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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 OSTI2026

Gradient-informed Hamiltonian Monte Carlo for multicomponent CALPHAD model optimization and uncertainty quantification

CALPHAD model parameter optimization is inherently challenging due to non-smooth objective functions, high-dimensional parameter spaces, and the need for uncertainty quantification (UQ). Traditional weighted nonlinear least squares approaches are computationally efficient but local, whereas black-box global optimizers and ensemble Markov Chain Monte Carlo (MCMC) methods provide broader exploration at substantial computational cost. The objective of this work is to combine the global exploration capability of gradient-informed Hamiltonian Monte Carlo – specifically the No-U-Turn Sampler (NUTS) – with local deterministic refinement using BFGS to efficiently optimize multicomponent CALPHAD models with minimal manual intervention. Analytic gradients are computed via the Jansson derivative framework. The methodology is demonstrated on the Cr—Fe binary system and extended to the Cr—Fe—Ni ternary system with 32 degrees of freedom. For Cr—Fe, NUTS achieves comparable or superior optimality relative to ensemble MCMC while requiring over an order-of-magnitude fewer likelihood evaluations. Parameter uncertainties are quantified through NUTS sampling and propagated to thermodynamic observables using local expansion, demonstrating a novel modular approach that combines binary and ternary parameter subsets without requiring global relaxation. These results establish gradient-informed exploration as a scalable strategy for multicomponent CALPHAD optimization and provide a practical route towards efficient higher-order database development with quantified uncertainty.

36 MATERIALS SCIENCE↗
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 OSTI2024

MITgcm-AD v2: Open source tangent linear and adjoint modeling framework for the oceans and atmosphere enabled by the Automatic Differentiation tool Tapenade

The Massachusetts Institute of Technology General Circulation Model (MITgcm) is widely used by the climate science community to simulate planetary atmosphere and ocean circulations. A defining feature of the MITgcm is that it has been developed to be compatible with an algorithmic differentiation (AD) tool, TAF, enabling the generation of tangent-linear and adjoint models. These provide gradient information which enables dynamics-based sensitivity and attribution studies, state and parameter estimation, and rigorous uncertainty quantification. Importantly, gradient information is essential for computing comprehensive sensitivities and performing efficient large-scale data assimilation, ensuring that observations collected from satellites and in-situ measuring instruments can be effectively used to optimize a large uncertain control space. As a result, the MITgcm forms the dynamical core of a key data assimilation product employed by the physical oceanography research community: Estimating the Circulation and Climate of the Ocean (ECCO) state estimate. Although MITgcm and ECCO are used extensively within the research community, the AD tool TAF is proprietary and hence inaccessible to a large proportion of these users. The new version 2 (MITgcm-AD v2) framework introduced here is based on the source-to-source AD tool Tapenade, which has recently been open-sourced. Another feature of Tapenade is that it stores required variables by default (instead of recomputing them) which simplifies the implementation of efficient, AD-compatible code. The framework has been integrated with the MITgcm model’s main branch and is now freely available.

Adjoints↗
DOE OSTI2022

GIGA-Lens: Fast Bayesian Inference for Strong Gravitational Lens Modeling

We present GIGA-Lens: a gradient-informed, GPU-accelerated Bayesian framework for modeling strong gravitational lensing systems, implemented in TensorFlow and JAX. The three components, optimization using multistart gradient descent, posterior covariance estimation with variational inference, and sampling via Hamiltonian Monte Carlo, all take advantage of gradient information through automatic differentiation and massive parallelization on graphics processing units (GPUs). We test our pipeline on a large set of simulated systems and demonstrate in detail its high level of performance. The average time to model a single system on four Nvidia A100 GPUs is 105 s. The robustness, speed, and scalability offered by this framework make it possible to model the large number of strong lenses found in current surveys and present a very promising prospect for the modeling of ${ \mathcal O }({10}^{5})$ lensing systems expected to be discovered in the era of the Vera C. Rubin Observatory, Euclid, and the Nancy Grace Roman Space Telescope.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Exploring Gradient-Based Multi-directional Controls in GANs

Generative Adversarial Networks (GANs) have been widely applied in modeling diverse image distributions. However, despite its impressive applications, the structure of the latent space in GANs largely remains as a black-box, leaving its controllable generation an open problem, especially when spurious correlations between different semantic attributes exist in the image distributions. To address this problem, previous methods typically learn linear directions or individual channels that control semantic attributes in the image space. However, they often suffer from imperfect disentanglement, or are unable to obtain multi-directional controls. Furthermore, in this work, in light of the above challenges, we propose a novel approach that discovers nonlinear controls, which enables multi-directional manipulation as well as effective disentanglement, based on gradient information in the learned GAN latent space. More specifically, we first learn interpolation directions by following the gradients from classification networks trained separately on the attributes, and then navigate the latent space by exclusively controlling channels activated for the target attribute in the learned directions. Empirically, with small training data, our approach is able to gain fine-grained controls over a diverse set of bi-directional and multi-directional attributes, and we showcase its ability to achieve disentanglement significantly better than state-of-the-art methods both qualitatively and quantitatively.

97 MATHEMATICS AND COMPUTING↗
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↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗
DOE OSTI2023

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Here, we consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients using finite differences of stochastic function evaluations within a common random number framework. We develop modified versions of a norm test and an inner product quasi-Newton test to control the sample sizes used in the stochastic approximations and provide global convergence results to the neighborhood of a locally optimal solution. We present numerical experiments on simulation optimization problems to illustrate the performance of the proposed algorithm. When compared with classical zeroth-order stochastic gradient methods, we observe that our strategies of adapting the sample sizes significantly improve performance in terms of the number of stochastic function evaluations required.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗
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 OSTI2023

Adaptive, problem-tailored variational quantum eigensolver mitigates rough parameter landscapes and barren plateaus

Abstract Variational quantum eigensolvers (VQEs) represent a powerful class of hybrid quantum-classical algorithms for computing molecular energies. Various numerical issues exist for these methods, however, including barren plateaus and large numbers of local minima. In this work, we consider the Adaptive, Problem-Tailored Variational Quantum Eiegensolver (ADAPT-VQE) ansätze, and examine how they are impacted by these local minima. We find that while ADAPT-VQE does not remove local minima, the gradient-informed, one-operator-at-a-time circuit construction accomplishes two things: First, it provides an initialization strategy that can yield solutions with over an order of magnitude smaller error compared to random initialization, and which is applicable in situations where chemical intuition cannot help with initialization, i.e., when Hartree-Fock is a poor approximation to the ground state. Second, even if an ADAPT-VQE iteration converges to a local trap at one step, it can still “burrow” toward the exact solution by adding more operators, which preferentially deepens the occupied trap. This same mechanism helps highlight a surprising feature of ADAPT-VQE: It should not suffer optimization problems due to barren plateaus and random initialization. Even if such barren plateaus appear in the parameter landscape, our analysis suggests that ADAPT-VQE avoids such regions by design.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Differentiable Simulation of a Liquid Argon Time Projection Chamber

Liquid argon time projection chambers (LArTPCs) are widely used in particle detection for their tracking and calorimetric capabilities. The particle physics community actively builds and improves high-quality simulators for such detectors in order to develop physics analyses in a realistic setting. The ability of these simulators to mimic real, measured data is limited by the modeling of the physical detectors used for data collection. This modeling can be improved by performing dedicated calibration measurements. Conventional approaches calibrate individual detector parameters or processes one at a time. However, the impact of detector processes is entangled, making this a poor description of the underlying physics. We introduce a differentiable simulator that enables a gradient-based optimization, allowing for the first time a simultaneous calibration of all detector parameters. We describe the procedure of making a differentiable simulator, highlighting the challenges of retaining the physics quality of the standard, non-differentiable version while providing meaningful gradient information. We further discuss the advantages and drawbacks of using our differentiable simulator for calibration. Finally, we provide a starting point for extensions to our approach, including applications of the differentiable simulator to physics analysis pipelines.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Gaussian processes meet NeuralODEs: a Bayesian framework for learning the dynamics of partially observed systems from scarce and noisy data

We present a machine learning framework (GP-NODE) for Bayesian model discovery from partial, noisy and irregular observations of nonlinear dynamical systems. The proposed method takes advantage of differentiable programming to propagate gradient information through ordinary differential equation solvers and perform Bayesian inference with respect to unknown model parameters using Hamiltonian Monte Carlo sampling and Gaussian Process priors over the observed system states. This allows us to exploit temporal correlations in the observed data, and efficiently infer posterior distributions over plausible models with quantified uncertainty. The use of the Finnish Horseshoe as a sparsity-promoting prior for free model parameters also enables the discovery of parsimonious representations for the latent dynamics. A series of numerical studies is presented to demonstrate the effectiveness of the proposed GP-NODE method including predator–prey systems, systems biology and a 50-dimensional human motion dynamical system. This article is part of the theme issue ‘Data-driven prediction in dynamical systems’.

Science & Technology - Other Topics↗
DOE OSTI2024

MULTI-LEADER: MULTI-source LEarning-Accelerated Design of high-Efficiency multi-stage compRessor (Final Technical Report)

The objective of MULTI-LEADER is to cut design costs by 80% while generating more energy-efficient designs of multi-stage compressors by developing and implementing novel machine learning (ML) techniques, which enable faster and fewer design iterations, improved solver performance, and concurrent multi-disciplinary design. Current industrial practices for the design of multi-stage compressors involve simulation-based design optimization with successive levels of model fidelity, iteratively evaluated between distinct disciplines, one stage at a time to tackle the high dimensional design variations. This project addresses these key design challenges: (1) concurrent optimization of multiple stages under many non-linear constraints; (2) multitude of evaluation of high-fidelity and expensive solvers and their gradients during optimization convergence in high-dimensional design; (3) multi-disciplinary design to maximize aerodynamic performance while guaranteeing structural integrity and additive manufacturability; (4) utilization of multiple fidelity of solvers with disparate parameterization and modeling assumptions. MULTI-LEADER achieved more than 5x speed up in detailed design of more energy-efficient compressors via these machine learning (ML) innovations: (i) rapid design surrogates by multi-source learning from diverse fidelities across multiple disciplines, (ii) physics-constrained data-augmented modeling for improved empiricism, (iii) generative manifold embedding for high dimensional concurrent design without gradient information; (iv) budget-constrained fidelity-adaptive sampling towards fewer design iterations.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2024

Differentiable Multiphysics Codes: A Breakthrough Technology for Simulation and Computing

This document summarizes the findings of a strategic planning exercise commissioned by the Weapons Simulation and Computing, Computational Physics (WSC/CP) program at the Lawrence Livermore National Laboratory (LLNL) in FY24. During the year, the committee met with multiple stakeholder communities to gather input, opinions, suggestions and concerns which have been incorporated throughout this document. The key findings from this exercise are summarized: • The development of multiphysics modelling and simulation (mod/sim) codes and software technologies, their deployment on exascale compute platforms, and their broad adoption across the NNSA is a major success of the Advanced Simulation and Computing (ASC) program and the Exascale Computing Project (ECP). Sustained investment in these core technologies is essential. • Today’s state of the art involves running ensembles of O(100K) simulations to perform uncertainty quantification (UQ) and design studies using multiple statistical methods such as Bayesian optimization to understand sensitivities of our models and explore parameterized design spaces. Even with exascale computing, we are practically limited to O(10) parameters in these studies since the number of simulations required to sample the space scales exponentially with the number of design parameters. • The data from these simulation ensembles is increasingly being used to train machine learned (ML) surrogates (or reduced order models, ROMs) which can then be used for optimization or real time design exploration. However, the trained surrogates are still limited in the number of parameters they can represent due to the sampling limitations previously noted. • Augmenting our suite of integrated multiphysics simulation codes, both current and emerging, with the ability to compute gradients (solution derivatives) of arbitrary simulation outputs with respect to (some or all) simulation inputs would be a breakthrough technology, opening the door to a new era of efficient and automated inverse design based on verified and validated mod/sim capabilities. • This capability, which we refer to as differentiable multiphysics codes (DMCs), would revolutionize both UQ and optimization studies by breaking the curse of dimensionality that presently limits our “gradient-free” ensemble based computing approach. A similar breakthrough occurred in the AI/ML community once the ability to compute gradients of arbitrary loss functions using back-propagation became commonplace. Gradient information from the multiphysics codes can also be used to dramatically improve the efficiency and scale of training of ML/ROM surrogates for rapid assessments. • Achieving this in our suite of codes will be a grand challenge, similar to the amount of effort that was required to transition from CPU to GPU computing. It will require buy-in from the entire WSC/CP program and beyond, including all integrated codes, physics and engineering models, third-party library dependencies and performance portability abstractions. It will also require investment in research and development of numerical methods for computing adjoints of coupled physics across multiple adaptively refined moving meshes and of stochastic (Monte Carlo) and mesh free (SPH) methods. • New software and numerical techniques, largely pioneered by the AI/ML community, make this feasible. Chief among these is automatic differentiation (AD), the ability to employ AD at point-wise locations in a physics calculation (instead of traditional black-box approaches) and the ability to perform “back-propagation in time” (or reverse mode AD) for non-linear partial differential equations (PDEs). Fundamentally, the conclusion of this strategic planning exercise is that the time is right to undertake a large scale effort in WSC, centered on the existing integrated codes, to continue the natural evolution of mod/sim in the age of AI/ML. Instead of attempting to replace mod/sim with purely data driven AI/ML models, we believe the key to success is to integrate AI/ML by building on top of the decades of hard-won knowledge and the verified/validated multiphysics modelling capability that is the hallmark of the ASC program.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Automated tuning for HMC mass ratios

We extended previous work on tuning HMC parameters using gradient information to include Hasenbusch mass ratios. The inclusion of mass ratios adds many more parameters that need to be tuned, and also allows for lots of variations in the choice of integrator pattern. We investigate the effectiveness of automatically tuning a large number of HMC parameters and compare the optimally tuned versions over a range of integrator variants.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Inexact Newton-CG algorithms with complexity guarantees

Abstract We consider variants of a recently developed Newton-CG algorithm for nonconvex problems (Royer, C. W. & Wright, S. J. (2018) Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477) in which inexact estimates of the gradient and the Hessian information are used for various steps. Under certain conditions on the inexactness measures, we derive iteration complexity bounds for achieving $\epsilon $-approximate second-order optimality that match best-known lower bounds. Our inexactness condition on the gradient is adaptive, allowing for crude accuracy in regions with large gradients. We describe two variants of our approach, one in which the step size along the computed search direction is chosen adaptively, and another in which the step size is pre-defined. To obtain second-order optimality, our algorithms will make use of a negative curvature direction on some steps. These directions can be obtained, with high probability, using the randomized Lanczos algorithm. In this sense, all of our results hold with high probability over the run of the algorithm. We evaluate the performance of our proposed algorithms empirically on several machine learning models. Our approach is a first attempt to introduce inexact Hessian and/or gradient information into the Newton-CG algorithm of Royer & Wright (2018, Complexity analysis of second-order line-search algorithms for smooth nonconvex optimization. SIAM J. Optim., 28, 1448–1477).

Mathematics↗