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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 OSTI2026

Score-based deterministic density sampling

We propose a deterministic sampling framework using Score-Based Transport Modeling for sampling an unnormalized target density π given only its score ∇ log π. Our method approximates the Wasserstein gradient flow on KL($f_t$∥π) by learning the time-varying score ∇ log $f_t$ on the fly using score matching. While having the same marginal distribution as Langevin dynamics, our method produces smooth deterministic trajectories, resulting in monotone noise-free convergence. We prove that our method dissipates relative entropy at the same rate as the exact gradient flow, provided sufficient training. Numerical experiments validate our theoretical findings: our method converges at the optimal rate, has smooth trajectories, and is often more sample efficient than its stochastic counterpart. Experiments on high-dimensional image data show that our method produces high-quality generations in as few as 15 steps and exhibits natural exploratory behavior. The memory and runtime scale linearly in the sample size.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), doi:10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. We examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 × 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

What is the gradient of a scalar function defined on a subspace of square matrices?

We illustrate a technique to calculate the gradient of scalar functions that are defined on any arbitrary matrix subspace. It generalizes our earlier work titled “What is the gradient of a scalar function of a symmetric matrix ?”(Indian Journal of Pure and Applied Mathematics (2022), https://doi.org/10.1007/s13226-022-00313-x), in which we considered the special case of the subspace of symmetric matrices. Extant methods to calculate the gradient in such cases have an inherent flaw which leads to spurious results that populate several publications, as well as respected textbooks and handbooks on matrix calculus. Here, we examine these sources and results in a rigorous and concrete mathematical setting of a finite-dimensional inner-product space and discover the inherent flaw and also a remedy. We demonstrate two ways to calculate the derivative/gradient and second derivative for scalar functions of matrices defined over an arbitrary matrix subspace; the first method is by considering any (differentiable) extension to the space of square matrices and projection of its gradient onto the given subspace. The second method utilizes an ordered basis and computes each component of the gradient through evaluation of the directional derivative. All the ideas presented are illustrated by non-trivial examples, namely, considering the subspace of 3 x 3 circulant and Toeplitz matrices and presenting the results of gradient-descent with both the spurious and correct gradients. Moreover, our bibliography makes it clear that a rigorous approach to matrix calculus is not common in practice, and our presentation of matrix calculus in the language of inner-product spaces will be significant and meaningful for applied mathematicians, engineers and researchers working in inter-disciplinary fields to avoid the conceptual pitfalls that exist.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Optimal Coordination of Distributed Energy Resources Using Deep Deterministic Policy Gradient

Recent studies showed that reinforcement learning (RL) is a promising approach for coordination and control of distributed energy resources (DER) under uncertainties. Many existing RL approaches, including Q-learning and approximate dynamic programming, are based on lookup table methods, which become inefficient when the problem size is large and infeasible when continuous states and actions are involved. In addition, when modeling battery energy storage system (BESS), the loss of life is not reasonably considered into the decision-making process. This paper proposes an innovative deep RL method for DER coordination considering BESS degradation. The proposed deep RL is designed based on an adaptive actor-critic architecture and employs an off-policy deterministic policy gradient method for determining the dispatch operation that minimizes the operation cost and BESS life loss. Case studies were performed to validate the proposed method and demonstrate the effects of incorporating degradation models into control design.

Das, Avijit↗
DOE OSTI2025

Estimation of intensity, footprint, and capacity of surface urban heat islands using a direction-enhanced adaptive synchronous extraction (DEASE) method

Here, the surface urban heat island (SUHI) effect, assessed through remotely sensed land surface temperature (LST), remains a focal point in urban climate research. Conventional indicators like SUHI intensity (SUHII) and footprint (SUHIF) capture peak values and spatial extent but fail to account for the cumulative thermal load—a critical dimension reflecting the total heat exposure imposed by spatially continuous warming, which directly limits a holistic assessment of ecological and societal impacts of the SUHI effect. Therefore, this study introduces an indicator termed SUHI capacity (SUHIC), designed to quantify the aggregated SUHI effect by integrating the magnitude of the warming signal across all affected areas, thereby enabling a more comprehensive evaluation of urban thermal environments. Furthermore, a direction-enhanced adaptive synchronous extraction (DEASE) method is proposed for the quantification of SUHIC. This method can dynamically identify the optimal background reference area based on the urban-rural LST gradients in various directions within the city, without relying on predefined mathematical models as previously. The results from 102 European cities first confirm that the directional variations in urban-rural LST gradients, and the DEASE method can effectively capture these distinctions for the simultaneous estimation of SUHII, SUHIF, and SUHIC. Secondly, the spatial patterns of absolute SUHIC values show strong associations with those of SUHIF (R2>0.86), while its relative values (normalized by the area of urban) align more closely with SUHII (R2 > 0.64). More importantly, SUHIC can serve as a crucial reference for assessing the urban thermal signal when SUHII and SUHIF diverge. The proposed method and framework contribute to standardizing the quantification of the SUHI effect.

Indicator↗
DOE OSTI2020

Value Gradient Learning Approach in Power and Frequency Regulation of Grid-Connected Synchronverters

In this paper, a neural network adaptive critic design (ACD) method based on value gradient learning (VGL) is used to optimally control a grid-connected synchronverter. The main drawback of the traditional synchronverters is their infeasibility to face non-inductive grids. To be able to implement a synchronverter technique in any impedance angle, a neural network-based adaptive controller is used. The advantage of adaptive dynamic programing is its ability to adjust itself when it faces changes and uncertainties in the power system. The proposed VGL consists of two subnetworks: the critic network and the action network. The action network is trained during the operation, and the critic network can be pretrained offline or can be simultaneously trained with the action network. To compare the effectiveness of the traditional synchronverter to the VGL-based synchronverter, the simulation results are provided.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10 −3 to 10 −1 , which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Optimizing lane reversals in transportation networks to reduce traffic congestion: A global optimization approach

This paper studies how to reduce the overall travel time of commuters in a transportation network by reversing the direction of some lanes in the network using a macroscopic network-wide perspective. Similar to the Network Design Problem, the lane reversal problem has been shown to be NP-hard given the dependence of the users’ route selection on the lane direction decision. Herein, we propose and compare three efficient methods to solve the routing and lane reversal problem jointly. First, we introduce an alternating method that decouples the routing and lane assignment problems. Second, we propose a Frank–Wolfe method that jointly takes gradient steps to adjust both the lane assignment and routing decisions. Third, we propose a convex approximation method that uses a threshold-based approach to convexify the joint routing and lane reversal objective. The convex approximation method is advantageous since it finds a global optimum solution for the approximated problem and it enables the possibility to include linear constraints. Using this method, we extend the main formulation to be able to limit a maximum number of reversed lanes, as well as to incorporate multiple origin–destination (OD) patterns. We test the proposed methods in a case study using the transportation network of Eastern Massachusetts where our results indicate an overall reduction in travel times of 4.7% by selecting the best 15 reversals. Moreover, using a small test network, we investigate the performance of the lane reversal strategies as a function of the OD demand symmetry. As expected, we observe that when the OD demand is very asymmetric (e.g., for a single OD pair, evacuations, large events), the reduction in travel times is larger than the symmetric case, reaching travel time reductions of 60%.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2023

Training material models using gradient descent algorithms

High temperature design requires accurate constitutive models to describe material inelastic deformation and failure behavior. Oftentimes, calibrating accurate models devolves into the problem of fitting the model parameters against experimental test data. Here, we present the pyopmat package, an open source framework for calibrating constitutive models against experiment data subjected to various loading conditions using machine learning techniques. The package calculates the exact gradient of the model response with respect to the parameters using a combination of automatic differentiation and the adjoint method. Given this exact gradient, we compare the performance of several gradient-based optimization techniques in fitting realistic constitutive models against data. Here, we demonstrate the efficiency and accuracy of our package through example problems using both synthetic data, generated using known parameter sets, under monotonic and cyclic loading conditions and also with an example applying the techniques developed here to actual high temperature creep-fatigue test data.

36 MATERIALS SCIENCE↗
DOE OSTI2021

A general approach to seismic inversion with automatic differentiation

Imaging Earth structure or seismic sources from seismic data involves minimizing a target misfit function, and is commonly solved through gradient-based optimization. The adjoint-state method has been developed to compute the gradient efficiently; however, its implementation can be time-consuming and difficult. We develop a general seismic inversion framework to calculate gradients using reverse-mode automatic differentiation. The central idea is that adjoint-state methods and reverse-mode automatic differentiation are mathematically equivalent. Here, the mapping between numerical PDE simulation and deep learning allows us to build a seismic inverse modeling library, ADSeismic, based on deep learning frameworks, which supports high performance reverse-mode automatic differentiation on CPUs and GPUs. We demonstrate the performance of ADSeismic on inverse problems related to velocity model estimation, rupture imaging, earthquake location, and source time function retrieval. ADSeismic has the potential to solve a wide variety of inverse modeling applications within a unified framework.

58 GEOSCIENCES↗
DOE OSTI2020

Bi-fidelity Gradient-Based Approach for Nonlinear Well Logging Inverse Problems

Solving a non-linear inverse problem is challenging in computational science and engineering. Sampling based methods require a large number of model valuations; gradientbased methods require fewer model evaluations but only find the local minima. Multifidelity optimization combines the low fidelity model and the high-fidelity model to achieve both high accuracy and high efficiency. In this paper, we present a bi-fidelity approach to solve non-linear inverse problems. In the bi-fidelity inversion method, the low-fidelity model is used to acquire a good initial guess, and the high-fidelity model is used to locate the global minimum. Combined with a multi-start optimization scheme, the proposed approach significantly increases the possibility of finding the global minimum for nonlinear inverse problems with many local minima. The method is tested with two toy problems and then applied to an electromagnetic well logging inverse problem, which is difficult to solve using traditional gradient-based methods. The bi-fidelity method provides promising inversion results and can be easily applied to traditional gradient-based methods.

42 ENGINEERING↗
DOE OSTI2024

Prediction of the SYM-H Index Using a Bayesian Deep Learning Method With Uncertainty Quantification

We propose a novel deep learning framework, named SYMHnet, which employs a graph neural network and a bidirectional long short-term memory network to cooperatively learn patterns from solar wind and interplanetary magnetic field parameters for short-term forecasts of the SYM-H index based on 1- and 5-min resolution data. SYMHnet takes, as input, the time series of the parameters' values provided by NASA's Space Science Data Coordinated Archive and predicts, as output, the SYM-H index value at time point t + w hours for a given time point t where w is 1 or 2. By incorporating Bayesian inference into the learning framework, SYMHnet can quantify both aleatoric (data) uncertainty and epistemic (model) uncertainty when predicting future SYM-H indices. Experimental results show that SYMHnet works well at quiet time and storm time, for both 1- and 5-min resolution data. The results also show that SYMHnet generally performs better than related machine learning methods. For example, SYMHnet achieves a forecast skill score (FSS) of 0.343 compared to the FSS of 0.074 of a recent gradient boosting machine (GBM) method when predicting SYM-H indices (1 hr in advance) in a large storm (SYM-H = -393 nT) using 5-min resolution data. When predicting the SYM-H indices (2 hr in advance) in the large storm, SYMHnet achieves an FSS of 0.553 compared to the FSS of 0.087 of the GBM method. In addition, SYMHnet can provide results for both data and model uncertainty quantification, whereas the related methods cannot.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Nonlinear dimension reduction for surrogate modeling using gradient information

We introduce a method for the nonlinear dimension reduction of a high-dimensional function $u:{\mathbb{R}}^d\rightarrow{\mathbb{R}}$, $d\gg 1$. Our objective is to identify a nonlinear feature map $g:{\mathbb{R}}^d\rightarrow{\mathbb{R}}^m$, with a prescribed intermediate dimension $m\ll d$, so that $u$ can be well approximated by $f\circ g$ for some profile function $f:{\mathbb{R}}^m\rightarrow{\mathbb{R}}$. We propose to build the feature map by aligning the Jacobian $\nabla g$ with the gradient $\nabla u$, and we theoretically analyze the properties of the resulting $g$. Once $g$ is built, we construct $f$ by solving a gradient-enhanced least squares problem. Our practical algorithm uses a sample $\{{\textbf{x}}^{(i)},u({\textbf{x}}^{(i)}),\nabla u({\textbf{x}}^{(i)})\}_{i=1}^N$ and builds both $g$ and $f$ on adaptive downward-closed polynomial spaces, using cross validation to avoid overfitting. We numerically evaluate the performance of our algorithm across different benchmarks, and explore the impact of the intermediate dimension $m$. We show that building a nonlinear feature map $g$ can permit more accurate approximation of $u$ than a linear $g$, for the same input data set.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Converting 2D Nanofiber Membranes to 3D Hierarchical Assemblies with Structural and Compositional Gradients Regulates Cell Behavior

Abstract New methods are described for converting 2D electrospun nanofiber membranes to 3D hierarchical assemblies with structural and compositional gradients. Pore‐size gradients are generated by tuning the expansion of 2D membranes in different layers with incorporation of various amounts of a surfactant during the gas‐foaming process. The gradient in fiber organizations is formed by expanding 2D nanofiber membranes composed of multiple regions collected by varying rotating speeds of mandrel. A compositional gradient on 3D assemblies consisting of radially aligned nanofibers is prepared by dripping, diffusion, and crosslinking. Bone mesenchymal stem cells (BMSCs) on the 3D nanofiber assemblies with smaller pore size show significantly higher expression of hypoxia‐related markers and enhanced chondrogenic differentiation compared to BMSCs cultured on the assemblies with larger pore size. The basic fibroblast growth factor gradient can accelerate fibroblast migration from the surrounding area to the center in an in vitro wound healing model. Taken together, 3D nanofiber assemblies with gradients in pore sizes, fiber organizations, and contents of signaling molecules can be used to engineer tissue constructs for tissue repair and build biomimetic disease models for studying disease biology and screening drugs, in particular, for interface tissue engineering and modeling.

Chen, Shixuan↗
DOE OSTI2023

Stochastic projective splitting

Here, we present a new, stochastic variant of the projective splitting (PS) family of algorithms for inclusion problems involving the sum of any finite number of maximal monotone operators. This new variant uses a stochastic oracle to evaluate one of the operators, which is assumed to be Lipschitz continuous, and (deterministic) resolvents to process the remaining operators. Our proposal is the first version of PS with such stochastic capabilities. We envision the primary application being machine learning (ML) problems, with the method’s stochastic features facilitating “mini-batch” sampling of datasets. Since it uses a monotone operator formulation, the method can handle not only Lipschitz-smooth loss minimization, but also min–max and noncooperative game formulations, with better convergence properties than the gradient descent-ascent methods commonly applied in such settings. The proposed method can handle any number of constraints and nonsmooth regularizers via projection and proximal operators. We prove almost-sure convergence of the iterates to a solution and a convergence rate result for the expected residual, and close with numerical experiments on a distributionally robust sparse logistic regression problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Bayesian sequential optimal experimental design for nonlinear models using policy gradient reinforcement learning

We present a mathematical framework and computational methods for optimally designing a finite sequence of experiments. This sequential optimal experimental design (sOED) problem is formulated as a finite-horizon partially observable Markov decision process (POMDP) under a Bayesian setting and with information-theoretic utilities. The formulation is general and may accommodate continuous random variables, non-Gaussian posteriors, and nonlinear forward models. The sOED design policy incorporates elements of feedback and lookahead simultaneously, and we show it to generalize the commonly-used batch and greedy design strategies. We solve for the sOED policy using the policy gradient (PG) method from reinforcement learning, and provide a derivation for the PG expression in the sOED context. Adopting an actor-critic approach, the policy and value functions are parameterized using deep neural networks and improved via PG estimates produced from simulated episodes of designs and observations. The new PG-sOED algorithm is first validated on a linear-Gaussian benchmark, and then compared against other design baselines on a sensor movement problem for contaminant source inversion in a convection-diffusion field. As a result, we provide explanation for the policy behaviors using knowledge of the underlying physical process.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Delegated Regressor, A Robust Approach for Automated Anomaly Detection in the Soil Radon Time Series Data

We propose a new method based on the idea of delegating regressors for predicting the soil radon gas concentration (SRGC) and anomalies in radon or any other time series data. The proposed method is compared to different traditional boosting e.g., Extreme Gradient Boosting (EGB) and simple regression methods e.g., support vector regressors with linear kernel and radial kernel in terms of accurate predictions. R language has been used for the statistical analysis of radon time series (RTS) data. The results obtained show that the proposed methodology predicts SRGC more accurately when compared to different traditional boosting and regression methods. The best correlation is found between the actual and predicted radon concentration for window size of 2 i.e., two days before and after the start of seismic activities. RTS data was collected from 05 February 2017 to 16 February 2018, including 7 seismic events recorded during the study period. Findings of study show that the proposed methodology predicts the SRGC with more precision, for all the window sizes, by overlapping predicted with the actual radon time series concentrations.

54 ENVIRONMENTAL SCIENCES↗