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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Leveraging operator learning to accelerate convergence of the preconditioned conjugate gradient method

We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient (PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on eigenvector approximations or recycled Krylov subspaces, we generate the deflation subspaces using operator learning, specifically the Deep Operator Network (DeepONet). To this aim, we introduce two complementary approaches for assembling the deflation operators. The first approach approximates near-null space vectors of the discrete PDE operator using the basis functions learned by the DeepONet. The second approach directly leverages solutions predicted by the DeepONet. To further enhance convergence, we also propose several strategies for prescribing the sparsity pattern of the deflation operator. Here, a comprehensive set of numerical experiments encompassing steady-state, time-dependent, scalar, and vector-valued problems posed on both structured and unstructured geometries is presented and demonstrates the effectiveness of the proposed DeepONet-based deflated PCG method, as well as its generalization across a wide range of model parameters and problem resolutions.

Deflation↗
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 OSTI2024

Stochastic average model methods

We consider the solution of finite-sum minimization problems, such as those appearing in nonlinear least-squares or general empirical risk minimization problems. We are motivated by problems in which the summand functions are computationally expensive and evaluating all summands on every iteration of an optimization method may be undesirable. Here we present the idea of stochastic average model (SAM) methods, inspired by stochastic average gradient methods. SAM methods sample component functions on each iteration of a trust-region method according to a discrete probability distribution on component functions; the distribution is designed to minimize an upper bound on the variance of the resulting stochastic model. We present promising numerical results concerning an implemented variant extending the derivative-free model-based trust-region solver POUNDERS, which we name SAM-POUNDERS.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

An Efficient Numerical Algorithm for Solving Coupled Time-Dependent Ginzburg-Landau Equation for Superconductivity and Elasticity

A decoupled finite element algorithm is developed for simulating the vortex dynamics on an elastic superconductor which couples the time-dependent Ginzburg- Landau equation with the complex-valued superconducting order parameter and the vector-valued magnetic potential, and the elasticity equation. We present an iterative algorithm for the decoupled system arising from the time and spatial discretization using a combination of preconditioner, algebraic multigrid method (AMG) and preconditioned conjugate gradient method (PCG). The iterative algorithm allows us to perform large-scale three-dimensional simulations of mesoscale pattern formation during superconducting phase transitions with arbitrary elastic boundary conditions. Here, the performance and efficiency of the algorithm are numerically verified by several benchmark problems, exhibiting up to two orders of magnitude improvement depending on the scale of discrete system compared to the exact solver.

Efficiency↗
DOE OSTI2024

Learning model combining convolutional deep neural network with a self-attention mechanism for AC optimal power flow

Alternating current optimal power flow (OPF) analysis is critical for efficient and reliable operation of power systems. For large systems or repetitive computations, the traditional methods such as the direct and gradient methods, or non-traditional methods, such as the genetic algorithm and simulating annealing, are time-consuming and unsuitable for real-time computing. The work in this paper proposes a novel framework to obtain the optimal solution of power flow in real-time using a combination of convolutional neural networks and a self-attention mechanism. All parameters of the power networks are rearranged in an image-like shape of a multi-channel image where each channel is a two-dimensional matrix. The proposed approach is adaptive with every input size of power systems as well as frequent variations of network topologies without intervention to the framework core. The encompassment of all power system contexts in which all parameters of internal elements, generation costs, and topology information are included, contributes to the higher accuracy of inference compared to other current machine-learning-based OPF-solving methods. Besides, the proposed framework established on ubiquitous platforms is effortlessly integrated into current infrastructures of power systems, and the great efficiency along with the computation speed may serve as a critical point for practical implications, such as enabling faster decision-making during real-time operations, predicting system contingencies, and remedial actions based on an offline pre-trained model. Furthermore, this supervised learning process is applied to the dataset of four case studies of meshed power systems: the IEEE 5-bus system (IEEE-5), the IEEE 30-bus system (IEEE-30), the IEEE 39-bus system (IEEE-39), and the IEEE 57-bus system (IEEE-57) to prove the efficacy of the proposed method.

42 ENGINEERING↗
DOE OSTI2025

Random Phase Approximation Correlation Energy Using Real-Space Density Functional Perturbation Theory

We present a real-space method for computing the random phase approximation (RPA) correlation energy within Kohn–Sham density functional theory, leveraging the low-rank nature of the frequency-dependent density response operator. In particular, we employ a cubic-scaling formalism based on density functional perturbation theory that circumvents the calculation of the response function matrix, instead relying on the ability to compute its product with a vector through the solution of the associated Sternheimer linear systems. We develop a large-scale parallel implementation of this formalism using the subspace iteration method in conjunction with the spectral quadrature method while employing the Kronecker product-based method for the application of the Coulomb operator and the conjugate orthogonal conjugate gradient method for the solution of the linear systems. We demonstrate convergence with respect to key parameters and verify the method’s accuracy by comparing with plane-wave results. We show that the framework achieves good strong scaling to many thousands of processors, reducing the time to solution for a lithium hydride system with 128 electrons to around 150 s on 4608 processors.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

CRCNS22 Learning Rules in the Hippocampus and their Mapping to Neuromorphic Systems (Final Technical Report)

Large scale biologically-realistic computational models are key to investigating the interplay between structure and function in nervous systems, thus paving the way to new clinical methods and neuro-inspired computing solutions. This project focuses on the hippocampus, in particular the CA3-CA1 regions, due to their role in associative learning and memory, pattern separation and completion, and spatial navigation. Investigations into the neuronal organization and learning rule(s) of this circuit can shed light into how declarative memories are formed, stored, recalled and forgotten and inform computational, experimental and clinical neuroscience work. Our project aims at developing a novel data-driven methodology supported by a broad heterogeneous base of neuroscience experimental knowledge and inspired from advances in computer science and engineering. Specifically, this work will benchmark existing and new learning rules within a full-scale spiking neural network simulation of the CA3-CA1 region. The model will be based on an open-source repository, called the Hippocampome, which contains neuronal morphologies, firing patterns, synapse probabilities, and most other required parameters for all known neuron types in the rodent hippocampal formation. The model will be first trained in a supervised fashion for associative memory tasks using backpropagation through time traditionally used in computer science, enhanced with a new technique called the surrogate gradient method. This optimization method will be used to obtain a global loss minimization, but it is not biologically inspired as it assumes the use of data not locally available to the synapses. However, we propose its use as a benchmarking tool, to compare the training performance of local biologically plausible and hardware-mappable learning rules at scale. New rules or combinations will be proposed and tested as needed, based on the obtained results. Progress in this area will also drive the development of novel hardware-mappable algorithms for continual lifelong learning and categorization of new events from few presented examples. This project goes beyond the existing state-of-the-art by looking at large scale realistic neuronal circuits as networks trainable via global optimization methods such as surrogate gradient descent. The objective function of the brain that supports learning is largely unknown, but it is likely that it operates through local learning rules. Studying network trajectories around local minima as proposed in this work represents a useful strategy for understanding whether a network is training by using a specific (set of) learning rule(s). Starting from a completely untrained network is a challenging test since it is difficult to determine how the learning rule affects the trajectory of the network. This interdisciplinary project will help understand what rule governs learning in these regions or if multiple learning rules are involved. The work will develop a robust methodology to measure if the network is converging to the target solution, oscillating around it, or diverging away.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2025

SymbolNet: neural symbolic regression with adaptive dynamic pruning for compression

Abstract Compact symbolic expressions have been shown to be more efficient than neural network (NN) models in terms of resource consumption and inference speed when implemented on custom hardware such as field-programmable gate arrays (FPGAs), while maintaining comparable accuracy (Tsoi et al 2024 EPJ Web Conf. 295 09036). These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming (GP), the search algorithm of most symbolic regression (SR) methods. Contrary to GP, the NN approach to SR offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose S y m b o l N e t , a NN approach to SR specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing SR methods that struggle with datasets containing more than O ( 10 ) inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).

Tsoi, Ho Fung (ORCID:0000000225502184)↗
DOE OSTI2023

Plant physical defenses contribute to a latitudinal gradient in resistance to insect herbivory within a widespread perennial grass

Premise: Herbivore pressure can vary across the range of a species, resulting in different defensive strategies. If herbivory is greater at lower latitudes, plants may be better defended there, potentially driving a latitudinal gradient in defense. However, relationships that manifest across the entire range of a species may be confounded by differences within genetic subpopulations, which may obscure the drivers of these latitudinal gradients. Methods: We grew plants of the widespread perennial grass Panicum virgatum in a common garden that included genotypes from three genetic subpopulations spanning an 18.5° latitudinal gradient. We then assessed defensive strategies of these plants by measuring two physical resistance traits—leaf mass per area (LMA) and leaf ash, a proxy for silica—and multiple measures of herbivory by caterpillars of the generalist herbivore fall armyworm (Spodoptera frugiperda). Results: Across all genetic subpopulations, low-latitude plants experienced less herbivory than high-latitude plants. Within genetic subpopulations, however, this relationship was inconsistent—the most widely distributed and phenotypically variable subpopulation (Atlantic) exhibited more consistent latitudinal trends than either of the other two subpopulations. The two physical resistance traits, LMA and leaf ash, were both highly heritable and positively associated with resistance to different measures of herbivory across all subpopulations, indicating their importance in defense against herbivores. Again, however, these relationships were inconsistent within subpopulations. Conclusions: Defensive gradients that occur across the entire species range may not arise within localized subpopulations. Thus, identifying the drivers of latitudinal gradients in herbivory defense may depend on adequately sampling the diversity within a species.

09 BIOMASS FUELS↗
DOE OSTI2025

Improved Guarantees for Optimal Nash Equilibrium Seeking and Bilevel Variational Inequalities

We consider a class of hierarchical variational inequality (VI) problems that subsumes VI-constrained optimization and several other problem classes, including the optimal solution selection problem and the optimal Nash equilibrium (NE) seeking problem. Our main contribution is threefold. (i) We consider bilevel VIs with monotone and Lipschitz continuous mappings and devise a single-timescale iteratively regularized extragradient method, named IR-EG 𝚖,𝚖 . We improve the existing iteration complexity results for addressing both bilevel VI and VI-constrained convex optimization problems. (ii) Under the strong monotonicity of the outer-level mapping, we develop a method named IR-EG 𝚜,𝚖 and derive faster guarantees than those in (i). We also study the iteration complexity of this method under a constant regularization parameter. These results appear to be new for both bilevel VIs and VI-constrained optimization. (iii) To our knowledge, complexity guarantees for computing the optimal NE in nonconvex settings do not exist. Motivated by this lacuna, we consider VI-constrained nonconvex optimization problems and devise an inexactly projected gradient method, named IPR-EG, where the projection onto the unknown set of equilibria is performed using IR-EG 𝚜,𝚖 with a prescribed termination criterion and an adaptive regularization parameter. We obtain new complexity guarantees in terms of a residual map and an infeasibility metric for computing a stationary point. Here, we validate the theoretical findings using preliminary numerical experiments for computing the best and the worst NEs.

bilevel optimization↗
DOE OSTI2025

A machine learning framework for accurate and robust analysis of radiation detector pulses

The microscopic properties of atomic nuclei are used to study various scientific questions. They are essential for understanding the fundamental forces of nature and the chemical evolution of the universe. Detecting decay radiation from radioactive nuclei makes it possible to probe these fundamental nuclear properties. Detector waveform traces may contain additional information about the radiation. Generally, advanced signal processing techniques are needed to extract this additional information, often involving fitting the waveform with model response functions using non-linear least-squares optimization with second-order gradient methods. While this is a powerful technique, it is also computationally expensive, leading to slow processing time, which scales with the volume of data. To address this problem, we have developed a machine learning (ML) approach that infers the characteristics of traces from a model detector response function. In particular, we are interested in classifying whether a single recorded trace consists of one or two pulse constituents and estimating the pulse parameters. Furthermore, our proposed ML method can precisely extract the pulses’ parameters, such as energy and timing information, and accurately classify the pulse multiplicity of a trace. Unlike non-learning-based approaches, our ML approach uses neural networks that are significantly faster at inference, as they do not require any optimization during this stage.

Curve fitting↗
DOE OSTI2025

Perspective on Many-Body Methods for Molecular Polaritonic Systems

Recent advances in strong light–matter interactions have revealed a wealth of new physical phenomena in molecules embedded in optical cavities, including modified chemical reactivity, altered excitation spectra, and novel quantum correlations. To describe these effects from first-principles, the field of ab initio quantum electrodynamics (QED) has emerged as a compelling extension of quantum chemistry that treats electronic and photonic degrees of freedom on equal footing. In this Perspective, we review the growing landscape of many-body QED methods, including Hartree–Fock, density functional theory (QEDFT), time-dependent DFT (QED-TDDFT), configuration interaction (QED-CI), complete active space (QED-CASSCF), coupled cluster (QED-CC), quantum Monte Carlo (QED-QMC), and density matrix renormalization group (QED-DMRG), highlighting recent developments and implementations. We further explore real-time methods, gradient and Hessian formalisms, and the integration of nonadiabatic nuclear dynamics. Applications range from benchmark simulations of polaritonic chemistry to quantum simulations on emerging quantum hardware. We conclude by outlining future directions for theory development and interdisciplinary efforts at the interface of quantum chemistry, condensed matter, and quantum optics.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Light in the dark forest. Part I. An efficient optimal estimator for 3D Lyman-alpha forest power spectrum

The highly anisotropic nature of the Lyman-alpha (Lyα) forest data introduces a complex survey window function that complicates the measurement of the three-dimensional power spectrum ( P 3D ). In this paper, we present the first fully optimal estimator for P 3D , which exactly deconvolves the survey window function and marginalizes contaminated modes that distort the power spectrum. Our approach adapts optimal estimator techniques developed for the 2D cosmic microwave background data to the 3D case. To achieve computational feasibility, we employ the conjugate gradient method and implement the P 3 M formalism to handle large-scale and small-scale operations separately and efficiently. We validate our estimator using Monte Carlo mocks and Gaussian simulations, demonstrating its accuracy and computational efficiency. We confirm that mode marginalization eliminates distortions arising from quasar continuum errors and delivers robust power spectrum estimation, though it also inflates errors at large scales. This first implementation works in the flat-sky case; we discuss the remaining steps needed to generalize it to the curved-sky case. This formalism offers a foundation for the Lyα forest P 3D measurements and a new path toward cosmological constraints from the Lyα forest data.

Lyman alpha forest↗
DOE OSTI2024

Efficient quantum circuits based on the quantum natural gradient

Efficient preparation of arbitrary entangled quantum states is crucial for quantum computation. This is particularly important for noisy intermediate-scale quantum simulators relying on variational hybrid quantum-classical algorithms. To that end, we propose symmetry-conserving modified quantum approximate optimization algorithm (SCom-QAOA) circuits. The depths of these circuits depend not only on the desired fidelity to the target state but also on the amount of entanglement the state contains. The parameters of the SCom-QAOA circuits are optimized using the quantum natural gradient method based on the Fubini-Study metric. The SCom-QAOA circuit transforms an unentangled state into a ground state of a gapped one-dimensional Hamiltonian with a circuit depth that depends not on the system size but rather on the finite correlation length. In contrast, the circuit depth grows proportionally to the system size for preparing low-lying states of critical one-dimensional systems. Even in the latter case, SCom-QAOA circuits with depth less than the system size were sufficient to generate states with fidelity in excess of 99%, which is relevant for near-term applications. The proposed scheme enlarges the set of the initial states accessible for variational quantum algorithms and widens the scope of investigation of nonequilibrium phenomena in quantum simulators. Published by the American Physical Society 2024

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2025

ARC-DPA 1-MeV Neutron Fluence Equivalence Model for GaAs

Here, the legacy data used in the production of the American Society for Testing and Materials (ASTM) E722 standard for gallium arsenide (GaAs) were fit with the athermal recombination corrected-displacements per atom (ARC-DPA) model for the development of a novel 1-MeV neutron equivalent fluence metric. Improving on previous work, the coefficients for the ARC-DPA model were optimized using a conjugate gradient method, and the uncertainties in the observed damage in different benchmark neutron fields were sampled to quantify their contribution to the damage metric. The optimized parameters of −0.474 ± 0.03 for b arcdpa and 0.016 ± 0.002 for c arcdpa provided good agreement and indicated that the solution is not sensitive to the corresponding fluence uncertainties. Compared to the current 1-MeV neutron fluence equivalence standard for displacement damage in GaAs, our results indicate that for a thermal reactor neutron environment, displacement damage has been underestimated by around 25% and that the saturation value for the damage efficiency had been higher than previously modeled.

1-MeV equivalent fluence↗
DOE OSTI2024

From Sim to Real: A Pipeline for Training and Deploying Traffic Smoothing Cruise Controllers

Designing and validating controllers for connected and automated vehicles to enhance traffic flow presents significant challenges, from the complexity of replicating real-world stop-and-go traffic dynamics in simulation, to the intricacies involved in transitioning from simulation to actual deployment. In this work, we present a full pipeline from data collection to controller deployment. Specifically, we collect 772 km of driving data from the I-24 in Tennessee, and use it to build a one-lane simulator, placing simulated vehicles behind real-world trajectories. Using policy-gradient methods with an asymmetric critic, we improve fuel efficiency by over 10% when simulating congested scenarios. Our comprehensive approach includes reinforcement learning for controller training, software verification, hardware validation and setup, and navigating various sim-to-real challenges. Furthermore, we analyze the controller's behavior and wave-smoothing properties, and deploy it on four Toyota Rav4’s in a real-world validation experiment on the I-24. Lastly, we release the driving dataset, the simulator and the trained controller, to enable future benchmarking and controller design.

42 ENGINEERING↗