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Results for “differentiable machine learning”

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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Understanding machine learning approaches for partial differential equations

Recent works in computational physics have been successful in the super-resolution of numerical solutions of partial differential equations (PDEs) via neural networks. In this paper we explore the possibilities and limitations of the data-driven discretization approach implemented by Bar-Sinai et. al., while contrasting it with a simpler yet weaker approach utilizing the nangs Python library. The results demonstrate what neural network parameters optimize accuracy and performance, as well as what conditions on PDEs are necessary to maintain convergence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Exploiting correlations in multi-coincidence Coulomb explosion patterns for differentiating molecular structures using machine learning

Coulomb explosion imaging (CEI) is a powerful technique for capturing the real-time motion of individual atoms during ultrafast photochemical reactions. CEI generates high-dimensional data with naturally embedded correlations that allow mapping the coordinated motion of nuclei in molecules. This enables reliable separation of competing reaction pathways and makes this approach uniquely suited for characterizing weak reaction channels. However, rich information contained in experimental CEI patterns remains largely underexploited due to challenges in visualizing correlations between multiple observables in multi-dimensional parameter space. Here we present a new approach to CEI of intermediate-sized polyatomic molecules, detecting up to eight ionic fragments in coincidence and leveraging machine-learning-based analysis to identify patterns and correlations in the resulting high-dimensional momentum-space data, enabling robust molecular structure identification and differentiation. Our approach provides high-dimensional background-free data encoding exceptionally rich structural information and establishes an automated, scalable framework for extracting insightful information from the data. As a demonstration, we apply this method to image and distinguish dichloroethylene isomers, showcasing its potential for broader applications in molecular imaging. Our results pave the way for channel-specific analysis of ultrafast structural dynamics in chemically relevant systems, particularly for disentangling mixed reaction pathways and detecting contributions from weak channels and minority species.

Chemical Physics (physics.chem-ph)↗
DOE OSTI2025

Balancing Trade-offs: Adaptive Differential Privacy in Interpretable Machine Learning Models

In the advancing field of machine learning, balancing accuracy, interpretability, and privacy represents a significant challenge. The problem is exacerbated by the widespread deployment of pre-trained models locally in diverse applications, which could lead to various amounts of privacy leakage. Conventional Differential Privacy strategies, in which uniform noises are applied to model gradients, guarantee data privacy at the expense of accuracy and interpretability. This paper introduces a Feature-Sensitive Adaptive Differential Privacy (FADP) framework with a unique noise-adding strategy. Noises are adaptively added based on feature importance clustering, where important features are considered for interpretability. By employing a unique masking technique, FADP selectively preserves crucial features with minimal noise interference, maintaining accuracy while enhancing interpretability. The FADP framework addresses the limitations of traditional DP methods by preserving critical channels and improving interpretability — a vital requirement in machine learning applications that demand transparency in model decisions. Through comprehensive testing, FADP is shown to balance the trade-offs among accuracy, privacy, and interpretability, marking a substantial advancement in the field of privacy-preserving machine learning.

Farhad Riya, Farhin [University of Tennessee, Knox↗
DOE OSTI2024

Machine-learning based model reduction for partial differential equations

We develop a novel synergistic approach between model reduction and machine learning. The specific goal of this project is to aid in the construction of reduced order models for basis functions that are custom-made to represent the solution of partial differential equations. Partial differential equations (PDEs) are one of the main mathematical tools for describing physical phenomena. However, due to either efficiency or necessity, for many real-world problems, we are interested in constructing reduced order models (ROMs) which focus only on the explicit computation of subsets of the active spatio-temporal scales in the problem, while treating the interaction with the rest of the scales approximately. The task of accurate representation of such interactions (usually called memory terms) constitutes a vast area of research known as model reduction. PI Stinis has significant expertise in the construction of ROMs for complex systems. In addition, in recent work with the project key participant Qadeer, they have utilized machine learning to acquire custom-made basis functions (CBFs) to expand the solutions of PDEs. In the proposed work, we will merge the two concepts by constructing ROMs for subsets of the CBFs needed to represent the solution of a PDE. Specifically, we will use the Mori-Zwanzig model reduction formalism to construct ROMs for subsets of CBFs for nonlinear PDEs of various complexity, as well as investigate the usage of CBFs in the spectral vanishing viscosity method for problems that can form shocks in finite time. The outcome of the research is aimed to be proof-of-concept about a novel synergistic approach between model reduction and machine learning, thus advancing the field of scientific machine learning. Such a capability will benefit the efficient modeling of physical systems appearing in various areas of interest to the DOE.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

When ancient numerical demons meet physics-informed machine learning: adjoint-based gradients for implicit differentiable modeling

Recent advances in differentiable modeling, a genre of physics-informed machine learning that trains neural networks (NNs) together with process-based equations, have shown promise in enhancing hydrological models' accuracy, interpretability, and knowledge-discovery potential. Current differentiable models are efficient for NN-based parameter regionalization, but the simple explicit numerical schemes paired with sequential calculations (operator splitting) can incur numerical errors whose impacts on models' representation power and learned parameters are not clear. Implicit schemes, however, cannot rely on automatic differentiation to calculate gradients due to potential issues of gradient vanishing and memory demand. Here we propose a “discretize-then-optimize” adjoint method to enable differentiable implicit numerical schemes for the first time for large-scale hydrological modeling. The adjoint model demonstrates comprehensively improved performance, with Kling–Gupta efficiency coefficients, peak-flow and low-flow metrics, and evapotranspiration that moderately surpass the already-competitive explicit model. Therefore, the previous sequential-calculation approach had a detrimental impact on the model's ability to represent hydrological dynamics. Furthermore, with a structural update that describes capillary rise, the adjoint model can better describe baseflow in arid regions and also produce low flows that outperform even pure machine learning methods such as long short-term memory networks. The adjoint model rectified some parameter distortions but did not alter spatial parameter distributions, demonstrating the robustness of regionalized parameterization. Despite higher computational expenses and modest improvements, the adjoint model's success removes the barrier for complex implicit schemes to enrich differentiable modeling in hydrology.

58 GEOSCIENCES↗
DOE OSTI2019

CT-based machine learning model to predict the Fuhrman nuclear grade of clear cell renal cell carcinoma

Purpose: To predict the Fuhrman grade of clear cell renal cell carcinoma (ccRCC) with a machine learning classifier based on single- or three-phase computed tomography (CT) images. Materials and methods: Patients with pathologically proven ccRCC from February 1, 2009 to September 31, 2018 who were not treated were retrospectively collected for machine learning-based analysis. The texture features were extracted and ranked from precontrast phase (PCP), corticomedullary phase (CMP), nephrographic phase (NP) and three-phase CT images, and open-source gradient boosting from the decision tree library of CatBoost was used to establish a machine learning classifier to differentiate low- from high-grade ccRCC. The performances of machine learning classifiers based on features from single- and three-phase CT images were compared with each other. Results: A total of 231 patients with 232 pathologically proven ccRCC lesions were retrospectively collected. 35, 36, 41, and 22 Features were extracted and ranked from PCP, CMP, NP, and three-phase CT images, respectively. The machine learning model based on three-phase CT images [area under the ROC curve (AUC) = 0.87] achieved the best diagnostic performance for differentiating low- from high-grade ccRCC, followed by single-phase NP (AUC = 0.84), CMP (AUC = 0.80), and PCP images (AUC = 0.82). Conclusion: Machine learning classifiers can be promising noninvasive techniques to differentiate low- and high-Fuhrman nuclear grade ccRCC, and classifiers based on three-phase CT images are superior to those based on features from each single phase.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2023

A differentiable, physics-informed ecosystem modeling and learning framework for large-scale inverse problems: demonstration with photosynthesis simulations

Photosynthesis plays an important role in carbon, nitrogen, and water cycles. Ecosystem models for photosynthesis are characterized by many parameters that are obtained from limited in situ measurements and applied to the same plant types. Previous site-by-site calibration approaches could not leverage big data and faced issues like overfitting or parameter non-uniqueness. Here we developed an end-to-end programmatically differentiable (meaning gradients of outputs to variables used in the model can be obtained efficiently and accurately) version of the photosynthesis process representation within the Functionally Assembled Terrestrial Ecosystem Simulator (FATES) model. As a genre of physics-informed machine learning (ML), differentiable models couple physics-based formulations to neural networks (NNs) that learn parameterizations (and potentially processes) from observations, here photosynthesis rates. We first demonstrated that the framework was able to correctly recover multiple assumed parameter values concurrently using synthetic training data. Then, using a real-world dataset consisting of many different plant functional types (PFTs), we learned parameters that performed substantially better and greatly reduced biases compared to literature values. Further, the framework allowed us to gain insights at a large scale. Our results showed that the carboxylation rate at 25 °C (V c,max25 ) was more impactful than a factor representing water limitation, although tuning both was helpful in addressing biases with the default values. This framework could potentially enable substantial improvement in our capability to learn parameters and reduce biases for ecosystem modeling at large scales.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Power System Frequency Dynamics Modeling, State Estimation, and Control using Neural Ordinary Differential Equations (NODEs) and Soft Actor-Critic (SAC) Machine Learning Approaches

With the global energy transition of the electric power system, grid control, supervision, and protection is becoming more challenging. With the increasing integration of renewable energy sources (RES), the system dynamics are changing, causing traditional power system dynamic modeling with swing equation-based modeling approaches to fail. Additionally, the converter-dominated power grid is decreasing the system inertia, making the power system more fragile to the frequency swings. This paper first investigates and compares the application of a model-based Kalman filter state estimation approach with (i) a model-free machine learning approach --- neural ordinary differential equations (NODEs) --- and (ii) a data-driven system identification (SysId) approach to model and infer critical state values of the power system frequency dynamics. Then a model predictive control (MPC) framework is compared to a model-free Soft Actor-Critic (SAC) reinforcement learning (RL) control algorithm in providing efficient fast frequency response (FFR) to the power system frequency dynamics. The approaches are compared in terms of their performance goals as well as their per-timestep computational efficiency. Furthermore, the comparative study for state estimation shows that for the model-free requirement, both NODEs and SysId can provide accurate state estimates; however, with increasing model complexity, NODEs can be a better choice for model identification. Similarly, the results from the FFR comparative study show that the SAC RL-based FFR, once trained, outperforms MPC with better control signals and faster computation time, making the SAC RL-based FFR better option for providing FFR to the power system.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Rapid 3D nanoscale coherent imaging via physics-aware deep learning

Phase retrieval, the problem of recovering lost phase information from measured intensity alone, is an inverse problem that is widely faced in various imaging modalities ranging from astronomy to nanoscale imaging. The current process of phase recovery is iterative in nature. As a result, the image formation is time consuming and computationally expensive, precluding real-time imaging. Here, we use 3D nanoscale X-ray imaging as a representative example to develop a deep learning model to address this phase retrieval problem. We introduce 3D-CDI-NN, a deep convolutional neural network and differential programing framework trained to predict 3D structure and strain, solely from input 3D X-ray coherent scattering data. Our networks are designed to be “physics-aware” in multiple aspects; in that the physics of the X-ray scattering process is explicitly enforced in the training of the network, and the training data are drawn from atomistic simulations that are representative of the physics of the material. We further refine the neural network prediction through a physics-based optimization procedure to enable maximum accuracy at lowest computational cost. 3D-CDI-NN can invert a 3D coherent diffraction pattern to real-space structure and strain hundreds of times faster than traditional iterative phase retrieval methods. Our integrated machine learning and differential programing solution to the phase retrieval problem is broadly applicable across inverse problems in other application areas.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2024

Temperature-dependent mechanical properties and crystal plasticity parameters for additively manufactured Haynes-214 alloy: Experiments and numerical modeling

Our experimental mechanical testing data demonstrated that the additively manufactured (AM) laser powder bed fusion (L-PBF) Haynes-214 alloy exhibits non-linear mechanical properties as the temperature rises from ambient to 870 °C. Crystal plasticity (CP) simulations provide an effective approach to gaining deeper insights into microstructure-property linkages under thermomechanical loading. This method can reduce the need for costly high-temperature mechanical testing while accounting for the effects of crystallographic texture and grain morphology on the mechanical behavior of AM materials. However, calibrating a CP model is time-consuming because individual simulations are computationally expensive and hundreds (or more) of iterations over parameter sets may be required. To address this issue, we have designed a machine learning-differential evolution (ML-DE) CP framework that can accurately interpolate the tensile properties of AM L-PBF Haynes-214 alloy across a wide temperature range from ambient to 870 °C, with minimal reliance on experimental data. The framework uses electron backscatter diffraction (EBSD) measurements to generate statistically equivalent microstructural volume elements to serve as inputs to the CP modeling framework. Stress–strain curves were generated from 1000 CP simulations, which serve as the training data set for the three ML regression algorithms explored: linear, extra-trees, and multi-layer perceptron. These three regression models were independently evaluated to compare their efficiency and identify the most suitable algorithm for the given problem. Results revealed that the extra-trees ML regressor outperforms the other models in both qualitative and quantitative aspects with an R 2 of 0.98. Subsequently, the differential evolution optimization approach is employed to calibrate the ML-based CP material parameters with experimental results obtained at various temperatures. Finally, temperature-dependent CP material parameters are formulated. The effectiveness and efficiency of the designed framework are validated through comparison with experimental results, demonstrating a high degree of agreement. These calibrated parametric constitutive equations enable further use of the CP model to study the deformation behavior of this alloy under a wide range of thermo-mechanical loading conditions.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Efficient six-dimensional phase space reconstructions from experimental measurements using generative machine learning

Next-generation accelerator concepts, which hinge on the precise shaping of beam distributions, demand equally precise diagnostic methods capable of reconstructing beam distributions within six-dimensional position-momentum spaces. However, the characterization of intricate features within six-dimensional beam distributions using current diagnostic techniques necessitates a substantial number of measurements, using many hours of valuable beam time. Novel phase space reconstruction techniques are needed to reduce the number of measurements required to reconstruct detailed, high-dimensional beam features in order to resolve complex beam phenomena and as a feedback in precision beam shaping applications. In this study, we present a novel approach to reconstructing detailed six-dimensional phase space distributions from experimental measurements using generative machine learning and differentiable beam dynamics simulations. We demonstrate that this approach can be used to resolve six-dimensional phase space distributions from scratch, using basic beam manipulations and as few as 20 two-dimensional measurements of the beam profile. We also demonstrate an application of the reconstruction method in an experimental setting at the Argonne Wakefield Accelerator, where it is able to reconstruct the beam distribution and accurately predict previously unseen measurements 75× faster than previous methods.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

MapsTorch : automatic differentiation for X-ray fluorescence data analysis

X-ray fluorescence (XRF) is a popular spectroscopy technique for elemental analysis. Spectrum fitting and parameter tuning are at the core of XRF analysis and are conventionally manually intensive, especially for synchrotron experiments involving large amounts of diverse samples. This work introduces the automatic differentiation (AD) technique to XRF and an open-source package called MapsTorch. By transforming an analytical model of the XRF spectrum into a differentiable computation graph with AD, MapsTorch enables robust optimization of parameters and elemental intensities. We evaluate MapsTorch by conducting computational experiments on a large number of historical synchrotron XRF datasets and compare its performance with the currently practiced fitting tool NLopt. The results show that MapsTorch consistently achieves high-quality fits and often leads to better fitting quality than NLopt, particularly in tasks such as initial spectrum fitting and elemental intensity refinement. The robust performance of MapsTorch paves the way for developing automated and high-throughput XRF data analysis workflows to handle the increasing data volumes expected from next-generation synchrotron facilities.

X-ray fluorescence↗
DOE OSTI2024

Designing observables for measurements with deep learning

Many analyses in particle and nuclear physics use simulations to infer fundamental, effective, or phenomenological parameters of the underlying physics models. When the inference is performed with unfolded cross sections, the observables are designed using physics intuition and heuristics. We propose to design targeted observables with machine learning. Unfolded, differential cross sections in a neural network output contain the most information about parameters of interest and can be well-measured by construction. The networks are trained using a custom loss function that rewards outputs that are sensitive to the parameter(s) of interest while simultaneously penalizing outputs that are different between particle-level and detector-level (to minimize detector distortions). We demonstrate this idea in simulation using two physics models for inclusive measurements in deep inelastic scattering. We find that the new approach is more sensitive than classical observables at distinguishing the two models and also has a reduced unfolding uncertainty due to the reduced detector distortions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Spectrometer-free quantitative vapor sensing and classification via spatiotemporal imaging of porous silicon metasurfaces

Metasurfaces offer a compact platform for optical vapor sensing, but their practical deployment has been limited by weak evanescent light–matter interactions and reliance on spectrally resolved instrumentation. Here, we report porous silicon (pSi) metasurfaces for spectrometer-free quantitative detection of volatile organic compounds (VOCs) with strongly enhanced light–matter interaction. The engineered porosity increases sensitivity by >100× relative to non-porous dielectric metasurfaces, enabling limits of detection of 1.65 ppm for methanol and 9.1 ppm for ethanol across a broad dynamic range (<10 ppm to >103 ppm). Imaging-based readout provides a lightweight, spectrometer-free pathway for real-time quantitative sensing. Beyond quantitative detection, the mesoporous architecture introduces adsorption–desorption kinetics as an additional information channel. Analysis of the resulting spatiotemporal signatures enables kinetic fingerprinting without reliance on infrared spectral features or surface functionalization, and a lightweight machine-learning classifier differentiates acetone, methanol, ethanol, and isopropanol with 91.6% accuracy. These results establish porous metasurfaces as spatiotemporal sensing elements that couple quantitative vapor detection with kinetic fingerprinting through real-time dynamical responses, enabling low-cost, high-performance optical sensors.

Dash, Tomoshree [Clemson University]↗
DOE OSTI2026

Differentiable multiphase flow model for physics-informed machine learning in reservoir pressure management

Accurate subsurface reservoir pressure control is extremely challenging due to geological heterogeneity and multiphase fluid-flow dynamics. Predicting behavior in this setting relies on high-fidelity physics-based simulations that are computationally expensive. Yet, the uncertain, heterogeneous properties that control these flows make it necessary to perform many of these expensive simulations, which is often prohibitive. To address these challenges, we introduce a physics-informed machine learning workflow that couples a fully differentiable multiphase flow simulator, which is implemented in the DPFEHM framework with a convolutional neural network (CNN). The CNN learns to predict fluid extraction rates from heterogeneous permeability fields to enforce pressure limits at critical reservoir locations. By incorporating transient multiphase flow physics into the training process, our method enables more practical and accurate predictions for realistic injection-extraction scenarios compared to previous works. To speed up training, we pretrain the model on single-phase, steady-state simulations and then finetune it on full multiphase scenarios, which dramatically reduces the computational cost. We demonstrate that high-accuracy training can be achieved with fewer than three thousand full-physics multiphase flow simulations – compared to previous estimates requiring up to ten million. This drastic reduction in the number of simulations is achieved by leveraging transfer learning from much less expensive single phase simulations.

25 ENERGY STORAGE↗
DOE OSTI2025

jaxhps: An elliptic PDE solver built with machine learning in mind

Elliptic partial differential equations (PDEs) can model many physical phenomena, such as electrostatics, acoustics, wave propagation, and diffusion. In scientific machine learning settings, a high-throughput PDE solver may be required to generate a training dataset, run in the inner loop of an iterative algorithm, or interface directly with a deep neural network. To provide value to machine learning users, such a PDE solver must be compatible with standard automatic differentiation frameworks, scale efficiently when run on graphics processing units (GPUs), and maintain high accuracy for a large range of input parameters. We have designed the jaxhps package with these use-cases in mind by implementing a highly efficient and accurate solver for elliptic problems with native hardware acceleration and automatic differentiation support.

97 MATHEMATICS AND COMPUTING↗