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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 487 records · Page 27
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

Explicit physics-informed neural networks for nonlinear closure: The case of transport in tissues

In upscaling methods, closures for nonlinear problems present a well-known challenge. While a number of theoretical methods have been proposed for handling such closures, nonlinearities still remain a significant obstacle for many problems. In this work, we use a combination of formal upscaling and data-driven machine learning for explicitly closing a nonlinear transport and reaction process in multiscale tissues. The classical effectiveness factor model is used to formulate the macroscale reaction kinetics. We train a multilayer perceptron network using training data generated by direct numerical simulations over microscale examples. Once trained, the network is used in an algorithm for numerically solving the upscaled (coarse-grained) differential equation describing mass transport and reaction in two example tissues. The network is described as being explicit in the sense that the network is trained using macroscale concentrations and gradients of concentration as components of the feature space rather than incorporating them as part of a constraint in the optimization process. Network training and solutions to the macroscale transport equations were computed for two different tissues. The two tissue types (brain and liver) exhibit markedly different geometrical complexity and spatial scale (cell size and sample size). The upscaled solutions for the average concentration are compared with numerical solutions derived from the microscale concentration fields by a posteriori averaging. There are three outcomes of this work of particular note. 1) Our overall approach results in an upscaled nonlinear PDE. The PDE is closed using a neural network, and our approach results in the definition of the classical effectiveness factor for effecting closure. 2) We identify particular source terms for the closure problem that are important for representing the structure of the closure. These source terms involve macroscale concentrations and their gradients. We adopt these source terms to use as explicit features in the learning algorithm. We find the trained networks that include the macroscale source terms generate models that are able to predict the correction factor with increased fidelity over those that do not. 3) We find that the trained network exhibits good generalizability, and it is able to predict the effectiveness factor with high fidelity for realistically-structured tissues despite the significantly different scale and geometrical complexity of the two example tissue types. This latter result emphasizes our purposeful connection between conventional averaging methods with the use of machine learning for closure; this contrasts with some machine learning methods for upscaling where the exact form of the macroscale equation remains unknown.

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↗
NASA NTRS1993

Adaptive fuzzy system for 3-D vision

An adaptive fuzzy system using the concept of the Adaptive Resonance Theory (ART) type neural network architecture and incorporating fuzzy c-means (FCM) system equations for reclassification of cluster centers was developed. The Adaptive Fuzzy Leader Clustering (AFLC) architecture is a hybrid neural-fuzzy system which learns on-line in a stable and efficient manner. The system uses a control structure similar to that found in the Adaptive Resonance Theory (ART-1) network to identify the cluster centers initially. The initial classification of an input takes place in a two stage process; a simple competitive stage and a distance metric comparison stage. The cluster prototypes are then incrementally updated by relocating the centroid positions from Fuzzy c-Means (FCM) system equations for the centroids and the membership values. The operational characteristics of AFLC and the critical parameters involved in its operation are discussed. The performance of the AFLC algorithm is presented through application of the algorithm to the Anderson Iris data, and laser-luminescent fingerprint image data. The AFLC algorithm successfully classifies features extracted from real data, discrete or continuous, indicating the potential strength of this new clustering algorithm in analyzing complex data sets. The hybrid neuro-fuzzy AFLC algorithm will enhance analysis of a number of difficult recognition and control problems involved with Tethered Satellite Systems and on-orbit space shuttle attitude controller.

Mitra, Sunanda↗
DOE OSTI2025

Learning and discovering multiple solutions using physics-informed neural networks with random initialization and deep ensemble

In this work we explore the capability of physics-informed neural networks (PINNs) to discover multiple solutions. Many real-world phenomena governed by nonlinear differential equations (DEs), such as fluid flow, exhibit multiple solutions under the same conditions, yet capturing this solution multiplicity remains a significant challenge. A key difficulty lies in providing appropriate initial conditions or guesses, as widely used time-marching schemes and Newton’s method are highly sensitive to these choices when solving complex computational problems. While machine learning models, particularly PINNs, have shown promise in solving DEs, their ability to capture multiple solutions remains underexplored. In this work, we propose a simple and practical approach using PINNs to learn and discover multiple solutions. We first demonstrate that PINNs, when combined with random initialization and deep ensemble method—originally developed for uncertainty quantification—can effectively uncover multiple solutions to nonlinear ordinary and partial DEs. Although training large ensembles of PINNs may appear computationally demanding, this can be done efficiently using vectorization techniques supported by modern deep learning frameworks, allowing many networks to be trained simultaneously. Our approach highlights the critical role of initialization in shaping solution diversity, addressing an often-overlooked aspect of machine learning for scientific computing. Furthermore, we propose utilizing PINN-generated solutions as initial conditions or initial guesses for conventional numerical solvers to enhance accuracy and efficiency in capturing multiple solutions. Extensive numerical experiments, including the Allen–Cahn equation and cavity flow, where our approach successfully identifies both stable and unstable solutions, validate the effectiveness of our method. These findings establish a general and efficient framework for addressing solution multiplicity in nonlinear DEs.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1992

Discrete time learning control in nonlinear systems

In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.

Longman, Richard W.↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
DOE OSTI2021

Landsat 8 monitoring of multi-depth suspended sediment concentrations in Lake Erie’s Maumee River using machine learning

Satellite remote sensing has been widely used to map suspended sediment concentration (SSC) in waterbodies. However, due to the complexity of sediment-water interactions, it has been difficult to derive linear and non-linear regression equations to reliably predict SSC, especially when trying to estimate depth of integrated sediment. Herein, this study uses Landsat 8 OLI (Operational Land Imager) sensor to map SSC within the Maumee River in Ohio, USA, at multiple depth intervals (15, 61, 91, and 182 cm). Simple linear least squares regression (LLSR), and three common machine learning models: random forest (RF), support vector regression (SVR), and model averaged neural network (MANN) were used to estimate SSC at the depth intervals. All machine learning models significantly outperformed LLSR while RF performed the best. In both RF and MANN, R2 (coefficient of determination) increases with depth with a maximum R2 of 0.89 and 0.83, respectively, at a depth of 0–182 cm. The results show that machine learning models can implement nonlinear relationships that produce better predictions than traditional linear regression methods in estimating depth integrated SSC, especially when samples are limited.

47 OTHER INSTRUMENTATION↗
DOE OSTI2025

Neural Active Manifolds: Nonlinear Dimensionality Reduction for Uncertainty Quantification

We present a new approach for nonlinear dimensionality reduction, specifically designed for computationally expensive mathematical models. We leverage autoencoders to discover a one-dimensional neural active manifold (NeurAM) capturing the model output variability, through the aid of a simultaneously learnt surrogate model with inputs on this manifold. Our method only relies on model evaluations and does not require the knowledge of gradients. The proposed dimensionality reduction framework can then be applied to assist outer loop many-query tasks in scientific computing, like sensitivity analysis and multifidelity uncertainty propagation. In particular, we prove, both theoretically under idealized conditions, and numerically in challenging test cases, how NeurAM can be used to obtain multifidelity sampling estimators with reduced variance by sampling the models on the discovered low-dimensional and shared manifold among models. Several numerical examples illustrate the main features of the proposed dimensionality reduction strategy and highlight its advantages with respect to existing approaches in the literature.

Autoencoders↗
DOE OSTI2022

Vapor–liquid equilibrium estimation of n-alkane/nitrogen mixtures using neural networks

Understanding fluid phase behavior, like VLE, in high P&T conditions is crucial for developing high-fidelity simulations of chemically reacting flows in liquid-fueled combustion systems and also forms an integral part of the design-modeling of the control processes in chemical industries. Two data-driven models have been proposed here in this study, each of which was competent in estimating VLE for the Type III binary systems of C 10 /N 2 and C 12 /N 2 , at pressures ranging up to 50–60 MPa. Both models showed better performance in predicting equilibrium pressure as compared to VLE modeled using PR-EOS. A modified model has also been proposed, capable of estimating the full phase envelope for the binary systems of C 10 /N 2 and C 12 /N 2 across a wide range of temperatures, and thus exhibit the mixture critical pressure at the concerned temperature. The diverse applicability of the proposed network architecture was further exhibited while estimating the VLE of a ternary system of C 1 /C 10 /N 2 .

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Nonlinear proper orthogonal decomposition for convection-dominated flows

Autoencoder techniques find increasingly common use in reduced order modeling as a means to create a latent space. This reduced order representation offers a modular data-driven modeling approach for nonlinear dynamical systems when integrated with a time series predictive model. In this Letter, we put forth a nonlinear proper orthogonal decomposition (POD) framework, which is an end-to-end Galerkin-free model combining autoencoders with long short-term memory networks for dynamics. By eliminating the projection error due to the truncation of Galerkin models, a key enabler of the proposed nonintrusive approach is the kinematic construction of a nonlinear mapping between the full-rank expansion of the POD coefficients and the latent space where the dynamics evolve. We test our framework for model reduction of a convection-dominated system, which is generally challenging for reduced order models. Our approach not only improves the accuracy, but also significantly reduces the computational cost of training and testing.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Diffusion-Model-Assisted Supervised Learning of Generative Models for Density Estimation

Here, we present a supervised learning framework of training generative models for density estimation. Generative models, including generative adversarial networks (GANs), normalizing flows, and variational auto-encoders (VAEs), are usually considered as unsupervised learning models, because labeled data are usually unavailable for training. Despite the success of the generative models, there are several issues with the unsupervised training, e.g., requirement of reversible architectures, vanishing gradients, and training instability. To enable supervised learning in generative models, we utilize the score-based diffusion model to generate labeled data. Unlike existing diffusion models that train neural networks to learn the score function, we develop a training-free score estimation method. This approach uses mini-batch-based Monte Carlo estimators to directly approximate the score function at any spatial-temporal location in solving an ordinary differential equation (ODE), corresponding to the reverse-time stochastic differential equation (SDE). This approach can offer both high accuracy and substantial time savings in neural network training. Once the labeled data are generated, we can train a simple, fully connected neural network to learn the generative model in the supervised manner. Compared with existing normalizing flow models, our method does not require the use of reversible neural networks and avoids the computation of the Jacobian matrix. Compared with existing diffusion models, our method does not need to solve the reverse-time SDE to generate new samples. As a result, the sampling efficiency is significantly improved. We demonstrate the performance of our method by applying it to a set of 2D datasets as well as real data from the University of California Irvine (UCI) repository.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Simple, low-cost and accurate data-driven geophysical forecasting with learned kernels

Modelling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison with classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North American continent, we observe significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.

58 GEOSCIENCES↗
DOE OSTI2020

Deep learning of free boundary and Stefan problems

Free boundary problems appear naturally in numerous areas of mathematics, science and engineering. These problems present a great computational challenge because they necessitate numerical methods that can yield an accurate approximation of free boundaries and complex dynamic interfaces. In this work, we propose a multi-network model based on physics-informed neural networks to tackle a general class of forward and inverse free boundary problems called Stefan problems. Specifically, we approximate the unknown solution as well as any moving boundaries by two deep neural networks. Besides, we formulate a new type of inverse Stefan problems that aim to reconstruct the solution and free boundaries directly from sparse and noisy measurements. We demonstrate the effectiveness of our approach in a series of benchmarks spanning different types of Stefan problems, and illustrate how the proposed framework can accurately recover solutions of partial differential equations with moving boundaries and dynamic interfaces. All code and data accompanying this manuscript are publicly available at https://github.com/PredictiveIntelligenceLab/DeepStefan.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Comparison of Machine Learning Approaches for Prediction of the Equivalent Alkane Carbon Number for Microemulsions Based on Molecular Properties

The chemical properties of oils are vital in the design of microemulsion systems. The hydrophilic–lipophilic difference equation used to predict microemulsions’ phase behavior expresses the oils’ physiochemical properties as the equivalent alkane carbon number (EACN). The experimental determination of EACN requires knowledge of the temperature dependence of the microemulsion system and the effects of different surfactant concentrations. Thus, the experimental determination is time-intensive and tedious, requiring days to months for proper separations. Furthermore, the experiments require high purity of chemicals because microemulsions are sensitive to impurities. Our work focuses on the quick and reliable predictions of the EACN with machine learning (ML) models. Due to the immaturity of ML chemical predictions, we compare three graph neural networks (GNNs) and a gradient-boosted tree algorithm, known as XGBoost. The GNNs use the molecular structures represented as simplified molecular-input line-entry system (SMILES) codes for the initial input, which allows us to assess whether geometry optimization is necessary for reliable results. The XGBoost model also begins with the SMILES representations of the molecules but uses molecular descriptors instead of geometry optimizations. As a result, the best model tested (crystal graph convolutional neural network with Merck molecular force field-94) has an error of 1.15 EACN units of the true EACN for unknown data with the errors skewed toward zero and an R² score of 0.9

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Physics-informed hybrid modeling methodology for building infiltration

Infiltration is responsible for one-third to one-half of the space conditioning load of a typical residential home, but the modeling of infiltration for building energy modeling is either represented by over-simplified equations or dependent on over-generalized rules of thumb. Here, this paper develops a physics-informed data-driven methodology for modeling infiltration using building-specific empirical measurements. The developed hybrid methodology combines machine-learning categorization and grey-box sub-modeling to improve the accuracy and generalization of commonly used grey-box infiltration models. The developed methodology excels at predicting infiltration by improving the ability to predict infiltration under unseen environmental conditions using machine learning algorithms with physical significance. In a case study conducted using the iUnit, a modular studio apartment experimental test facility located at the National Renewable Energy Laboratory, we use empirical airtightness measurements to fit an infiltration model using the developed methodology. We find that the developed methodology can improve the overall model accuracy by 43% and improve extrapolation by 38%, compared with the model based on the common grey-box infiltration equation. We also notice that the selected features can improve the performance of a pure machine-learning model, indicating that our methodology identifies the features with the most physical significance to infiltration modeling.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A methodology for decay heat characterization in molten salt reactors

Accurate decay heat prediction in molten salt reactors (MSRs) faces dual challenges: complex operational uncertainties and the need for interpretable models compatible with engineering workflows. This work presents a hybrid machine learning and segmented polynomial methodology that addresses both requirements through three key innovations. First, a modular data architecture encodes MSR-specific operational parameters (power density: 1-100 W cm -3 , humidity: 0-0.1 wt %, air ingress: 0-0.1 mol %) with uncertainty-aware temporal discretization spanning 15 orders of magnitude. Second, region-optimized machine learning models achieve 92.3 % root mean square error (RMSE) reduction over conventional polynomials while maintaining physical interpretability through automated piecewise equation generation. Third, dual front-end interfaces accelerate safety analyses — a Jupyter environment enables researchers to explore 10,000+ parameter combinations via interactive widgets, while a Streamlit web application reduces design iteration cycles through production-grade visualization tools. Operational deployment demonstrates prediction times of only a couple hundred milliseconds for 10 4 years decay profiles, enabling real-time optimization of spent fuel container designs.

42 - ENGINEERING↗
DOE OSTI2024

A Novel Method to Train Classification Models for Structure Detection in In Situ Spacecraft Data

We present a method for creating spacecraft-like data which can be used to train Machine Learning (ML) models to detect and classify structures in in situ spacecraft data. First, we use the Grad-Shafranov equation to numerically solve for several magnetohydrostatic equilibria which are variations on a known analytic equilibrium. These equilibria are then used as the initial conditions for Particle-In-Cell simulations in which the structures of interest are observed and labeled. We then take one-dimensional slices through the simulations to replicate what a spacecraft collecting data from the simulation would observe. This sliced data then can be used as training data for the initial training of ML models intended for use on spacecraft data. We demonstrate the method applied to the problem of detecting small-scale plasmoids in the magnetotail, which is important for understanding complex magnetotail reconnection dynamics. The simple 1D classifier we train is able to detect more than 70% of the plasmoid points in the data set but also produces a large number of false positives. Our further work on this example problem is detailed, and further potential uses of the method are discussed.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2020

Physics-guided Deep Learning for Power System State Estimation

In the past decade, dramatic progress has been made in the field of machine learning. This paper explores the possibility of applying deep learning in power system state estimation. Traditionally, physics-based models are used including weighted least square (WLS) or weighted least absolute value (WLAV). These models typically consider a single snapshot of the system without capturing temporal correlations of system states. In this paper, a physics-guided deep learning (PGDL) method is proposed. Specifically, inspired by autoencoders, deep neural networks (DNNs) are used to learn the temporal correlations. The estimated system states from DNNs are then checked against physics laws by running through a set of power flow equations. Hence, the proposed PGDL is both data-driven and physics-guided. The accuracy and robustness of the proposed PGDL method are compared with traditional methods in standard IEEE cases. Simulations show promising results and the applicability is further discussed.

24 POWER TRANSMISSION AND DISTRIBUTION↗