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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Dynamic realization of emergent high-dimensional optical vortices

The dimensionality of vortical structures has recently been extended beyond two dimensions, providing additional topological complexity and robustness for high-capacity information processing and turbulence control. The generation of high-dimensional vortical structures has mostly been demonstrated in classical systems through the complex interference of fluidic, acoustic, or electromagnetic waves. However, natural materials rarely support three- or higher-dimensional vortical structures and their physical interactions. Here, we experimentally demonstrate a high-dimensional gradient thickness optical cavity (GTOC) in which the optical coupling of planar metal-dielectric multilayers implements topological interactions across multiple dimensions. At non-trivial topological phases, high-dimensional GTOC induces high-dimensional vortical structures in generalized parameter space in three, four dimensions, and beyond. These emergent high-dimensional vortical structures are observed under electro-optic tomography as optical vortex dynamics in two-dimensional real-space, employing the optical thicknesses of dielectric layers as synthetic dimensions. Our findings hold significant promise for emulating high-dimensional physics and developing active topological photonic devices.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Bias-Variance Trade-Off in Physics-Informed Neural Networks with Randomized Smoothing for High-Dimensional PDEs

Physics-Informed Neural Networks (PINNs) have triggered a paradigm shift in scientific computing, leveraging mesh-free properties and robust approximation capabilities. While proving effective for low-dimensional partial differential equations (PDEs), the computational cost of PINNs remains a hurdle in high-dimensional scenarios. This is particularly pronounced when computing high-order and high-dimensional derivatives in the physics-informed loss. Randomized Smoothing PINN (RS-PINN) introduces Gaussian noise for stochastic smoothing of the original neural net model, enabling the use of Monte Carlo methods for derivative approximation, which eliminates the need for costly automatic differentiation. Despite its computational efficiency, especially in the approximation of high-dimensional derivatives, RS-PINN introduces biases in both loss and gradients, negatively impacting convergence, especially when coupled with stochastic gradient descent (SGD) algorithms. We present a comprehensive analysis of biases in RS-PINN, attributing them to the nonlinearity of the Mean Squared Error (MSE) loss as well as the intrinsic nonlinearity of the PDE itself. We propose tailored bias correction techniques, delineating their application based on the order of PDE nonlinearity. The derivation of an unbiased RS-PINN allows for a detailed examination of its advantages and disadvantages compared to the biased version. Specifically, the biased version has a lower variance and runs faster than the unbiased version, but it is less accurate due to the bias. To optimize the bias-variance trade-off, we combine the two approaches in a hybrid method that balances the rapid convergence of the biased version with the high accuracy of the unbiased version. In addition to methodological contributions, we present an enhanced implementation of RS-PINN. Extensive experiments on diverse high-dimensional PDEs, including Fokker-Planck, Hamilton-Jacobi-Bellman (HJB), viscous Burgers’, Allen-Cahn, and Sine-Gordon equations, illustrate the bias-variance trade-off and highlight the effectiveness of the hybrid RS-PINN. Empirical guidelines are provided for selecting biased, unbiased, or hybrid versions, depending on the dimensionality and nonlinearity of the specific PDE problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Forecasting high-dimensional spatio-temporal systems from sparse measurements

This paper introduces a new neural network architecture designed to forecast high-dimensional spatio-temporal data using only sparse measurements. The architecture uses a two-stage end-to-end framework that combines neural ordinary differential equations (NODEs) with vision transformers. Initially, our approach models the underlying dynamics of complex systems within a low-dimensional space; and then it reconstructs the corresponding high-dimensional spatial fields. Many traditional methods involve decoding high-dimensional spatial fields before modeling the dynamics, while some other methods use an encoder to transition from high-dimensional observations to a latent space for dynamic modeling. In contrast, our approach directly uses sparse measurements to model the dynamics, bypassing the need for an encoder. This direct approach simplifies the modeling process, reduces computational complexity, and enhances the efficiency and scalability of the method for large datasets. We demonstrate the effectiveness of our framework through applications to various spatio-temporal systems, including fluid flows and global weather patterns. Although sparse measurements have limitations, our experiments reveal that they are sufficient to forecast system dynamics accurately over long time horizons. Our results also indicate that the performance of our proposed method remains robust across different sensor placement strategies, with further improvements as the number of sensors increases. This robustness underscores the flexibility of our architecture, particularly in real-world scenarios where sensor data is often sparse and unevenly distributed.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Score-Based Physics-Informed Neural Networks for High-Dimensional Fokker–Planck Equations

The Fokker-Planck (FP) equation is a foundational partial differential equation (PDE) in stochastic processes involving Brownian motions. However, the curse of dimensionality (CoD) poses a formidable challenge when dealing with high-dimensional FP equations. Although Monte Carlo simulation and (vanilla) Physics-Informed Neural Networks (PINNs) have shown the potential to tackle CoD, both methods exhibit significant numerical errors in high dimensions when dealing with the probability density function (PDF) associated with Brownian motion. The point-wise PDF values tend to decrease exponentially as dimensionality increases, surpassing the precision of numerical simulations and resulting in substantial errors. In addition, due to its massive sampling, Monte Carlo fails to offer fast sampling. Modeling the logarithm likelihood (LL) via vanilla PINNs transforms the FP equation into a notoriously difficult Hamilton-Jacobi-Bellman (HJB) equation, which is impractical for PINN learning, whose error grows rapidly with dimension. To this end, we propose a novel approach utilizing a score-based solver to fit the score function in stochastic differential equations (SDEs). The score function, defined as the gradient of the LL, plays a fundamental role in inferring LL and PDF and enables fast SDE sampling, offering an effective means to overcome the CoD. Three fitting methods, Score Matching (SM), Sliced Score Matching (SSM), and Score-PINN, are introduced, each contributing unique advantages in computational complexity, accuracy, and generality. The proposed score-based SDE solver operates in two stages: first, employing score matching or Score-PINN to acquire the score function; and second, solving the LL via an ordinary differential equation (ODE) using the obtained score function. Comparative evaluations across these methods showcase varying trade-offs. The proposed methodology is evaluated across diverse SDEs, including anisotropic Ornstein-Uhlenbeck processes, geometric Brownian motion, and Brownian motion with varying eigenspace. We also test various distributions, including Gaussian, Log-normal, Laplace, and Cauchy distributions. The numerical results demonstrate the score-based SDE solver’s stability, speed, and performance across different experimental settings, solidifying its potential as a solution to CoD for high-dimensional FP equations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Scalable Algorithms for Inverse Problems With High-Dimensional Parameter Spaces

Inverse problems, which involve inferring unknown parameters from observed data, present significant computational challenges, especially in large-scale settings with high-dimensional unknown parameters and nonlinear relationships between the unknowns and observations. Bayesian inference provides an approach for addressing these problems, often relying on sequential sampling methods like Markov chain Monte Carlo (MCMC) to approximate the posterior distribution of the parameters. However, MCMC methods become computationally demanding as the dimensionality of the problem increases, particularly in large-scale systems where likelihood evaluations rely on solving partial differential equations (PDEs) on large spatial domains with finely resolved meshes. To overcome these limitations, recent advancements have focused on designing scalable computa tional techniques – for both PDE simulations and sampling strategies – to make Bayesian methods feasible for high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SympGNNs: Symplectic Graph Neural Networks for identifying high-dimensional Hamiltonian systems and node classification

Existing neural network models to learn Hamiltonian systems, such as SympNets, although accurate in low-dimensions, struggle to learn the correct dynamics for high-dimensional many-body systems. Herein, we introduce Symplectic Graph Neural Networks (SympGNNs) that can effectively handle system identification in high-dimensional Hamiltonian systems, as well as node classification. SympGNNs combine symplectic maps with permutation equivariance, a property of graph neural networks. Specifically, we propose two variants of SympGNNs: (i) G-SympGNN and (ii) LA-SympGNN, arising from different parameterizations of the kinetic and potential energy. We demonstrate the capabilities of SympGNN on two physical examples: a 40-particle coupled Harmonic oscillator, and a 2000-particle molecular dynamics simulation in a two-dimensional Lennard-Jones potential. Furthermore, we demonstrate the performance of SympGNN in the node classification task, achieving accuracy comparable to the state-of-the-art. Finally, we also empirically show that SympGNN can overcome the oversmoothing and heterophily problems, two key challenges in the field of graph neural networks.

Deep learning↗
DOE OSTI2025

High-dimensional maximum-entropy phase space tomography

Reconstructing 4D or 6D phase space distributions from 1D or 2D measurements is a challenging inverse problem encountered in particle accelerators. Entropy maximization is an established method to incorporate prior information in the reconstruction, but it is typically infeasible in high-dimensional spaces. In this paper, I review two recent approaches to high-dimensional entropy maximization. The first approach utilizes differentiable simulations and a class of generative models known as normalizing flows, whereas the second approach employs the method of Lagrange multipliers and Markov Chain Monte Carlo (MCMC) sampling. My aim is to provide a short explanation of each method using a common notation. I conclude by mentioning several unsolved problems in phase space tomography.

Hoover, Austin [ORNL] (ORCID:0000000153136962)↗
DOE OSTI2025

HighDimMixedModels.jl: Robust high-dimensional mixed-effects models across omics data

High-dimensional mixed-effects models are an increasingly important form of regression in which the number of covariates rivals or exceeds the number of samples, which are collected in groups or clusters. The penalized likelihood approach to fitting these models relies on a coordinate descent algorithm that lacks guarantees of convergence to a global optimum. Here, we empirically study the behavior of this algorithm on simulated and real examples of three types of data that are common in modern biology: transcriptome, genome-wide association, and microbiome data. Our simulations provide new insights into the algorithm’s behavior in these settings, and, comparing the performance of two popular penalties, we demonstrate that the smoothly clipped absolute deviation (SCAD) penalty consistently outperforms the least absolute shrinkage and selection operator (LASSO) penalty in terms of both variable selection and estimation accuracy across omics data. To empower researchers in biology and other fields to fit models with the SCAD penalty, we implement the algorithm in a Julia package, HighDimMixedModels.jl .

Gorstein, Evan↗
DOE OSTI2025

Data-driven high-dimensional statistical inference with generative models

Crucial to many measurements at the LHC is the use of correlated multi-dimensional information to distinguish rare processes from large backgrounds, which is complicated by the poor modeling of many of the crucial backgrounds in Monte Carlo simulations. In this work, we introduce HI-SIGMA, a method to perform unbinned high-dimensional statistical inference with data-driven background distributions. In contradistinction to many applications of Simulation Based Inference in High Energy Physics, HI-SIGMA relies on generative ML models, rather than classifiers, to learn the signal and background distributions in the high-dimensional space. These ML models allow for interpretable inference while also incorporating model errors and other sources of systematic uncertainties. We showcase this methodology on a simplified version of a di-Higgs measurement in the bbγγ final state, where the di-photon resonance allows for background interpolation from sidebands into the signal region. We demonstrate that HI-SIGMA provides improved sensitivity as compared to standard classifier-based methods, and that systematic uncertainties can be straightforwardly incorporated by extending methods which have been used for histogram based analyses.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Solving high-dimensional partial integral differential equations: The finite expression method

Partial integro-differential equations (PIDEs) have broad applications in the sciences, from electro-magnetism to options pricing. Here, in this paper, we introduce a new finite expression method (FEX) to solve PIDEs. This approach builds upon the original FEX and its inherent advantages with new advances: 1) A novel method of parameter grouping is proposed to reduce the number of coefficients in high-dimensional function approximation; 2) A Taylor series approximation method is implemented to significantly improve the computational efficiency and accuracy of the evaluation of the integral terms of PIDEs. The new FEX based method, denoted FEX-PG to indicate the addition of the parameter grouping (PG) step to the algorithm, provides both high accuracy and interpretable numerical solutions, with the outcome being an explicit equation that facilitates intuitive understanding of the underlying solution structures. These features are often absent in traditional methods, such as finite element methods (FEM) and finite difference methods, as well as in deep learning-based approaches. To benchmark our method against recent advances, we apply the new FEX-PG to solve benchmark PIDEs in the literature. In high-dimensional settings, FEX-PG exhibits strong and robust performance, achieving relative errors on the order of single precision machine epsilon, significantly outperforming existing approaches based on neural networks.

Combinatorial optimization↗
DOE OSTI2024

Data-driven projection pursuit adaptation of polynomial chaos expansions for dependent high-dimensional parameters

Uncertainty quantification (UQ) and inference involving a large number of parameters are valuable tools for problems associated with heterogeneous and non-stationary behaviors. The difficulty with these problems is exacerbated when these parameters are statistically dependent requiring statistical characterization over joint measures. Probabilistic modeling methodologies stand as effective tools in the realms of UQ and inference. Among these, polynomial chaos expansions (PCE), when adapted to low-dimensional quantities of interest (QoI), provide effective yet accurate approximations for these QoI in terms of an adapted orthogonal basis. These adaptation techniques have been cast as projection pursuits in Gaussian Hilbert space in what has been referred to as a projection pursuit adaptation (PPA) by Xiaoshu Zeng and Roger Ghanem (2023). The PPA method efficiently identifies an optimal low-dimensional space for representing the QoI and simultaneously evaluates an optimal PCE within that space. The quality of this approximation clearly depends on the size of the training dataset, which is typically a function of the adapted reduced dimension. Here, the complexity of the problem is thus mediated by the complexity of the low-dimensional quantity of interest and not the complexity of the high-dimensional parameter space.

Data-driven↗
DOE OSTI2025

Hierarchical Bayesian Inverse Problems: A High-Dimensional Statistics Viewpoint

This paper analyzes hierarchical Bayesian inverse problems using techniques from highdimensional statistics. Furthermore, our analysis leverages a property of hierarchical Bayesian regularizers that we call approximate decomposability to obtain non-asymptotic bounds on the reconstruction error attained by maximum a posteriori estimators. The new theory explains how hierarchical Bayesian models that exploit sparsity, group sparsity, and sparse representations of the unknown parameter can achieve accurate reconstructions in high-dimensional settings.

MAP estimation↗
DOE OSTI2025

A Linear-Complexity Tensor Butterfly Algorithm for Compressing High-Dimensional Oscillatory Integral Operators

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and integral transforms such as Radon transforms and Fourier transforms. The proposed algorithm leverages a tensor extension of the so-called complementary low-rank property of existing matrix butterfly algorithms. The algorithm partitions the discretized integral operator tensor into subtensors of multiple levels and factorizes each subtensor at the middle level as a Tucker-type interpolative decomposition, whose factor matrices are formed in a multilevel fashion. For a d-dimensional (d > 1) integral operator discretized into a 2d-mode tensor with n2d entries, the overall CPU time and memory requirement scale as O(nd), in stark contrast to the O(nd log n) complexity of existing matrix algorithms such as matrix butterfly algorithms and fast Fourier transforms (FFTs), where n is the number of points per direction. When comparing with other tensor algorithms such as quantized tensor train (QTT), the proposed algorithm also shows superior CPU and memory performance for tensor contraction. Remarkably, the tensor butterfly algorithm can efficiently model high-frequency Green's function interactions between two unit cubes, each spanning 512 wavelengths per direction, which represents problems of scale over 512× larger than that existing butterfly algorithms can handle, with the same amount of computation resources. On the other hand, for a problem representing 64 wavelengths per direction, which is the largest size existing algebraic matrix algorithms can handle, our tensor butterfly algorithm exhibits 200x speedups and 30× memory reduction compared with existing ones. Moreover, the tensor butterfly algorithm also permits O(nd)-complexity FFTs and Radon transforms up to d = 6 dimensions.

Kielstra, P Michael↗
DOE OSTI2025

Solving high-dimensional inverse problems using amortized likelihood-free inference with noisy and incomplete data

Here, we present a likelihood-free probabilistic inversion method based on normalizing flows for high-dimensional inverse problems. The proposed method is composed of two complementary networks: a summary network for data compression and an inference network for parameter estimation. The summary network encodes raw observations into a fixed-size vector of summary features, while the inference network generates samples of the approximate posterior distribution of the model parameters based on these summary features. The posterior samples are produced in a deep generative fashion by sampling from a latent Gaussian distribution and passing these samples through an invertible transformation. We construct this invertible transformation by sequentially alternating conditional invertible neural network and conditional neural spline flow layers. The summary and inference networks are trained simultaneously. We apply the proposed method to an inversion problem in groundwater hydrology to estimate the posterior distribution of the log-conductivity field conditioned on spatially sparse time-series observations of the system’s hydraulic head responses. The conductivity field is represented with 706 degrees of freedom in the considered problem. Comparison with the likelihood-based iterative ensemble smoother PEST-IES method demonstrates that the proposed method accurately estimates the parameter posterior distribution and the observations’ predictive posterior distribution at a fraction of the inference time of PEST-IES.

conditional invertible neural network↗
DOE OSTI2024

Navigating high-dimensional process-structure–property relations in nanocrystalline Pt-Au alloys with machine learning

For decades, materials scientists have relied on the process-structure–property paradigm to guide investigations into material behaviors. Traditional studies often examine a limited number of process-structure–property variables, striving to elucidate mechanisms governing material response. However, this approach is time consuming and can limit exploration, as well as the discovery of process-structure–property relations in novel materials. In this paper, we combined combinatorial sputter deposition and multi-modal high-throughput materials characterization with feedforward neural networks to establish high-dimensional process-structure–property relations in Pt-Au alloys, yielding nanocrystalline alloys with high hardness and low resistivity relevant to electrical contact switch applications. We mapped three indicators of process conditions (composition and two atomic deposition characteristics) onto four indicators of material structure (X-ray diffraction, film thickness, density, and surface roughness) and two indicators of material properties (hardness and resistivity), resulting in 784 unique combinations evaluated over a 13-dimensional space. The neural networks predicted Pt-Au alloys with 18–24 at.% Au, when deposited at specific conditions, to have a nanoindentation hardness up to 7.2 GPa. This high hardness value, comparable to some steels, represents a 3-fold improvement in hardness over “hard gold”, a commonly used electrical contact alloy, while maintaining requisite electrical conductivity. The neural network models provide an avenue to identify expected process windows capable of maximizing material performance.

Electrical contact materials↗
DOE OSTI2024

Get Non-Real: Randomized Sketching for High-Dimensional Non-Real Valued Data (Final Report)

In our final report for DE-C0022186, we describe the work we did on this grant towards the goals we proposed. Our first goal was characterizing fundamental limits for sketching of discrete high-dimensional matrices with low-dimensional structures. Our second main goal was designing algorithms for data reconstruction from sketches. We focus on approaches that are either specifically designed for non-real-valued data (binary, finite field) or that will translate more readily to that setting.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Predicting Drug Effects from High-dimensional Asymmetric Drug Data Sets using Graph Neural Networks: A Comprehensive Analysis of Multi-target Drug Effect Prediction

Graph neural networks (GNNs) have emerged as one of the most effective Machine learning (ML) techniques for drug effect prediction from drug molecular graphs. Despite having immense potential, GNN models lack performance when using data sets that contain high dimensional asymmetrically co-occurrent drug effects as targets with complex correlations between them. Training individual learning models for each drug effect and incorporating every prediction result for a wide spectrum of drug effects is beyond practicality. Such an implication provides a testbed to address this challenge as multi-target prediction problems, aiming to predict all drug effects at a time. We develop standard and hybrid graph neural networks (GNNs)to perform two separate tasks that are multi-regression for continuous values and multi-label classification for categorical values contained in our data sets. Since this step makes the target data even more sparse and introduces asymmetric label co-occurrence, the learning of multi-label classification models becomes difficult and heavily impacts the GNN's performance. To address these challenges, we propose a new data oversampling technique to improve multi-label classification performances on all the given imbalanced molecular graph data sets. Using the technique, we improve the data imbalance ratio of the drug effects better than before while protecting the data set's integrity. Finally, we evaluate multi-label classification performance using the best-performant hybrid GNN model on all the oversampled data sets obtained from the proposed oversampling technique. These results outperform those of other ML models including GNN models when they are trained on the original data sets or oversampled data sets using MLSMOTE (a well-known oversampling technique) in all evaluation metrics precision, recall, and F1 score by a significant margin.

Bose, Avishek [ORNL]↗
DOE OSTI2025

Normalizing flows for high-dimensional detector simulations

Whenever invertible generative networks are needed for LHC physics, normalizing flows show excellent performance. In this work, we investigate their performance for fast calorimeter shower simulations with increasing phase space dimension. We use fast and expressive coupling spline transformations applied to the CaloChallenge datasets. In addition to the base flow architecture we also employ a VAE to compress the dimensionality and train a generative network in the latent space. We evaluate our networks on several metrics, including high-level features, classifiers, and generation timing. Our findings demonstrate that invertible neural networks have competitive performance when compared to autoregressive flows, while being substantially faster during generation.

Ernst, Florian↗