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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 19 records
All sourcesNASA NTRSDOE OSTI
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↗
DOE OSTI2025

A framework to evaluate machine learning crystal stability predictions

The rapid adoption of machine learning in various scientific domains calls for the development of best practices and community agreed-upon benchmarking tasks and metrics. We present Matbench Discovery as an example evaluation framework for machine learning energy models, here applied as pre-filters to first-principles computed data in a high-throughput search for stable inorganic crystals. We address the disconnect between (1) thermodynamic stability and formation energy and (2) retrospective and prospective benchmarking for materials discovery. Alongside this paper, we publish a Python package to aid with future model submissions and a growing online leaderboard with adaptive user-defined weighting of various performance metrics allowing researchers to prioritize the metrics they value most. To answer the question of which machine learning methodology performs best at materials discovery, our initial release includes random forests, graph neural networks, one-shot predictors, iterative Bayesian optimizers and universal interatomic potentials. We highlight a misalignment between commonly used regression metrics and more task-relevant classification metrics for materials discovery. Accurate regressors are susceptible to unexpectedly high false-positive rates if those accurate predictions lie close to the decision boundary at 0 eV per atom above the convex hull. The benchmark results demonstrate that universal interatomic potentials have advanced sufficiently to effectively and cheaply pre-screen thermodynamic stable hypothetical materials in future expansions of high-throughput materials databases.

Riebesell, Janosh↗
NASA NTRS2020

Genetic Algorithm for Optimization of Neural Networks for Bayesian Inference of Model Uncertainty

The objective of this work was to develop a genetic optimization algorithm that can design a neural network capable of producing uncertainty estimates along with predictions. This algorithm is necessary because the inclusion of uncertainty modeling in a neural network greatly complicates the network’s design space, making the development of a converging model extremely difficult and time consuming. The genetic algorithm presented in this work uses a number of value ranges for various configurable neural network parameters to create a randomly generated population of network architectures. The initially generated population is then evolved over the course of several generations, with the best performing models breeding to produce novel network configurations. Mutations are randomly applied to the network designs to facilitate the development of adaptations beneficial to the task being performed. An experiment was conducted to validate the proposed algorithm, in which the genetic optimizer was tasked with producing a neural network capable of predicting the sound pressure level (SPL) resulting from jet-surface interaction (JSI) noise. The data used for this task was generated at the NASA Glenn Research Center in the Aero-Acoustic Propulsion Laboratory. Starting with an initial population size of 35 randomly generated networks, and evolved over the course of 10 generations, the genetic algorithm produced a design able to predict SPL as a result of JSI noise within 0.272 dB, on average.

Genetic algorithm↗
DOE OSTI2025

Ensemble cure kinetics network (ECK-Net): A method to derive cure kinetics of thermosetting resin

This paper introduces an Ensemble Cure Kinetics Network (ECK-Net), a neural network (NN)–based framework for modeling the cure kinetics of thermosetting resins within a phenomenological context. ECK-Net replaces traditional analytic models, which require extensive chemical insight and multiple isothermal/non-isothermal experiments, with a data-driven surrogate that maps nonlinear relationships between temperature, degree of cure, and reaction rate from differential scanning calorimetry data. The proposed approach predicts input-dependent kinetic coefficients of a generalized nth-order reaction equation rather than reaction rates directly, enabling a single unified model to represent various epoxy systems without relying on iso-conversional analysis or predefined functional forms. To ensure robustness, multiple independently trained networks under different random initializations are blended through an ensemble strategy, effectively mitigating the stochastic variability inherent to neural networks. The framework is validated using experimental datasets from multiple resin systems, including aerospace-grade materials (Toray 3900-2, Cycom 5320-1, and Hexcel 8552) and a windmill-grade resin (RIMR 035c). The model accurately reproduces the temporal evolution of the degree of cure under manufacturers’ recommended cure cycles across all tested resins systems, yielding Pearson’s correlation coefficients of 0.992, 0.994, 0.993, 0.997, respectively. To demonstrate process-level applicability, the trained network was implemented within the Abaqus environment to simulate out-of-autoclave (OOA) curing process of the CFRP panel composed of Toray T830H-6K/3900-2D prepreg. The simulation results showed excellent agreement with experimental temperature response (maximum peak temperature, simulation: 189.6 °C, experiment: 188.5 °C) and the final degree of cure (simulation: 0.948, experiment: 0.960 ± 0.013), confirming ECK-Net’s capability as a reliable alternative to conventional cure kinetics modeling methods.

Composite curing↗
DOE OSTI2025

Testing convolutional neural network based deep learning systems: a statistical metamorphic approach

Machine learning technology spans many areas and today plays a significant role in addressing a wide range of problems in critical domains,i.e., healthcare, autonomous driving, finance, manufacturing, cybersecurity,etc. Metamorphic testing (MT) is considered a simple but very powerful approach in testing such computationally complex systems for which either an oracle is not available or is available but difficult to apply. Conventional metamorphic testing techniques have certain limitations in verifying deep learning-based models (i.e., convolutional neural networks (CNNs)) that have a stochastic nature (because of randomly initializing the network weights) in their training. In this article, we attempt to address this problem by using a statistical metamorphic testing (SMT) technique that does not require software testers to worry about fixing the random seeds (to get deterministic results) to verify the metamorphic relations (MRs). We propose seven MRs combined with different statistical methods to statistically verify whether the program under test adheres to the relation(s) specified in the MR(s). We further use mutation testing techniques to show the usefulness of the proposed approach in the healthcare space and test two CNN-based deep learning models (used for pneumonia detection among patients). The empirical results show that our proposed approach uncovers 85.71% of the implementation faults in the classifiers under test (CUT). Furthermore, we also propose an MRs minimization algorithm for the CUT, thus saving computational costs and organizational testing resources.

Computer Science↗
NASA NTRS1988

How to cluster in parallel with neural networks

Partitioning a set of N patterns in a d-dimensional metric space into K clusters - in a way that those in a given cluster are more similar to each other than the rest - is a problem of interest in astrophysics, image analysis and other fields. As there are approximately K(N)/K (factorial) possible ways of partitioning the patterns among K clusters, finding the best solution is beyond exhaustive search when N is large. Researchers show that this problem can be formulated as an optimization problem for which very good, but not necessarily optimal solutions can be found by using a neural network. To do this the network must start from many randomly selected initial states. The network is simulated on the MPP (a 128 x 128 SIMD array machine), where researchers use the massive parallelism not only in solving the differential equations that govern the evolution of the network, but also by starting the network from many initial states at once, thus obtaining many solutions in one run. Researchers obtain speedups of two to three orders of magnitude over serial implementations and the promise through Analog VLSI implementations of speedups comensurate with human perceptual abilities.

Kamgar-Parsi, Behzad↗
NASA NTRS1993

A review and analysis of neural networks for classification of remotely sensed multispectral imagery

A literature survey and analysis of the use of neural networks for the classification of remotely sensed multispectral imagery is presented. As part of a brief mathematical review, the backpropagation algorithm, which is the most common method of training multi-layer networks, is discussed with an emphasis on its application to pattern recognition. The analysis is divided into five aspects of neural network classification: (1) input data preprocessing, structure, and encoding; (2) output encoding and extraction of classes; (3) network architecture, (4) training algorithms; and (5) comparisons to conventional classifiers. The advantages of the neural network method over traditional classifiers are its non-parametric nature, arbitrary decision boundary capabilities, easy adaptation to different types of data and input structures, fuzzy output values that can enhance classification, and good generalization for use with multiple images. The disadvantages of the method are slow training time, inconsistent results due to random initial weights, and the requirement of obscure initialization values (e.g., learning rate and hidden layer size). Possible techniques for ameliorating these problems are discussed. It is concluded that, although the neural network method has several unique capabilities, it will become a useful tool in remote sensing only if it is made faster, more predictable, and easier to use.

Paola, Justin D.↗
NASA NTRS1992

Neural networks for structural design - An integrated system implementation

The development of powerful automated procedures to aid the creative designer is becoming increasingly critical for complex design tasks. In the work described here Artificial Neural Nets are applied to acquire structural analysis and optimization domain expertise. Based on initial instructions from the user an automated procedure generates random instances of structural analysis and/or optimization 'experiences' that cover a desired domain. It extracts training patterns from the created instances, constructs and trains an appropriate network architecture and checks the accuracy of net predictions. The final product is a trained neural net that can estimate analysis and/or optimization results instantaneously.

Berke, Laszlo↗
DOE OSTI2026

Parallel-in-Time Solution of Allen-Cahn Equations by Integrating Operator Learning into the Parareal Method

While recent advances in deep learning have shown promising efficiency gains in solving time-dependent partial differential equations (PDEs), matching the accuracy of conventional numerical solvers still remains a challenge. One strategy to improve the accuracy of deep learning-based solutions for time-dependent PDEs is to use the learned model as the coarse propagator in the Parareal method and a traditional numerical method as the fine solver. However, successful integration of deep learning into the Parareal method requires consistency between the coarse and fine solvers, particularly for PDEs exhibiting rapid changes such as sharp transitions. Here, to ensure this consistency, we propose using convolutional neural networks (CNNs) to learn the fully discrete time-stepping operator defined by the same numerical scheme employed as the fine solver. We demonstrate the effectiveness of the proposed method in solving the classical and mass-conservative Allen–Cahn (AC) equations. Through iterative updates in the Parareal algorithm, our approach achieves a significant computational speedup compared to traditional fine solvers while converging to high-accuracy solutions. Our results highlight that the proposed hybrid Parareal algorithm effectively accelerates simulations, particularly when implemented on multiple GPUs, and converges to the desired accuracy in only a few iterations. Another advantage of our method is that the CNN model is trained on trajectory-based data generated from random initial conditions, such that the trained model can be used to solve the AC equations with various initial conditions without retraining. This work demonstrates the potential of integrating neural network methods into parallel-in-time frameworks for efficient and accurate simulations of time-dependent PDEs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

GrainGNN: A dynamic graph neural network for predicting 3D grain microstructure

We propose GrainGNN, a surrogate model for the evolution of polycrystalline grain structure under rapid solidification conditions in metal additive manufacturing. High fidelity simulations of solidification microstructures are typically performed using multicomponent partial differential equations (PDEs) with moving interfaces. The inherent randomness of the PDE initial conditions (grain seeds) necessitates ensemble simulations to predict microstructure statistics, e.g., grain size, aspect ratio, and crystallographic orientation. Here, currently such ensemble simulations are prohibitively expensive and surrogates are necessary.In GrainGNN, we use a dynamic graph to represent interface motion and topological changes due to grain coarsening. We use a reduced representation of the microstructure using hand-crafted features; we combine pattern finding and altering graph algorithms with two neural networks, a classifier (for topological changes) and a regressor (for interface motion). Both networks have an encoder-decoder architecture; the encoder has a multi-layer transformer long-short-term-memory architecture; the decoder is a single layer perceptron.We evaluate GrainGNN by comparing it to high-fidelity phase field simulations for in-distribution and out-of-distribution grain configurations for solidification under laser power bed fusion conditions. GrainGNN results in 80%–90% pointwise accuracy; and nearly identical distributions of scalar quantities of interest (QoI) between phase field and GrainGNN simulations compared using Kolmogorov-Smirnov test. GrainGNN's inference speedup (PyTorch on single x86 CPU) over a high-fidelity phase field simulation (CUDA on a single NVIDIA A100 GPU) is 150×–2000× for 100-initial grain problem. Further, using GrainGNN, we model the formation of 11,600 grains in 220 seconds on a single CPU core.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bayesian Optimized Deep Ensemble for Uncertainty Quantification of Deep Neural Networks: a System Safety Case Study on Sodium Fast Reactor Thermal Stratification Modeling

Deep neural networks (DNNs) are increasingly important to scientific computing and engineering system simulations. Accurate uncertainty quantification (UQ) for DNNs is critical in safety-sensitive engineering domains. Traditional Deep Ensemble (DE) methods, while easy to implement, frequently suffer from poorly calibrated uncertainty estimates and limited predictive accuracy due to reliance on fixed architectures with varied weight initializations. To address these issues, we introduce a workflow that combines Bayesian Optimization (BO) and DE. The workflow is modular, scalable, and integrates parallel BO initialized with Sobol sequences to individually optimize the hyperparameters of each ensemble member. This method enhances ensemble diversity, improves predictive accuracy, and provides reliable uncertainty estimates. We evaluate the proposed BODE approach in a sodium fast reactor thermal stratification modeling case study, where we used a densely connected convolutional neural network to predict turbulent viscosity during the reactor transient with consideration of data noise. We benchmark its performance against several optimization approaches, including baseline deep ensemble, evolutionary algorithm-optimized ensemble, ensemble formed via random search combined with greedy selection, and a BO ensemble using random initialization. Here, our results demonstrate superior performance of the developed BODE approach. In noise-free scenarios, BODE notably reduces incorrect aleatoric uncertainty and significantly enhances predictive accuracy. Under conditions of 5% and 10% Gaussian noise, BODE adaptively quantifies uncertainty proportional to data noise, achieving up to an 80% reduction in root mean square error compared to baseline methods and producing well-calibrated prediction intervals.

Bayesian optimization↗
NASA NTRS1991

From biological neural networks to thinking machines: Transitioning biological organizational principles to computer technology

The three-dimensional organization of the vestibular macula is under study by computer assisted reconstruction and simulation methods as a model for more complex neural systems. One goal of this research is to transition knowledge of biological neural network architecture and functioning to computer technology, to contribute to the development of thinking computers. Maculas are organized as weighted neural networks for parallel distributed processing of information. The network is characterized by non-linearity of its terminal/receptive fields. Wiring appears to develop through constrained randomness. A further property is the presence of two main circuits, highly channeled and distributed modifying, that are connected through feedforward-feedback collaterals and biasing subcircuit. Computer simulations demonstrate that differences in geometry of the feedback (afferent) collaterals affects the timing and the magnitude of voltage changes delivered to the spike initiation zone. Feedforward (efferent) collaterals act as voltage followers and likely inhibit neurons of the distributed modifying circuit. These results illustrate the importance of feedforward-feedback loops, of timing, and of inhibition in refining neural network output. They also suggest that it is the distributed modifying network that is most involved in adaptation, memory, and learning. Tests of macular adaptation, through hyper- and microgravitational studies, support this hypothesis since synapses in the distributed modifying circuit, but not the channeled circuit, are altered. Transitioning knowledge of biological systems to computer technology, however, remains problematical.

Ross, Muriel D.↗
DOE OSTI2025

Triangle Method for Dense ReLU Layers [SWR-25-72]

This software is an implementation of the methods for initializing and training neural networks to be more efficient per parameter, described more fully below and in the related publication: In theory, depth should make a ReLU network EXPONENTIALLY more efficient by enabling it to produce an exponential number of piecewise linear sections in its output. This reasoning is largely based on the work of mathematicians that have hand-constructed networks that make good use of depth. In practice however, even very deep ReLU networks that have been randomly initialized will behave identically to their shallow counterparts - missing an entire exponential dimension of efficiency. The triangle method is a first attempt at realizing the exponential potential of deep networks. Instead of randomly setting weights, we force pairs of neurons in each layer learn to build triangles (i.e. functions from [0,1] -> [0,1] that look like triangles). This is a very efficient pattern for generating lots of linear pieces because composing two triangular functions doubles the number of pieces with each composition. The triangle method is more than just a different initialization, it is a new paradigm of training. Instead of making direct updates to the matrix weights, we do an extra step of backpropagation to collect the derivatives of the loss function with respect to the shapes of the triangles, training them to tilt left or right. This process essentially holds the networks hand throughout the loss landscape and forces it to always use depth effectively by producing triangular shapes internally. This can produce several orders of magnitude of improvement on convex one-dimensional regression problems. Much more theoretical work is needed to realize its full potential beyond this context, but the implementation in this repository will still work in arbitrary numbers of dimensions. The file Triangle_Method.py is a generalized form of the method that will build each neuron its own custom 1-d convex activation function (with exponential efficiency). Example usage on one dimensional problems can be found in Example_Usage.ipynb and an example of using this in a real neural network can be found in Example_VGG16_CIFAR10.ipynb.

Milkert, Max [National Renewable Energy Laboratory↗
DOE OSTI2025

Towards robust surrogate models: Benchmarking machine learning approaches to expediting phase field simulations of brittle fracture

Data-driven approaches have the potential to make modeling complex, nonlinear physical phenomena significantly more computationally tractable. For example, computational modeling of fracture is a core challenge where machine learning techniques have the potential to provide a much needed speedup that would enable progress in areas such as multi-scale modeling and uncertainty quantification. Currently, phase field modeling (PFM) of fracture is one such approach that offers a convenient variational formulation to model crack nucleation, branching and propagation. To date, machine learning techniques have shown promise in approximating PFM simulations. While standard fracture benchmarks represent realistic scenarios frequently observed in practice, they typically do not provide sufficiently challenging tests for data-driven methods. Here, to address this gap, we introduce a challenging dataset based on PFM simulations designed to benchmark and advance ML methods for fracture modeling. This dataset includes three energy decomposition methods, two boundary conditions, and 1000 random initial crack configurations for a total of 6000 simulations. Each sample contains 100 time steps capturing the temporal evolution of the crack field. Alongside this dataset, we also implement and evaluate Physics Informed Neural Networks (PINN), Fourier Neural Operators (FNO), and UNet models as baselines, and explore the impact of ensembling strategies on prediction accuracy. With this combination of our dataset and baseline models drawn from the literature we aim to provide a standardized and challenging benchmark for evaluating machine learning approaches to solid mechanics. Our results highlight both the promise and limitations of popular current models, and demonstrate the utility of this dataset as a testbed for advancing machine learning in fracture mechanics research.

Benchmark dataset↗
NASA NTRS2026

Benchmarking Bayesian Optimization Frameworks and Acquisition Strategies for Materials Discovery and Autonomous Laboratories

Bayesian optimization (BO) can accelerate materials discovery by guiding expensive experiments toward the most promising processing conditions. We systematically compare five BO surrogate and framework combinations (Gaussian processes in Ax, Gaussian processes and Monte-Carlo neural networks in BayBE, random forests in Lolopy, and tree-structured Parzen (TPE) estimators in Hyperopt) on three benchmarks that mimic common materials design tasks (a discrete solid-electrolyte composition space, a hybrid discrete/continuous laminate-composite design problem solved with micromechanics modeling, and the continuous Ishigami analytic function which is a standard optimization benchmark). Each BO surrogate is paired with posterior mean, probability of improvement, and expected improvement acquisition functions and run for 100 trials from randomized initial samples with uniform random search providing a control. Across five random seeds per setting, BayBE’s Gaussian-process surrogate with expected improvement consistently reached ≥95 % of the known optimum in the fewest evaluations, while Lolopy’s random forest matched or exceeded GP performance on purely categorical or mixed spaces at a higher computational cost. Posterior mean alone often stagnated at local optima, underscoring the need for exploration, whereas probability and expected improvement balanced exploration and exploitation leading to better optimization in fewer trials. Execution times ranged from milliseconds for TPE to minutes for neural-network and random-forest surrogates. These results establish baseline expectations for BO in automated materials laboratories and highlight expected improvement with Gaussian processes as a reliable first choice, with random forests offering a strong alternative when categorical variables dominate. The benchmark suite and code are released to facilitate future surrogate, acquisition, and constraint-handling research in data-driven materials optimization.

Bayesian optimization↗
DOE OSTI2024

Zero-Power Analog Optical Processing

The motivation behind this research is the growing challenge of handling the massive amounts of data generated by modern imaging systems. Conventional digital image processing techniques are struggling to keep pace with the demands of high-resolution and high-speed imaging systems for remote sensing due to their high-power consumption and data storage requirements. We present a novel approach based on analog photonics to address this challenge. The proposed system utilizes a silicon-photonics-based image encoder positioned after image formation and initial optical-to-electrical conversion. The photonic encoder compresses image data using a passive disordered photonic structure to perform kernel-type random projections of the raw data. The compressed data is then processed by a back-end neural network, which reconstructs the original image with high fidelity (structural similarity exceeding 90%). Our proposed approach has the potential to compress images with ~ 1000X lower power consumption compared to digital approaches with data rates exceeding 1 terapixel/second.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Newton-Raphson AC Power Flow Convergence Based on Deep Learning Initialization and Homotopy Continuation

Power flow forms the basis of many power system studies. With the increased penetration of renewable energy, grid planners tend to perform multiple power flow simulations under various operating conditions and not just selected snapshots at peak or light load conditions. Getting a converged AC power flow (ACPF) case remains a significant challenge for grid planners especially in large power grid networks. This paper proposes a two-stage approach to improve Newton-Raphson ACPF convergence and was applied to a 6102 bus Electric Reliability Council of Texas (ERCOT) system. The first stage utilizes a deep learning-based initializer with data re-training. Here a deep neural network (DNN) initializer is developed to provide better initial voltage magnitude and angle guesses to aid in power flow convergence. This is because Newton-Raphson ACPF is quite sensitive to the initial conditions and bad initialization could lead to divergence. The DNN initializer includes a data re-training framework that improves the initializer's performance when faced with limited training data. The DNN initializer successfully solved 3,285 cases out of 3,899 non-converging dispatch and performed better than random forest and DC power flow initialization methods. ACPF cases not solved in this first stage are then passed through a hot-starting algorithm based on homotopy continuation with switched shunt control. The hot-starting algorithm successfully converged 416 cases out of the remaining 614 non-converging ACPF dispatch. In conclusion, the combined two-stage approach achieved a 94.9% success rate, by converging a total of 3,701 cases out of the initial 3,899 unsolved cases.

Deep learning↗
NASA NTRS2004

Shortcomings with Tree-Structured Edge Encodings for Neural Networks

In evolutionary algorithms a common method for encoding neural networks is to use a tree structured assembly procedure for constructing them. Since node operators have difficulties in specifying edge weights and these operators are execution-order dependent, an alternative is to use edge operators. Here we identify three problems with edge operators: in the initialization phase most randomly created genotypes produce an incorrect number of inputs and outputs; variation operators can easily change the number of input/output (I/O) units; and units have a connectivity bias based on their order of creation. Instead of creating I/O nodes as part of the construction process we propose using parameterized operators to connect to preexisting I/O units. Results from experiments show that these parameterized operators greatly improve the probability of creating and maintaining networks with the correct number of I/O units, remove the connectivity bias with I/O units and produce better controllers for a goal-scoring task.

Hornby, Gregory S.↗