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Results for “Neural ordinary differential equations”

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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186 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

An attention-based neural ordinary differential equation framework for modeling inelastic processes

To preserve strictly conservative behavior as well as model the variety of dissipative behavior displayed by solid materials, we propose a significant enhancement to the internal state variable-neural ordinary differential equation (ISV-NODE) framework. In this data-driven, physics-constrained modeling framework internal states are inferred rather than prescribed. The ISV-NODE consists of: (a) a stress model dependent on observable deformation and inferred internal state, and (b) a model of the evolution of the internal states. The enhancements to ISV-NODE proposed in this work are multifold: (a) a partially input convex neural network stress potential provides polyconvexity in terms of observed strain while leaving the inferred state unconstrained, and (b) an internal state flow model uses common latent features to inform novel attention-based gating and drives the flow of internal state only in dissipative regimes. We demonstrated that this architecture can accurately model dissipative and conservative behavior across an isotropic, isothermal elastic-viscoelastic-elastoplastic spectrum with three exemplars, while maintaining fundamental principles by design.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

SODAs: sparse optimization for the discovery of differential and algebraic equations

Differential-algebraic equations (DAEs) integrate ordinary differential equations (ODEs) with algebraic constraints, providing a fundamental framework for developing models of dynamical systems characterized by time-scale separation, conservation laws and physical constraints. While sparse optimization has revolutionized model development by allowing data-driven discovery of parsimonious models from a library of possible equations, existing approaches for dynamical systems assume DAEs can be reduced to ODEs by eliminating variables before model discovery. This assumption limits the applicability of such methods for DAE systems with unknown constraints and time scales. We introduce sparse optimization for differential-algebraic systems (SODAs), a data-driven method for the identification of DAEs in their explicit form. By discovering the algebraic and dynamic components sequentially without prior identification of the algebraic variables, this approach leads to a sequence of convex optimization problems. It has the advantage of discovering interpretable models that preserve the structure of the underlying physical system. To this end, SODAs improves since SODAs is singular numerical stability when handling high correlations between library terms, caused by near-perfect algebraic relationships, by iteratively refining the conditioning of the candidate library. We demonstrate the performance of our method on biological, mechanical and electrical systems, showcasing its robustness to noise in both simulated time series and real-time experimental data.

DAE↗
DOE OSTI2025

From PINNs to PIKANs: recent advances in physics-informed machine learning

Physics-Informed Neural Networks (PINNs) have emerged as a key tool in Scientific Machine Learning since their introduction in 2017, enabling the efficient solution of ordinary and partial differential equations using sparse measurements. Over the past few years, significant advancements have been made in the training and optimization of PINNs, covering aspects such as network architectures, adaptive refinement, domain decomposition, and the use of adaptive weights and activation functions. A notable recent development is the Physics-Informed Kolmogorov-Arnold Networks (PIKANS), which leverage a representation model originally proposed by Kolmogorov in 1957, offering a promising alternative to traditional PINNs. In this review, we provide a comprehensive overview of the latest advancements in PINNs, focusing on improvements in network design, feature expansion, optimization techniques, uncertainty quantification, and theoretical insights. We also survey key applications across a range of fields, including biomedicine, fluid and solid mechanics, geophysics, dynamical systems, heat transfer, chemical engineering, and beyond. Lastly, we review computational frameworks and software tools developed by both academia and industry to support PINN research and applications.

Kolmogorov-Arnold networks↗
DOE OSTI2025

Generative learning of densities on manifolds

A generative modeling framework is proposed that combines diffusion models and manifold learning to efficiently sample data densities on manifolds. The approach utilizes Diffusion Maps to uncover possible low-dimensional underlying (latent) spaces in the high-dimensional data (ambient) space. Two approaches for sampling from the latent data density are described. The first is a score-based diffusion model, which is trained to map a standard normal distribution to the latent data distribution using a neural network. The second one involves solving an Itô stochastic differential equation in the latent space. Additional realizations of the data are generated by lifting the samples back to the ambient space using Double Diffusion Maps , a recently introduced technique typically employed in studying dynamical system reduction; here the focus lies in sampling densities rather than system dynamics. The proposed approaches enable sampling high dimensional data densities restricted to low-dimensional, a priori unknown manifolds. The efficacy of the proposed framework is demonstrated through a benchmark problem and a material with multiscale structure.

Double diffusion maps↗
DOE OSTI2026

A Data-Driven Method for Modeling Creep-Fatigue Stress- Strain Behavior Using Neural ODEs

In this paper, we introduce a data-driven machine learning approach for modeling one-dimensional stress–strain behavior under cyclic loading, utilizing experimental data from the nickel-based Alloy 617. The study employs uniaxial creep–fatigue test data acquired under various loading histories and compares two distinct neural network-based ODE models. The first model, known as the black-box model, comprehensively describes the strain–stress relationship using a Neural ODE equation. To interpret this black-box model, we apply the Sparse Identification of Nonlinear Dynamical Systems (SINDy) technique, transforming the black-box model into an equation-based model using symbolic regression. The second model, the Neural flow rule model, incorporates Hooke’s Law for the linear elastic component, with the nonlinear part characterized by a Neural ODE. Both models are trained with experimental data to accurately reflect the observed stress–strain behavior. We conduct a detailed comparison with the standard Chaboche model, which includes three back stresses. Our results demonstrate that the neural network-based ODE models precisely capture the experimental creep–fatigue mechanical behavior, exceeding the standard Chaboche model’s accuracy. Furthermore, an interpretable model derived from the black-box neural ODE model through symbolic regression achieves accuracy comparable to the Chaboche model, enhancing its interpretability. The results highlight the potential of neural network-based ODE models to depict complex creep–fatigue behavior, eliminating the necessity for experts to define a specific, material-focused model form.

creep-fatigue↗
NASA NTRSDate not supplied

Usage-based Lifing of Lithium-Ion Battery with HybridPhysics-Informed Neural Networks

Lithium-ion batteries are commonly used to power unmanned aircraft vehicles (UAVs).The ability to model and forecast the remaining useful life of these batteries enables UAV reliability assurance. Building accurate models for battery state of charge and state of health based on first principles is challenging due to the complex electrochemistry that governs battery operations and computational complexity required to solve them. Therefore, reduced order models are often used due to their ability to capture the overall battery discharge. Un-fortunately, these simplifications lead to residual discrepancy between model predictions and observed data. In this paper, we present a hybrid modeling approach merging reduced-order models and neural networks. In this approach, while most of the input-output relationship is captured by Nernst and Butler-Volmer equations, data-driven kernels reduce the gap between predictions and observations. We validate our approach using data publicly available through the NASA Prognostics Center of Excellence repository. Results showed that our hybrid battery prognosis model can be successfully calibrated, even with a limited number of observations.

Lithium-ion Battery↗
DOE OSTI2025

Structure–Property Linkage in Alloys Using Graph Neural Network and Explainable Artificial Intelligence

Deep learning tools have recently shown significant potential for accelerating the prediction of microstructure–property linkage in materials. While deep neural networks like convolution neural networks (CNNs) can extract physics information from 3D microstructure images, they often require a large network architecture and substantial training time. In this research, we trained a graph neural network (GNN) using phase field generated microstructures of Ni-Al alloys to predict the evolution of mechanical properties. We found that a single GNN is capable of accurately predicting the strengthening of Ni-Al alloys with microstructures of varying sizes and dimensions, which cannot otherwise be done with a CNN. Additionally, GNN requires significantly less GPU utilization than CNN and offers more interpretable explanation of predictions using saliency analysis as features are manually defined in the graph. We also utilize explainable artificial intelligence tool Bayesian Inference to determine the coefficients in the power law equation that governs coarsening of precipitates. Overall, our work demonstrates the ability of the GNN to accurately and efficiently extract relevant information from material microstructures without having restrictions on microstructure size or dimension and offers an interpretable explanation.

Chemistry↗
NASA NTRSDate not supplied

Li-ion Battery Aging with Hybrid Physics-Informed Neural Networks and Fleet-wide Data

In this work, we propose a hybrid model for Li-ion battery discharge and aging prediction that leverages fleet-wide data to predict future capacity drops.The model is built upon an hybrid approach merging physics-based and empirical equations, as well as neural network models in a recurrent neural network cell. The hybrid physics-informed neural network can predict voltage discharge cycles given the loading profile, and estimate the used capacity of the battery under random-loading conditions by tracking aging parameters connected to the residual capacity of the battery. By merging information on the battery aging parameters with existing fleet-wide aging data, the model can predict the future residual capacity of the battery that is being monitored, and therefore enable predictions of voltage discharge curves far ahead in the battery life cycle. We validated the approach using the NASA Prognostics Data Repository Battery data-set, which contains experimental data on Li-ion batteries discharged at random loading conditions in a controlled environment. The approach also allows the identification of discrepancies between the battery aging trend and the trend observed at the fleet level, so that batteries behaving differently from the rest of the fleet can be subject to closer monitoring and further testing to refine predictions.

PINN↗
NASA NTRS1977

Calculations of the Moon's Thermal History at Different Concentrations of Radioactive Elements, Taking Into Account Differentiation on Melting

Calculations of the thermal history of the moon were carried out by solving the thermal conductivity equation for the case in which the heat sources are the long-lived radioactive elements Th, U, and K 40 . The concentrations of these elements were adjusted to give four variations of the heat flow: 1.35 x 10 -8 and 0.91 x 10 -6 cal cm -2 s -1 (I and I**), 0.61 x 10 -6 (variant II, the terrestrial mixture of Lyubimova and Starkova), and 0.236 x 10 -6 (variant III, the chondrite model of Urey and MacDonald). In the same calculations, we considered layering of the differentiated material with transport to the surface of the radioactive elements after the temperature of the layer rose to 200 K above the melting temperature, which is considered in five variants that differ in the amount of transported radioactive elements: 100 percent ( n = 1), 80 percent n = 0.8), 40 percent, 20 percent ( n = 0.6, 0.4, 0.2). During fusion the heat capacity and heat conductivity were changed. We considered two variants of an initially cold (273 K) and hot (900 K) Moon. Calculations show that the interior of the Moon was heated to melting during the first 0.7 to 2.3 x 10 9 years. The maximum fusion involved practically the entire Moon to a distance from 15 to 45 km beneath the surface, and started 3.5 to 4.0 x 10 9 years ago (I, I**), or 2.5 to 3.0 x 10 9 years ago (II, III) and continued for 1 to 2 x 10 9 years. Today the Moon is cooling. The current thickness of the solid crust is from 150 to 200 km and the heat flow exceeds the stationary value 1.5 fold. Apparently the most realistic variant is II (terrestrial mixture) for an initially hot Moon, and gives, regardless of the moderate concentration of radioactive elements, a heat flow of 0.9 to 0.95 x 10 -6 cal cm -2 s -1 , which agrees with the radioastronomical measurements of Troitsky and Krotikov and with the Apollo 15 data.

O I Ornatskaya↗
NASA NTRS1995

Extensional Flow Convecting a Reactant Undergoing a First Order Homogeneous Reaction and Diffusional Mass Transfer From a Sphere at Low to Intermediate Peclet and Damkohler Numbers

Forced convective diffusion-reaction is considered for viscous axisymmetric extensional convecting velocity in the neighborhood of a sphere. For Peclet numbers in the range 0.1 ≤ Pe ≤ 500 and for Damkohler numbers increasing with increasing Pe but in the overall range 0.02 ≤ Da ≤ 10, average and local Sherwood numbers have been computed. By introducing the eigenfunction expansion c(r,Θ) = Σ c n (r)P n (cosΘ) into the forced convective diffusion equation for the concentration of a chemical species undergoing a first order homogeneous reaction and by using properties of the Legendre functions P n (cosΘ), the variable coefficient PDE can be reduced to a system of N+1 second order ODEs for the radial functions C n (r), n=0,1,2, ... ,N. The adaptive grid algorithm of Pereyra and Lentini can be used to solve the corresponding 2(N+ 1) first order differential equations as a two-point boundary value problem on 1 ≤ r ≤ r •• . Convergence of the expansion for a specific value of N can thus be established and provides "spectral" behavior as well as the full concentration field c(r,Θ).

N Y Shah↗
NASA NTRS1995

Analysis of Gas Absorption to A Thin Liquid Film in the Presence of A Zero-Order Chemical Reaction

The paper presents a detailed theoretical analysis of the process of gas absorption to a thin liquid film adjacent to a horizontal rotating disk. The film is formed by the impingement of a controlled liquid jet at the center of the disk and subsequent radial spreading of liquid along the disk. The chemical reaction between the gas and the liquid film can be expressed as a zero-order homogeneous reaction. The process was modeled by establishing equations for the conservation of mass, momentum, and species concentration and solving them analytically. A scaling analysis was used to determine dominant transport processes. Appropriate boundary conditions were used to solve these equations to develop expressions for the local concentration of gas across the thickness of the film and distributions of film height, bulk concentration, and Sherwood number along the radius of the disk. The partial differential equation for species concentration was solved using the separation of variables technique along with the Duhamel's theorem and the final analytical solution was expressed using confluent hypergeometric functions. Tables for eigenvalues and eigenfunctions are presented for a number of reaction rate constants. A parametric study was performed using Reynolds number, Ekman number, and dimensionless reaction rate as parameters. At all radial locations, Sherwood number increased with Reynolds number (flow rate) as well as Ekman number (rate of rotation). The enhancement of mass transfer due to chemical reaction was found to be small when compared to the case of no reaction (pure absorption), but the enhancement factor was very significant when compared to pure absorption in a stagnant liquid film. The zero-order reaction processes considered in the present investigation included the absorption of oxygen in aqueous alkaline solutions of sodiumdithionite and rhodium complex catalyzed carbonylation of methanol. Present analytical results were compared to previous theoretical results for limiting conditions, and were found to have very good agreement.

S Rajagopalan↗
NASA NTRSDate not supplied

Autonomous Detection and Classification of Lunar Minerals Using a Convolutional Neural Network Based Framework for the SUCR DALI Project

NASA’s long-term goal is to deploy humans to the Moon and, from there, advance human exploration to Mars, with Artemis missions as pivotal milestones. Raman spectroscopy can uniquely identify minerals, compounds, water states, and other materials, providing distinctive fingerprints for classification. A Raman instrument has been successfully deployed and utilized on the Mars surface via the Perseverance rover, but has not yet been utilized at the lunar surface The SUCR DALI project is working towards developing a Raman spectroscopy instrument to be applied in various lunar mission concepts, including within the Artemis program. The objective of my research is to assist in the maturation of the proposed SUCR DALI lunar Raman instrument through the development of an autonomous detection and classification model capable of identifying minerals and water states on the Moon’s surface.

Convolutional Neural Networks↗
DOE OSTI2026

Surrogate modeling of Monte Carlo radiation transport with convolutional neural networks for shielding optimization

Here, we present a machine learning (ML)-based surrogate model using convolutional neural networks (CNN) designed to emulate the attenuation of neutron fields as they pass through various shielding materials. This model can compute the outgoing neutron flux almost instantaneously and achieves reasonable accuracy compared to traditional Monte Carlo (MC)-based codes, which are computationally intensive. This emulator alleviates the complexity of neutron radiation transport through shielding materials by reducing the dimensionality and enables shielding optimization for a known radiation environment. This optimization process, which would have taken an unrealistic timeline due to several complex radiation transport simulations, can now be achieved in minutes, thus increasing computational capabilities in radiation shielding assessment. We demonstrate the applications of this emulator in computing effective dose rates and optimizing shielding solutions for a heavy-ion accelerator facility, such as the Facility for Rare Isotope Beams, where secondary neutrons produced via beam interactions dominate the radiation environment.

accelerator shielding↗
NASA NTRSDate not supplied

Differential Drag Efficacy for Close Approach Remediation

Differential drag has become a viable alternative to propulsion for satellites to avoid collisions, but there is little guidance in the literature to aid mission designers in developing a differential drag capability that verifiably meets collision avoidance efficacy standards or requirements, if such requirements were to exist. This paper proposes a differential drag efficacy determination approach based on empirical conjunctions from the NASA Conjunction Assessment Risk Analysis historical database, focusing on energy dissipation rate and change in ballistic coefficient as the key satellite parameters correlated to efficacy. The data analysis informs the discussion toward adoption of recommended differential drag requirements. A case study is presented to walk through the process to determine efficacy of a proposed mission assuming several potential requirements.

conjunction remediation↗
DOE OSTI2026

Multitask graph neural networks for elastoplastic response prediction in dual-phase polycrystals

Microstructure-sensitive prediction of elastoplastic response remains a recurring bottleneck in multiscale damage and fatigue modeling, where large ensembles of statistically distinct polycrystals are required to quantify variability and extreme-value behavior. In this work, we develop a multitask graph neural network (GNN) surrogate that maps dual-phase ferrite–martensite polycrystal microstructures to Statistical Volume Element (SVE)-level elastoplastic Quantities of Interest (QoIs). Each SVE is represented as a grain-adjacency graph, with node features encoding phase, geometry, and crystallographic orientation, and edge features encoding relative misorientation. A message-passing graph convolution generates node embeddings, which are pooled into a graph representation and passed to a multitask regression head that jointly predicts 10 scalar QoIs and vector-valued stress–strain responses in orthogonal loading directions across multiple martensite volume fractions and SVE sizes. Results show high accuracy for scalar QoIs and strong agreement for full stress–strain trajectories, with population envelopes reproducing both median behavior and finite-SVE variability across compositions and partition scales. A unified model trained on pooled volume-fraction data preserves most within-regime accuracy relative to regime-specific models while also capturing the broader cross-regime variation reflected in the pooled test set. Distributional comparisons further demonstrate that the surrogate preserves heterogeneity under SVE partitioning, enabling statistically consistent block-wise random-field construction for mesoscale analyses. Overall, the proposed grain-graph surrogate provides a practical pathway to accelerate ensemble-based studies of SVE-level constitutive variability in dual-phase polycrystals.

Crystal plasticity↗
DOE OSTI2024

Neuromorphic overparameterisation and few-shot learning in multilayer physical neural networks

Abstract Physical neuromorphic computing, exploiting the complex dynamics of physical systems, has seen rapid advancements in sophistication and performance. Physical reservoir computing, a subset of neuromorphic computing, faces limitations due to its reliance on single systems. This constrains output dimensionality and dynamic range, limiting performance to a narrow range of tasks. Here, we engineer a suite of nanomagnetic array physical reservoirs and interconnect them in parallel and series to create a multilayer neural network architecture. The output of one reservoir is recorded, scaled and virtually fed as input to the next reservoir. This networked approach increases output dimensionality, internal dynamics and computational performance. We demonstrate that a physical neuromorphic system can achieve an overparameterised state, facilitating meta-learning on small training sets and yielding strong performance across a wide range of tasks. Our approach’s efficacy is further demonstrated through few-shot learning, where the system rapidly adapts to new tasks.

Science & Technology - Other Topics↗