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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

Leveraging interpolation models and error bounds for verifiable scientific machine learning

Effective verification and validation techniques for modern scientific machine learning workflows are challenging to devise. Statistical methods are abundant and easily deployed, but often rely on speculative assumptions about the data and methods involved. Error bounds for classical interpolation techniques can provide mathematically rigorous estimates of accuracy, but often are difficult or impractical to determine computationally. Here, in this work, we present a best-of-both-worlds approach to verifiable scientific machine learning by demonstrating that (1) multiple standard interpolation techniques have informative error bounds that can be computed or estimated efficiently; (2) comparative performance among distinct interpolants can aid in validation goals; (3) deploying interpolation methods on latent spaces generated by deep learning techniques enables some interpretability for black-box models. We present a detailed case study of our approach for predicting lift-drag ratios from airfoil images. Code developed for this work is available in a public Github repository.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Weak Form Scientific Machine Learning: Test Function Construction for System Identification

Weak form Scientific Machine Learning (WSciML) is a recently developed framework for data-driven modeling and scientific discovery. It leverages the weak form of equation error residuals to provide enhanced noise robustness in system identification via convolving model equations with test functions, reformulating the problem to avoid direct differentiation of data. The performance, however, relies on wisely choosing a set of compactly supported test functions. In this work, we mathematically motivate a novel data-driven method for constructing Single-scale-Local reference functions for creating the set of test functions. Our approach numerically approximates the integration error introduced by the quadrature and identifies the support size for which the error is minimal, without requiring access to the model parameter values. Through numerical experiments across various models, noise levels, and temporal resolutions, we demonstrate that the selected supports consistently align with regions of minimal parameter estimation error. We also compare the proposed method against the strategy for constructing Multi-scale-Global (and orthogonal) test functions introduced in our prior work, demonstrating the improved computational efficiency.

FOS: Computer and information sciences↗
DOE OSTI2024

Scientific machine learning for closure models in multiscale problems: A review

Here, closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accuracy. Recently, scientific machine learning approaches have been proposed as a way to tackle the closure problem, combining traditional (physics-based) modeling with data-driven (machine-learned) techniques, typically through enriching differential equations with neural networks. This paper reviews the different reduced model forms, distinguished by the degree to which they include known physics, and the different objectives of a priori and a posteriori learning. The importance of adhering to physical laws (such as symmetries and conservation laws) in choosing the reduced model form and choosing the learning method is discussed. The effect of spatial and temporal discretization and recent trends toward discretization-invariant models are reviewed. In addition, we make the connections between closure problems and several other research disciplines: inverse problems, Mori-Zwanzig theory, and multi-fidelity methods. In conclusion, much progress has been made with scientific machine learning approaches for solving closure problems, but many challenges remain. In particular, the generalizability and interpretability of learned models is a major issue that needs to be addressed further.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Artificial to Spiking Neural Networks Conversion with Calibration in Scientific Machine Learning

Here, we introduce a method to convert physics-informed neural networks (PINNs), commonly used in scientific machine learning, to spiking neural networks (SNNs), which are expected to have higher energy efficiency compared to traditional artificial neural networks (ANNs). We first extend the calibration technique of SNNs to arbitrary activation functions beyond ReLU, making it more versatile, and we prove a theorem that ensures the effectiveness of the calibration. We successfully convert PINNs to SNNs, enabling computational efficiency for diverse regression tasks in solving multiple differential equations, including the unsteady Navier–Stokes equations. We demonstrate great gains in terms of overall efficiency, including separable PINNs (SPINNs), which accelerate the training process. Overall, this is the first work of this kind and the proposed method achieves relatively good accuracy with low spike rates.

PINN↗
DOE OSTI2025

Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications

In this work we introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additive Schwarz preconditioner. The neural network parameters are decomposed into groups (subdomains) with overlapping regions. In addition, the network’s feed-forward structure is indirectly imposed through a novel subdomain-wise synchronization strategy and a coarse-level training step. Through a series of numerical experiments, which consider physicsinformed neural networks and operator learning approaches, we demonstrate that the proposed two-level preconditioner significantly speeds up the convergence of the standard (LBFGS) optimizer while also yielding more accurate machine learning models. Moreover, the devised preconditioner is designed to take advantage of model-parallel computations, which can further reduce the training time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning

This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov–Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure of UQ, enhancing interpretability and robustness in modeling complex functions. Building on this, we introduce Conformalized-KANs, which integrate conformal prediction, a distribution-free UQ technique, with KAN ensembles to generate calibrated prediction intervals with guaranteed coverage.} Extensive numerical experiments are conducted to evaluate the effectiveness of these methods, focusing particularly on the robustness and accuracy of the prediction intervals under various hyperparameter settings. We show that the conformal KAN predictions can be applied to recent extensions of KANs, including Finite Basis KANs (FBKANs) and multifideilty KANs (MFKANs). The results demonstrate the potential of our approaches to significantly improve the reliability and applicability of KANs in scientific machine learning.

• Artificial intelligence (AI) / machine learning ↗
DOE OSTI2025

UQpy Version 4.2: Uncertainty quantification with Python

We introduce a new module for the UQpy software package which extends its capabilities into the field of Scientific Machine Learning. This module builds on PyTorch to create a flexible and robust platform for uncertainty quantification in machine learning. The scientific machine learning module of UQpy introduces custom layers, neural networks, and neural network trainers that are compatible with torch version 2.2.2 and allow for “plug and play” integration into existing torch code.

Neural networks↗
DOE OSTI2025

An MLCommons Scientific Benchmarks Ontology

Scientific machine learning research spans diverse domains and data modalities, yet existing benchmark efforts remain siloed and lack standardization. This makes novel and transformative applications of machine learning to critical scientific use-cases more fragmented and less clear in pathways to impact. This paper introduces an ontology for scientific benchmarking developed through a unified, community-driven effort that extends the MLCommons ecosystem to cover physics, chemistry, materials science, biology, climate science, and more. Building on prior initiatives such as XAI-BENCH, FastML Science Benchmarks, PDEBench, and the SciMLBench framework, our effort consolidates a large set of disparate benchmarks and frameworks into a single taxonomy of scientific, application, and system-level benchmarks. New benchmarks can be added through an open submission workflow coordinated by the MLCommons Science Working Group and evaluated against a six-category rating rubric that promotes and identifies high-quality benchmarks, enabling stakeholders to select benchmarks that meet their specific needs. The architecture is extensible, supporting future scientific and AI/ML motifs, and we discuss methods for identifying emerging computing patterns for unique scientific workloads. The MLCommons Science Benchmarks Ontology provides a standardized, scalable foundation for reproducible, cross-domain benchmarking in scientific machine learning. A companion webpage for this work has also been developed as the effort evolves: https://mlcommons-science.github.io/benchmark/

Hawks, Ben [Fermilab] (ORCID:0000000157000288)↗
DOE OSTI2025

Machine learning for reparameterization of multi-scale closures

Scientific machine learning (ML) is becoming increasingly useful in learning closure models for multi-scale physics problems; however, many ML approaches require a vast array of training data and can struggle with generalization and interpretability. Here, rather than learning an entire closure operator, we adopt an existing reduced-dimension model of the microphysics and learn an optimal re-parameterization of the solver. We demonstrate two approaches for training the reduced dimension closure model (1) an a priori method that optimizes the closure parameterization and the neural network parameters separately and (2) an a posteriori method that simultaneously optimizes both. Using the simulation of biomass pyrolysis as a motivating example, we show that the a posteriori method achieves better target losses and is less dependent on training dataset size for generalizability. We then demonstrate the impact that implementing this reparameterization has at the macroscale, showing improved predictive performance with no modification to the underlying macroscale solvers.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗