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Results for “gradient-based algorithms”

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

A direct-adjoint approach for material point model calibration with application to plasticity

Here, this paper proposes a new approach for the calibration of material parameters in local elastoplastic constitutive models. The calibration is posed as a constrained optimization problem, where the constitutive model evolution equations for a single material point serve as constraints. The objective function quantifies the mismatch between the stress predicted by the model and corresponding experimental measurements. To improve calibration efficiency, a novel direct-adjoint approach is presented to compute the Hessian of the objective function, which enables the use of second-order optimization algorithms. Automatic differentiation is used for gradient and Hessian computations. Two numerical examples are employed to validate the Hessian matrices and to demonstrate that the Newton–Raphson algorithm consistently outperforms gradient-based algorithms such as L-BFGS-B.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Efficient wind farm layout optimization with the FLOWERS AEP model and analytic gradients

Wind farm layout optimization (WFLO) studies often aim to maximize the annual energy production (AEP) of a wind farm by choosing an arrangement of turbines that minimizes wake interactions. One way to reduce the cost of WFLO studies is by using more computationally efficient AEP models. The cost of standard AEP modeling approaches, based on the numerical integration of low-fidelity engineering wake models, scales poorly with the number of simulated discrete wind conditions. A second way to reduce cost when using a gradient-based algorithm is to supply exact gradient information instead of finite-difference estimates. However, analytical functions for the derivatives of AEP with respect to turbine positions are not always available in the conventional modeling approach. FLOWERS is a computationally inexpensive, analytical model for wind farm AEP that is specifically developed for WFLO applications. In this paper, we analyze the performance of the FLOWERS AEP model with analytic gradients in a layout optimization study compared with a reference optimization framework across three wind farm case studies. We find that the FLOWERS-based approach reduces computation time by a factor of 50–4000 and improves optimal AEP by about 0.3% with less than half of the variability in AEP across instances with randomized initial conditions. We also find the optimal layouts to be insensitive to model parameter tuning, making FLOWERS-based layout optimization a streamlined, user-friendly approach.

17 WIND ENERGY↗
DOE OSTI2026

JAXtronomy: A JAX port of lenstronomy

Gravitational lensing is a phenomenon where light bends around massive objects, resulting in distorted images seen by an observer. Studying gravitationally lensed systems provides insights into cosmology and astrophysics, including constraints of the expansion rate of the Universe and the distribution of dark matter. Thus, we introduce JAXtronomy, a re-implementation of the gravitational lensing software package lenstronomy (Birrer, 2021; Birrer & Amara, 2018) using JAX (Bradbury et al., 2018). JAX is a Python library that uses an accelerated linear algebra (XLA) compiler to improve the performance of computing software. Our core design principle of JAXtronomy is to maintain an identical API to that of lenstronomy. The main JAX features utilized in JAXtronomy are just-in-time compilation, which can lead to significant reductions in execution time, and automatic differentiation, which allows for the implementation of gradient-based algorithms that were previously impossible. Additionally, JAX allows code to be run on GPUs or parallelized across CPU cores, further boosting the performance of JAXtronomy.

astronomy↗
DOE OSTI2025

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full Waveform Inversion

Concrete is a major construction material worldwide and plays a crucial role in the nuclear industry. The elastic properties of concrete are prone to change and degrade while in service, as it is often subjected to extreme operational and environmental conditions. An accurate evaluation of concrete's elastic properties is thus essential to ensure structural integrity and safety. This is especially true for concrete in nuclear power plants, where irradiation effects significantly impact concrete mechanical properties. There are various methods to assess these properties, with ultrasound-based techniques showing high potential due to their nondestructive nature, cost-effectiveness, and safety. While several nondestructive evaluation methods exist, most rely on idealizations such as assuming homogeneous material and plane wavefronts. In this work, we address these issues by introducing an ultrasound-based nondestructive method aimed at reconstructing spatially varying images of concrete mechanical properties. By accurately modeling wave physics, including scattering and reflection, we overcome several of the aforementioned idealizations and aim to utilize the full waveform for imaging material properties through depth, resulting in more reliable images. Full waveform inversion (FWI) was first introduced by geophysicists to reconstruct subsurface elastic property images. The goal is to minimize the difference between simulated and recorded wavefield signals, often through gradient-based optimization algorithms. While FWI is primarily conducted using the acoustic approximation of the wave equation, few works focus on elastic FWI, where the goal is to reconstruct images of not only the pressure wave speed but also the shear wave speed and density (or their equivalents). This work explores the potential of using elastic FWI to predict concrete mechanical properties as an initial effort for a more accurate monitoring of concrete conditions in service. Reconstructing images of different elastic parameters enables more specificity and accurate condition diagnosis. This paper will detail this approach and provide examples demonstrating the effectiveness of elastic FWI in reconstructing comprehensive maps of concrete mechanical properties.

42 - ENGINEERING↗
DOE OSTI2025

Nondestructive Evaluation of Concrete: Elastic Property Imaging Through Full-Waveform Inversion

Concrete is a vital material in construction—especially in the nuclear industry, where it is used in critical structures such as containment vessels. Over time, concrete can degrade due to harsh operational and environmental conditions, necessitating that its elastic properties be accurately evaluated to ensure structural integrity and safety. Traditional nondestructive evaluation methods such as ultrasound-based techniques often rely on simplifying assumptions that may not hold true for concrete. This paper presents an advanced ultrasound-based method that uses elastic full-waveform inversion (EFWI) to create detailed images of concrete’s mechanical properties. By accurately modeling wave behaviors such as scattering and reflection, we aim to overcome the limitations of conventional ultrasonic-based methods. In this work, the imaging problem involved reconstructing the various elastic properties of a heterogenous concrete block with three steel rebars embedded in it. The ultrasonic measurements were synthetically generated from multiple sources and receivers, and the reconstruction process was performed using a gradient-based optimization algorithm. Our approach leveraged EFWI to reconstruct high-resolution images of the pressure wave speed, shear wave speed, and density. Multiple misfit functions—including L2-norm, cross-correlation (CC), and L1-norm—combined with total variation (TV) regularization and parameter constraints using a Sigmoid function—were explored for the reconstruction. The results demonstrated that using the L1-norm misfit function in conjunction with TV regularization and Sigmoid constraints significantly improved the reconstruction quality in comparison to traditional methods. This approach provided clearer images with fewer artifacts and better captured background heterogeneity. Our findings highlight that, when properly designed, EFWI carries great potential for providing comprehensive, more accurate, and more reliable assessments of concrete conditions, as is crucial for the maintenance and safety of nuclear power plant structures.

97 - MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Efficient derivative computation for unsteady fatigue-constrained nonlinear aero-structural wind turbine blade optimization

Gradient-based optimization offers significant efficiency advantages for wind turbine blade design, but its application has often been limited by the cost and accuracy of finite-difference derivative calculations, especially when fatigue constraints are considered. In this work, we systematically compare and evaluate four differentiation techniques, namely algorithmic differentiation, implicit differentiation, sparsity exploitation, and parallelization, to determine their effectiveness in computing accurate gradients through time-domain aero-structural simulations. By integrating these techniques with unsteady nonlinear aerodynamic and structural models, we develop software designed for accurate gradient computation. We show that combining these techniques addresses memory and runtime challenges associated with long simulations required by design load cases. Specifically, the most effective combination reduces derivative computation wall time by over an order of magnitude compared to finite differencing while maintaining superior accuracy. We demonstrate this approach in a proof-of-concept aero-structural optimization of a wind turbine blade that improves the cost of energy by 12.78 %. This comparative study establishes a viable approach for fatigue-aware blade design that balances computational efficiency with modeling accuracy.

17 WIND ENERGY↗
DOE OSTI2024

SNNVis: Visualizing Graph Embedding of Evolutionary Optimization for Spiking Neural Networks

While Spiking Neural Networks (SNNs) show a lot of promise, it is difficult to optimize them because applying traditional gradient-based optimization techniques is difficult. Even though evolutionary algorithms (EAs) have been shown to promise to optimize SNNs, understanding the relationship between evolving the characteristics of SNNs and their performance to improve the optimization algorithm is challenging because of the complex characteristics and huge population size. We propose visual analytics with novel graph embedding for evolutionary SNNs to address the challenges. While existing graph embedding techniques have limitations in preserving the specific features of the nodes and edges, our approach maintains them. Also, we develop visual analytics for understanding the relationship between the network performance and the features of nodes and edges and exploring and analyzing the evolving SNNs to build insights into improving the EA.

Chae, Junghoon [ORNL] (ORCID:0000000206016746)↗
DOE OSTI2025

Harnessing the power of gradient-based simulations for multi-objective optimization in particle accelerators

Abstract Particle accelerator operation requires simultaneous optimization of multiple objectives. Multi-objective optimization (MOO) is particularly challenging due to trade-offs between the objectives. Evolutionary algorithms, such as genetic algorithms (GAs), have been leveraged for many optimization problems, however, they do not apply to complex control problems by design. This paper demonstrates the power of differentiability for solving MOO problems in particle accelerators using a deep differentiable reinforcement learning (DDRL) algorithm. We compare the DDRL algorithm with model-free reinforcement learning (MFRL), GA, and Bayesian optimization (BO) for simultaneous optimization of heat load and trip rates in the continuous electron beam accelerator facility. The underlying problem enforces strict constraints on both individual states and actions as well as cumulative (global) constraints on energy requirements of the beam. Using historical accelerator data, we develop a physics-based surrogate model which is differentiable and allows for back-propagation of gradients. The results are evaluated in the form of a Pareto-front with two objectives. We show that the DDRL outperforms MFRL, BO, and GA on high dimensional problems.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Deep Learning without Global Optimization by Random Fourier Neural Networks

Here we introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴ speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously previously impossible with conventional tools while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2025

Digital Twin Framework for PIP-II Linac: AI-Driven Multi-Scale Modeling from Ion Source to 800 MeV

The PIP-II linac will enable >1.2 MW beam power for DUNE, requiring unprecedented operational reliability across its warm front-end (RFQ, MEBT) and five distinct SRF sections operating at 162.5/325/650 MHz. We present a comprehensive digital twin framework uniquely combining a fully differentiable fast beam transport code with neural network surrogates trained on high-fidelity PIC simulations, capturing space charge and nonlinear dynamics beyond traditional envelope codes while achieving 10⁴× speedup at <1% accuracy. End-to-end differentiability enables gradient-based optimization across 500+ parameters simultaneously—previously impossible with conventional tools—while the model incorporates static/dynamic errors and serves as a virtual commissioning platform for diverse hardware integration. The framework facilitates reinforcement learning for pulsed/CW mode transitions, predictive maintenance through anomaly detection, and autonomous tuning algorithm development with real-time execution capability. Validation against physics simulations shows excellent agreement for the front-end, with initial results demonstrating potential for 30% commissioning time reduction and proactive fault mitigation, providing a scalable blueprint for operating next-generation high-intensity accelerators.

Pathak, Abhishek [Fermilab] (ORCID:000000021704208↗
DOE OSTI2025

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

adaptation models↗
DOE OSTI2024

Learning with Adaptive Conservativeness for Distributionally Robust Optimization: Incentive Design for Voltage Regulation: Preprint

Information asymmetry between the Distribution System Operator (DSO) and Distributed Energy Resource Aggregators (DERAs) obstructs designing effective incentives for voltage regulation. To capture this effect, we employ a Stackelberg game-theoretic framework, where the DSO seeks to overcome the information asymmetry and refine its incentive strategies by learning from DERA behavior over multiple iterations. We introduce a model-based online learning algorithm for the DSO, aimed at inferring the relationship between incentives and DERA responses. Given the uncertain nature of these responses, we also propose a distributionally robust incentive design model to control the probability of voltage regulation failure and then reformulate it into a convex problem. This model allows the DSO to periodically revise distribution assumptions on uncertain parameters in the decision model of the DERA. Finally, we present a gradient-based method that permits the DSO to adaptively modify its conservativeness level, measured by the size of a Wasserstein metric-based ambiguity set, according to historical voltage regulation performance. The effectiveness of our proposed method is demonstrated through numerical experiments.

distribution system operator↗
DOE OSTI2025

Alternating and Gaussian Fermionic Isometric Tensor Network States

Isometric tensor networks in two dimensions enable efficient and accurate study of quantum many-body states, yet the effect of the isometric restriction on the represented quantum states is not fully understood. We address this question in two main contributions. First, we introduce an improved variant of isometric tensor network states (isoTNS) in two dimensions, where the isometric arrows on the columns of the network alternate between pointing upward and downward; hence the name alternating isometric tensor network states. Second, we introduce a numerical tool—the isometric Gaussian fermionic TNS (isoGfTNS)—that incorporates isometric constraints into the framework of Gaussian fermionic tensor network states. We demonstrate in numerous ways that alternating isoTNSs represent many-body ground states of two-dimensional quantum systems significantly better than the original isoTNSs. First, we show that the entanglement in an isoTNS is mediated along the isometric arrows and that alternating isoTNSs mediate entanglement more efficiently than conventional isoTNSs. Second, alternating isoTNSs correspond to a deeper, and thus more representative, sequential-circuit construction of depth 𝒪⁢(𝐿𝑥 ⋅𝐿𝑦) compared to the original isoTNSs of depth 𝒪⁢(𝐿𝑥 +𝐿𝑦). Third, using the Gaussian framework and gradient-based energy minimization, we provide numerical evidence of better bond-dimension scaling and variational energy of alternating isoGfTNSs for ground states of various free-fermionic models, including the Fermi surface, the band insulator, and the 𝑝𝑥 +𝑖⁢𝑝𝑦 mean-field superconductor. Finally, benchmarking on the transverse-field Ising model, we demonstrate that an alternating isoTNS provides substantially improved performance and stability relative to the original isoTNS for the ground-state search algorithm in interacting systems.

Wu, Yantao [Chinese Academy of Sciences, Beijing (↗
DOE OSTI2025

Analytical gradient-based optimization of CALPHAD model parameters

The calibration of CALPHAD (CALculation of PHAse Diagrams) models involves the solution of a very challenging high-dimensional multiobjective optimization problem. Traditional approaches to parameter fitting predominantly rely on gradient-free methods, which while robust, are computationally inefficient and often scale poorly with model complexity. In this work, we introduce and demonstrate a generalizable framework for analytic gradient-based optimization of the parameters of the CALPHAD model enabled by the recently formalized Jansson derivative technique. This method allows for efficient evaluation of gradients of thermodynamic properties at equilibrium with respect to model parameters, even in the presence of arbitrarily complex internal degrees of freedom. Leveraging these semi-analytic gradients, we employ the conjugate gradient (CG) method to optimize thermodynamic model parameters for four binary alloy systems: Cu-Mg, Fe-Ni, Cr-Ni, and Cr-Fe. Across all systems, CG achieves comparable or superior optimality relative to Bayesian ensemble Markov Chain Monte Carlo (MCMC) with improvements in computational efficiency ranging from one to three orders of magnitude. Furthermore, our results establish a new paradigm for CALPHAD assessments in which high fidelity data-rich model calibration becomes tractable using deterministic gradient-informed algorithms.

CALPHAD↗
DOE OSTI2024

Optimization using pathwise algorithmic derivatives of electromagnetic shower simulations

Among the well-known methods to approximate derivatives of expectancies computed by Monte-Carlo simulations, averages of pathwise derivatives are often the easiest one to apply. Computing them via algorithmic differentiation typically does not require major manual analysis and rewriting of the code, even for very complex programs like simulations of particle-detector interactions in high-energy physics. However, the pathwise derivative estimator can be biased if there are discontinuities in the program, which may diminish its value for applications. This work integrates algorithmic differentiation into the electromagnetic shower simulation code HepEmShow based on G4HepEm, allowing us to study how well pathwise derivatives approximate derivatives of energy depositions in a sampling calorimeter with respect to parameters of the beam and geometry. We found that when multiple scattering is disabled in the simulation, means of pathwise derivatives converge quickly to their expected values, and these are close to the actual derivatives of the energy deposition. Additionally, we demonstrate the applicability of this novel gradient estimator for stochastic gradient-based optimization in a model example.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Reduced-dimension Bayesian optimization for model calibration of transient vapor compression cycles

Development and calibration of first-principles dynamic models of vapor compression cycles (VCCs) is of critical importance for applications that include control design and fault detection and diagnostics. Nevertheless, the inherent complexity of models that are represented by large systems of differential–algebraic equations leads to significant challenges for model calibration processes that utilize classical gradient-based methods. Bayesian optimization (BO) is a sample-efficient and gradient-free approach using a probabilistic surrogate model and optimal search over a feasible parameter space. Despite the benefits of BO in reducing computational costs, challenges remain in dealing with a high-dimensional calibration task resulting from a large set of parameters that have significant impacts on system behavior and need to be calibrated simultaneously. This paper presents a reduced-dimension BO framework for calibrating transient VCCs models where the calibration space is projected to a low-dimensional subspace for accelerating convergence of the solution algorithm and consequently reducing the number of transient simulations. The proposed approach was demonstrated via two case studies associated with different VCC applications where 10 parameters were calibrated in each case using laboratory measurements. The reduced-dimension BO framework only required 1 / 8 th of the iterations associated with a standard BO method that deals with high-dimensional calibration parameters for converged solutions and yielded comparable accuracy. Furthermore, both calibrated models revealed significant accuracy improvements compared to uncalibrated models.

Ma, Jiacheng↗
DOE OSTI2026

Classical-Quantum Algorithm for Solving Stochastic Programs

Stochastic programming provides a rigorous mathematical framework for making decisions under uncertainty in a risk-aware manner. Two-stage stochastic programming is, perhaps, the simplest form of this framework. Here the first-stage variables represent decisions that must be made "here and now" in the face of uncertainty, while the second-stage variables are decisions made after uncertain events. However, the broad adoption of stochastic programming has been hindered by computational challenges caused by the two-stage stochastic programming formulation which requires solving an ensemble of optimization problems. Using quantum amplitude estimation (QAE), quantum computers have shown the theoretic ability to compute expectations with Monte-Carlo methods with quadratically fewer samples than classical methods. In this work, we present a quantum algorithm for computing the expectation term using QAE for given first-stage decisions. Further, we detail methods of computing gradient information from the quantum calculation enabling the application of classical gradient-based optimization techniques. The result is a classical-quantum hybrid method of solving two-stage stochastic programs. These techniques are demonstrated with computational experiments based an engineering optimization problem.

97 MATHEMATICS AND COMPUTING↗