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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

CONCURRENT, CONDENSED STEIN VARIATIONAL GRADIENT DESCENT FOR UNCERTAINTY QUANTIFICATION OF NEURAL NETWORKS

In this work, we propose a Stein variational gradient descent (SVGD) method to concurrently sparsify, train, and provide uncertainty quantification (UQ) of a complexly parameterized model, such as a neural network (NN). It employs a graph reconciliation and condensation process to reduce complexity and increase similarity in the Stein ensemble of parameterizations. Therefore, the proposed concurrent, condensed SVGD (ccSVGD) method can provide UQ on parameters, not just outputs. Furthermore, the parameter reduction speeds up the convergence of the Stein gradient descent as it reduces the combinatorial complexity by aligning and differentiating the sensitivity to parameters. These properties are demonstrated with an illustrative example and an application to a mechanical response representation problem in solid mechanics.

42 ENGINEERING↗
DOE OSTI2025

Benchmarking optimization methods for materials research: Gradient descent and Bayesian optimization for lithium-ion battery aging diagnostics

Accurate and efficient parameter estimation is essential for battery diagnostics and aging analysis. Here, in this study, we compare two optimization-based approaches—gradient descent and Bayesian optimization—for extracting parameters from differential voltage analysis in lithium-ion batteries. While these techniques are widely used, their relative strengths and limitations for this application are not well understood. The study evaluates the trade-offs between these methods in terms of result quality, computational cost, and reliability within this specific application. The diagnostic results from our battery data suggest adopting gradient descent as an initial method for rapid and efficient analysis, while employing more stable optimization techniques, such as Bayesian optimization, as a verification step to mitigate potential instability. Comparing the two methods provides information on algorithmic choice, while inspiring further discussions on selecting appropriate techniques for specific research tasks.

Zhao, Ziqing [Boston Univ., MA (United States)] (O↗
DOE OSTI2025

Convergence analysis for a nonlocal gradient descent method via directional Gaussian smoothing

We analyze the convergence of a nonlocal gradient descent method for minimizing a class of high-dimensional non-convex functions, where a directional Gaussian smoothing (DGS) is proposed to define the nonlocal gradient (also referred to as the DGS gradient). The method was first proposed in [Zhang et al., Enabling long-range exploration in minimization of multimodal functions, UAI 2021], in which multiple numerical experiments showed that replacing the traditional local gradient with the DGS gradient can help the optimizers escape local minima more easily and significantly improve their performance. However, a rigorous theory for the efficiency of the method on nonconvex landscape is lacking. In this work, we investigate the scenario where the objective function is composed of a convex function, perturbed by deterministic oscillating noise. We provide a convergence theory under which the iterates exponentially converge to a tightened neighborhood of the solution, whose size is characterized by the noise wavelength. Here, we also establish a correlation between the optimal values of the Gaussian smoothing radius and the noise wavelength, thus justifying the advantage of using moderate or large smoothing radii with the method. Furthermore, if the noise level decays to zero when approaching the global minimum, we prove that DGS-based optimization converges to the exact global minimum with linear rates, similarly to standard gradient-based methods in optimizing convex functions. Several numerical experiments are provided to confirm our theory and illustrate the superiority of the approach over those based on the local gradient.

Tran, Hoang [Oak Ridge National Laboratory (ORNL),↗
DOE OSTI2025

Enhancing ACPF Analysis: Integrating Newton-Raphson Method with Gradient Descent and Computational Graphs

This paper presents a new method for enhancing Alternating Current Power Flow (ACPF) analysis. The method integrates the Newton-Raphson (NR) method with Enhanced-Gradient Descent (GD) and computational graphs. The integration of renewable energy sources in power systems introduces variability and unpredictability, and this method addresses these challenges. It leverages the robustness of NR for accurate approximations and the flexibility of GD for handling variable conditions, all without requiring Jacobian matrix inversion. Furthermore, computational graphs provide a structured and visual framework that simplifies and systematizes the application of these methods. The goal of this fusion is to overcome the limitations of traditional ACPF methods and improve the resilience, adaptability, and efficiency of modern power grid analyses. We validate the effectiveness of our advanced algorithm through comprehensive testing on established IEEE benchmark systems. Furthermore, our findings demonstrate that our approach not only speeds up the convergence process but also ensures consistent performance across diverse system states, representing a significant advancement in power flow computation.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Implementation of Stochastic Gradient Descent in an Automated Glow Peak Identification Software for Multiple Thermoluminescent Dosimeter Types

A glow-curve analysis code was previously developed in C++ to analyze thermoluminescent dosimeter glow curves using automated peak detection while applying a first-order kinetics model. A newer version of this code was implemented to improve the automated peak detection and curve fitting models. The Stochastic Gradient Descent Algorithm was introduced to replace the prior approach of taking first and second-order derivatives for peak detection. Additionally, early stopping mechanisms were invoked to improve the previously used Levenberg-Marquardt Algorithm employed for curve fitting. The two software versions were compared through glow curve analysis of different thermoluminescent dosimeter materials and calculation of the corresponding figures of merit. Altogether improvements were shown, namely an increase in the number of peaks detected and a reduction of the mean figure of merit by approximately 46%.

137Cs↗
DOE OSTI2024

Using the Metropolis algorithm to explore the loss surface of a recurrent neural network

In the limit of small trial moves the Metropolis Monte Carlo algorithm is equivalent to gradient descent on the energy function in the presence of Gaussian white noise. This observation was originally used to demonstrate a correspondence between Metropolis Monte Carlo moves of model molecules and overdamped Langevin dynamics, but it also applies in the context of training a neural network: making small random changes to the weights of a neural network, accepted with the Metropolis probability, with the loss function playing the role of energy, has the same effect as training by explicit gradient descent in the presence of Gaussian white noise. We explore this correspondence in the context of a simple recurrent neural network. We also explore regimes in which this correspondence breaks down, where the gradient of the loss function becomes very large or small. In these regimes the Metropolis algorithm can still effect training, and so can be used as a probe of the loss function of a neural network in regimes in which gradient descent struggles. We also show that training can be accelerated by making purposely-designed Monte Carlo trial moves of neural-network weights.

Casert, Corneel↗
DOE OSTI2026

Optimality of Gradient-MUSIC for Spectral Estimation

We introduce the Gradient-MUSIC algorithm for estimating the unknown frequencies and amplitudes of a nonharmonic signal from noisy time samples. While the classical MUSIC algorithm performs a computationally expensive search over a fine grid, Gradient-MUSIC is significantly more efficient and eliminates the need for discretization over a fine grid by using optimization techniques. It coarsely scans the 1D landscape to find initialization simultaneously for all frequencies followed by parallelizable local refinement via gradient descent. We also analyze its performance when the noise level is sufficiently small and the signal frequencies are separated by at least 8π/m, where π/m is the standard resolution of this problem. Even though the 1D landscape is nonconvex, we prove a global convergence result for Gradient-MUSIC: coarse scanning provably finds suitable initialization and gradient descent converges at a linear rate. In addition to convergence results, we also upper bound the error between the true signal frequencies and amplitudes with those found by Gradient-MUSIC. For example, if the noise has $\ell^\infty$ norm at most ϵ, then the frequencies and amplitudes are recovered up to error at most Cϵ/m and Cϵ respectively, which are minimax optimal in m and ϵ. Our theory can also handle stochastic noise with performance guarantees under nonstationary independent Gaussian noise. Our main approach is a comprehensive geometric analysis of the landscape, a perspective that has not been explored before.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Uncertainty quantification of graph convolution neural network models of evolving processes

The application of neural network models to scientific machine learning tasks has proliferated in recent years. In particular, neural networks have proved to be adept at modeling processes with spatial–temporal complexity. Nevertheless, these highly parameterized models have garnered skepticism in their ability to produce outputs with quantified error bounds over the regimes of interest. Hence there is a need to find uncertainty quantification methods that are suitable for neural networks. In this work we present comparisons of the parametric uncertainty quantification of neural networks modeling complex spatial–temporal processes with Hamiltonian Monte Carlo and Stein variational gradient descent and its projected variant. Specifically we apply these methods to graph convolutional neural network models of evolving systems modeled with recurrent neural network and neural ordinary differential equations architectures. We show that Stein variational inference is a viable alternative to Monte Carlo methods with some clear advantages for complex neural network models. For our exemplars, Stein variational interference gave similar pushed forward uncertainty profiles through time compared to Hamiltonian Monte Carlo, albeit with generally more generous variance. As a result, projected Stein variational gradient descent also produced similar uncertainty profiles to the non-projected counterpart, but large reductions in the active weight space were confounded by the stability of the neural network predictions and the convoluted likelihood landscape.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Stochastic noise can be helpful for variational quantum algorithms

Saddle points constitute a crucial challenge for first-order gradient descent algorithms. In notions of classical machine learning, they are avoided, for example, by means of stochastic gradient descent methods. In this work, we provide evidence that the saddle-points problem can be naturally avoided in variational quantum algorithms by exploiting the presence of stochasticity. We prove convergence guarantees and present practical examples in numerical simulations and on quantum hardware. We argue that the natural stochasticity of variational algorithms can be beneficial for avoiding strict saddle points, i.e., those saddle points with at least one negative Hessian eigenvalue. This insight that some levels of shot noise could help is expected to add a new perspective to notions of near-term variational quantum algorithms. Published by the American Physical Society 2025

Liu, Junyu↗
DOE OSTI2024

Finding MIDDLE Ground: Scalable and Secure Distributed Learning

Edge computing methods allow devices to efficiently train a high-performing, robust, and personalized model for predictive tasks. However, these methods succumb to privacy and scalability concerns such as adversarial data recovery and expensive model communication. Furthermore, edge computing methods unrealistically assume that all devices train an identical model. In practice, edge devices have varying computational and memory constraints which may not allow certain devices to have the space or speed to train a specific model. To overcome these issues, we propose MIDDLE: a model independent distributed learning algorithm which allows heterogeneous edge devices to assist each other’s training while communicating only non-sensitive information. MIDDLE unlocks the ability for edge devices, regardless of computational or memory constraints, to assist each other even with completely different model architectures. Furthermore, MIDDLE does not require model or gradient communication which greatly reduces communication size and time. We prove that MIDDLE attains the optimal convergence rate O(1/sqrt(TM)) of stochastic gradient descent for convex and non-convex smooth optimization (for total iterations T and batch size M). Finally, our experimental results demonstrate that MIDDLE (even in non-IID data settings) attains robust and high-performing models without model or gradient communication.

Bornstein, Marc I.↗
DOE OSTI2024

Stochastic Optimization and Uncertainty Quantification of Natrium-based Nuclear-Renewable Energy Systems for Flexible Power Applications in Deregulated Markets

Rapid integration of variable renewable energy sources (VRES) has made modeling and stochastic optimization of hybrid energy systems crucial for studying their long-term performance and viability. However, most studies have focused on just historical data, which may be unreliable for capturing short-term fluctuations, rare events, and long-term patterns of energy demand, price, and the variability of renewable energy sources. For this study, optimal synthetic time series models were developed using Wasserstein distance. The models were validated by comparing the key statistical measures against those of the historical data. They were then used to optimize the integrated Natrium-style advanced energy systems and their long-term (30 years) economics. The stochastic model performs bi-level optimization to find the optimal sizes for the balance of plant and thermal energy storage, while also optimizing energy dispatch to achieve the maximum net present value. In studies of two deregulated markets (California ISO and the Electric Reliability Council of Texas), the integrated Natrium-style system performed better in CAISO than in ERCOT, given higher and more consistent electricity prices during peak-demand periods. The potentially enlarged cost associated with the variable operation and maintenance of the TES system also plays a significant role in driving the system sizing, thus its impacts on the system are investigated in detail through comparison against a baseline case. The study also finds that the bi-level optimization results based on stochastic gradient descent closely match the grid search results. The uncertainty quantification of the stochastic signals provides further NPV-related insights and probability distributions for the case studies. The normal standard error of the mean of NPV for the case with and without TES VOM for CAISO were found to be 7.73M (plus-minus sign) 1.09M USD and 104.99M (plus-minus sign) 1.25M USD, respectively based on a 95% confidence. Given the relatively small NPV variance based on 150 samples, the analysis affords the most robust possible prediction of the techno-economic performance of the integrated Natrium-style energy systems.

25 ENERGY STORAGE↗
DOE OSTI2024

A Kaczmarz-inspired approach to accelerate the optimization of neural network wavefunctions

Neural network wavefunctions optimized using the variational Monte Carlo method have been shown to produce highly accurate results for the electronic structure of atoms and small molecules, but the high cost of optimizing such wavefunctions prevents their application to larger systems. We propose the Subsampled Projected-Increment Natural Gradient Descent (SPRING) optimizer to reduce this bottleneck. SPRING combines ideas from the recently introduced minimum-step stochastic reconfiguration optimizer (MinSR) and the classical randomized Kaczmarz method for solving linear least-squares problems. We demonstrate that SPRING outperforms both MinSR and the popular Kronecker-Factored Approximate Curvature method (KFAC) across a number of small atoms and molecules, given that the learning rates of all methods are optimally tuned. For example, on the oxygen atom, SPRING attains chemical accuracy after forty thousand training iterations, whereas both MinSR and KFAC fail to do so even after one hundred thousand iterations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Krajewski, Adam M. (ORCID:0000000222660099)↗
DOE OSTI2025

Single-shot in-line x-ray phase-contrast imaging of void-shockwave interactions in fusion energy materials

Recent breakthroughs in nuclear fusion, specifically the report of reactions exceeding scientific breakeven at the National Ignition Facility (NIF), highlight the potential of inertial fusion energy (IFE) as a sustainable and virtually limitless energy source. However, further progress in IFE requires characterization of defects in ablator materials and how they affect fuel capsule compression. Voids within the ablator can degrade energy yield, but their impact on the density distribution has primarily been studied through simulations, with limited high-resolution experimental validation. To address this, we used the x-ray free-electron laser (XFEL) at the matter in extreme conditions (MECs) instrument at the Linac coherent light source (LCLS) to capture 2D x-ray phase-contrast (XPC) images of a void-bearing sample with a composition similar to inertial confinement fusion (ICF) ablators. By driving a compressive shockwave through the sample using MEC's long-pulse laser system, we analyzed how voids influence shockwave propagation and density distribution during compression. To quantify this impact, we extracted phase information using two phase retrieval algorithms. First, we applied the contrast transfer function (CTF) method, paired with Tikhonov regularization and a fast optimization approach to generate an initial phase estimate. We then refined the result using a projected gradient descent (PGD) method that works directly with the sample's refractive index. Comparing these results with radiation adaptive grid Eulerian (xRAGE) radiation hydrodynamic simulations enables identification of model validation needs or improvements. By calculating phase maps in situ, it becomes possible to reconstruct areal density maps, improving understanding of laser-capsule interactions and advancing IFE research.

Hodge, D. S. [Colorado State Univ., Fort Collins, ↗
DOE OSTI2024

Stochastic Optimization to Find Optimum Beginning-of-Life Core Configuration of Stable Salt Reactor with Online Refueling

A stochastic optimization method has been developed to find an optimum equilibrium cycle core configuration of the waste-burning stable salt reactor, which is a fast-spectrum molten salt reactor with frequent online refueling. An optimum core configuration was determined with the goal of minimizing radial power peaking. Because of the vast number of potential candidate core configurations, stochastic optimization was applied based on simulated annealing and an additional acceleration method, which screened out unpromising core configurations. It has been demonstrated that the developed stochastic optimization method successfully finds the optimal core configuration regardless of the initial guess and outperforms the gradient descent approach. In addition, it has been observed that the use of a so-called out-in core configuration as the initial guess speeds up convergence of the iterative solution more than five times. Based on the searched optimum equilibrium cycle core configuration, new beginning-of-life (BOL) core configurations have been developed. In conclusion, the new BOL core configurations will be used in developing optimum refueling strategies.

Moltex static salt reactor↗
DOE OSTI2025

Criticality analysis of nuclear binding energy neural networks

Machine learning methods, in particular deep learning methods such as artificial neural networks (ANNs) with many layers, have become widespread and useful tools in nuclear physics. However, these ANNs are typically treated as ‘black boxes’, with their architecture (width, depth, and weight/bias initialization) and the training algorithm and parameters chosen empirically by optimizing learning based on limited exploration. We test a non-empirical approach to understanding and optimizing nuclear physics ANNs by adapting a criticality analysis based on renormalization group flows in terms of the hyperparameters for weight/bias initialization, training rates, and the ratio of depth to width. This treatment utilizes the statistical properties of neural network initialization to find a generating functional for network outputs at any layer, allowing for a path integral formulation of the ANN outputs as a Euclidean statistical field theory. We use a prototypical example to test the applicability of this approach: a simple ANN for nuclear binding energies. We find that with training using a stochastic gradient descent optimizer, the predicted criticality behavior is realized, and optimal performance is found with critical tuning. However, the use of an adaptive learning algorithm leads to somewhat superior results without concern for tuning and thus obscures the analysis. Nevertheless, the criticality analysis offers a way to look within the black box of ANNs, which is a first step towards potential improvements in network performance beyond using adaptive optimizers.

artificial neural network↗
DOE OSTI2025

Feature learning and generalization in deep networks with orthogonal weights

Fully-connected deep neural networks with weights initialized from independent Gaussian distributions can be tuned to criticality, which prevents the exponential growth or decay of signals propagating through the network. However, such networks still exhibit fluctuations that grow linearly with the depth of the network, which may impair the training of networks with width comparable to depth. We show analytically that rectangular networks with tanh activations and weights initialized from the ensemble of orthogonal matrices have corresponding preactivation fluctuations which are independent of depth, to leading order in inverse width. Moreover, we demonstrate numerically that, at initialization, all correlators involving the neural tangent kernel (NTK) and its descendants at leading order in inverse width—which govern the evolution of observables during training—saturate at a depth of ~20, rather than growing without bound as in the case of Gaussian initializations. We speculate that this structure preserves finite-width feature learning while reducing overall noise, thus improving both generalization and training speed in deep networks with depth comparable to width. We provide some experimental justification by relating empirical measurements of the NTK to the superior performance of deep non-linear orthogonal networks trained under full-batch gradient descent on the MNIST and CIFAR-10 classification tasks.

97 MATHEMATICS AND COMPUTING↗