to predict the concentrations of all species that are not available from the experiment, along with gas and electron temperatures. The results, therefore, obey all the physical laws we provided and can have a chemical balance with the measured concentrations. In conclusion, this methodology holds promise for describing and potentially regulating complex systems with limited experimental datasets.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Physics-Informed Machine Learning for Epidemiological Models

One challenge of using compartmental SEIR models for public health planning is the difficulty in manually tuning parameters to capture behavior reflected in the real-world data. This team conducted initial, exploratory analysis of a novel technique to use physics-informed machine learning tools to rapidly develop data-driven models for physical systems. This machine learning approach may be used to perform data assimilation of compartment models which account for unknown interactions between geospatial domains (i.e. diffusion processes coupling across neighborhoods/counties/states/etc.). Results presented here are early, proof-of-concept ideas that demonstrate initial success in using a physically informed neural network (PINN) model to assimilate data in a compartmental epidemiology model. The results demonstrate initial success and warrant further research and development.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

LossLens: Diagnostics for Machine Learning Through Loss Landscape Visual Analytics

Modern machine learning often relies on optimizing a neural network's parameters using a loss function to learn complex features. Beyond training, examining the loss function with respect to a network's parameters (i.e., as a loss landscape) can reveal insights into the architecture and learning process. While the local structure of the loss landscape surrounding an individual solution can be characterized using a variety of approaches, the global structure of a loss landscape, which includes potentially many local minima corresponding to different solutions, remains far more difficult to conceptualize and visualize. To address this difficulty, we introduce LossLens, a visual analytics framework that explores loss landscapes at multiple scales. LossLens integrates metrics from global and local scales into a comprehensive visual representation, enhancing model diagnostics. Here we demonstrate LossLens through two case studies: visualizing how residual connections influence a ResNet-20, and visualizing how physical parameters influence a physics-informed neural network (PINN) solving a simple convection problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

EFIT‐AI: Machine Learning and Artificial Intelligence Assisted Equilibrium Reconstruction for Tokamak Experiments and Burning Plasmas (Final Report)

The EFIT-AI project is creating a modern advanced equilibrium reconstruction code suitable for tokamak experiments of burning plasmas. EFIT [1,2] was the first and is the most extensively used equilibrium reconstruction code in the world. This project builds on the production-level experience and adds key elements as follows. 1. A Model Order Reduction (MOR) version of the two-dimensional (2D) Grad-Shafranov equation solver (EFIT-MORNN) using physics-informed neural networks. 2. Improved optimization and data analysis capabilities using a Bayesian framework enhanced with machine learning. 3. A MOR version of the three-dimensional (3D) perturbed equilibrium reconstruction tool.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

NeuroSEM: A hybrid framework for simulating multiphysics problems by coupling PINNs and spectral elements

Multiphysics problems that are characterized by complex interactions among fluid dynamics, heat transfer, structural mechanics, and electromagnetics, are inherently challenging due to their coupled nature. While experimental data on certain state variables may be available, integrating these data with numerical solvers remains a significant challenge. Physics-informed neural networks (PINNs) have shown promising results in various engineering disciplines, particularly in handling noisy data and solving inverse problems in partial differential equations (PDEs). However, their effectiveness in forecasting nonlinear phenomena in multiphysics regimes, particularly involving turbulence, is yet to be fully established. Here, this study introduces NeuroSEM, a hybrid framework integrating PINNs with the highfidelity Spectral Element Method (SEM) solver, Nektar++. NeuroSEM leverages the strengths of both PINNs and SEM, providing robust solutions for multiphysics problems. PINNs are trained to assimilate data and model physical phenomena in specific subdomains, which are then integrated into the Nektar++ solver. We demonstrate the efficiency and accuracy of NeuroSEM for thermal convection in cavity flow and flow past a cylinder. The framework effectively handles data assimilation by addressing those subdomains and state variables where the data is available. We applied NeuroSEM to the Rayleigh-B´enard convection system, including cases with missing thermal boundary conditions and noisy datasets. Finally, we applied the proposed NeuroSEM framework to real particle image velocimetry (PIV) data to capture flow patterns characterized by horseshoe vortical structures. Our results indicate that NeuroSEM accurately models the physical phenomena and assimilates the data within the specified subdomains. The framework’s plug-and-play nature facilitates its extension to other multiphysics or multiscale problems. Furthermore, NeuroSEM is optimized for efficient execution on emerging integrated GPU-CPU architectures. This hybrid approach enhances the accuracy and efficiency of simulations, making it a powerful tool for tackling complex engineering challenges in various scientific domains.

42 ENGINEERING↗
DOE OSTI2026

Leveraging Inequality-Constrained Data for Enhanced Liquidus Temperature Prediction in Nuclear Waste Glass Melts

Inequality-constrained data are frequently discarded in engineering, leading to significant information loss in data-scarce domains like glass characterization in nuclear waste vitrification. This paper presents a nonparametric censored-data regression framework based on an l1-norm optimization criterion that leverages slack variables to integrate left-, right-, and interval-constrained observations into training without distributional assumptions. Validated on synthetic data and a Physics-Informed Neural Network (PINN) for predicting liquidus temperature (TL), the method improved R2 from 0.60 to 0.89 and reduced Mean Absolute Error (MAE) by 48% (51.46 to 26.89?rC) on deterministic values. The traditional models failed to satisfy any inequality constraints while the proposed l1-norm PINN satisfies 81.25% of the constraints. The proposed framework effectively extracts actionable information from previously unusable data to enhance predictive accuracy, reduce epistemic uncertainty, and ensure physical consistency in complex industrial applications.

Garcia-Morado, Erick↗
DOE OSTI2026

Optimization techniques in self-similar compressible flow

We investigate the one-dimensional (1D) inviscid compressible flow equations for an ideal gas through the lens of optimization techniques. It is the case that, to our knowledge, optimization analysis applied to the so-called “linear velocity” solutions of the Euler compressible flow equations has not been previously conducted. Through both gradient-based and variational techniques, new variants of well-studied flow scenarios, i.e., self-similar, 1D, linear velocity solution class to idealized inviscid compressible flow equations, are determined, as encoded in both the kinematic and thermodynamic properties of this self-similar solution class. With the kinematics of the said solutions being driven by a self-similar “scale radius” and the thermodynamics being driven separately through the appearance of an arbitrary function, a myriad of new solution classes is possible. Acting as a guide to more realistic physical circumstances as well as discovery, it is the hope that the presented cases serve as the framework for future investigations into the intersection of self-similarity and optimization techniques. Fields of study that may find this work to be of interest include aerodynamic design, flow control, inertial confinement fusion, physics-informed neural networks, and other related areas of interest.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗