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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 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Searching for the Most Harmful Field Errors in the HSR IR Superconducting Magnets

In this project, we improve beam stability for the Electron-Ion Collider. Magnetic field errors can reduce beam stability, making it essential to identify the field errors that have the greatest impact on accelerator performance. However, this is particularly challenging because beam stability depends on the complex interactions of many magnetic field errors, resulting in a high-dimensional and nonlinear optimization problem. We determine which field errors are the most influential for the large physical aperture superconducting magnet B2PF, a critical magnet in the Interaction Region (IR) in the Hadron Storage Ring (HSR). We complete and analyze nearly 30,000 simulations on the Brookhaven National Laboratory Linux Cluster by varying 18 nonlinear magnetic field errors. We evaluate beam stability using the dynamic aperture and the tune diffusion. We identify the field errors that most strongly influence beam stability and establish quantitative field error tolerances that improve accelerator performance.

43 PARTICLE ACCELERATORS↗
DOE OSTI2026

Using Filter Methods to Guide Convergence for ADMM, with Applications to Nonnegative Matrix Factorization Problems

Nonconvex, nonlinear optimization problems arise naturally in parameter fitting and machine learning. While augmented Lagrangian methods have demonstrated robust convergence for classes of these problems, their convergence for block updates has been relatively unexplored outside of the context of the alternating direction method of multipliers (ADMM). ADMM has seen extensive use in these applications, but may exhibit uncertain convergence behavior in many practical nonconvex settings, and struggles with general nonlinear constraints. In contrast, filter methods have proved effective in enforcing convergence for sequential quadratic programming methods and interior point methods with feasibility criteria. We develop an ADMM-filter method for highly nonlinear and nonconvex problems. Here, we show convergence under mild assumptions for several types of coordinate descent schemes, and demonstrate our algorithm on nonnegative matrix factorization and completion problems in imaging and chemical spectrum analysis.

Nonconvex optimization↗
DOE OSTI2025

Solid State Transformer Controls for Mitigation of E3a High-Altitude Electromagnetic Pulse Insults

This paper explores the use of a solid state transformer (SST) to mitigate the 𝐸 3𝐴 component of a high-altitude electromagnetic pulse (HEMP) insult using external energy storage optimal control techniques. In lieu of conventional passive blocking devices or feedback-controlled energy storage devices, a novel implementation of Hamiltonian error tracking is utilized to develop a feedback control law for the variable converter ratio in an SST. The findings of the simulations performed in this paper suggest that additional energy storage is not necessary to protect an individual load from a HEMP insult. The simulations performed examine the response of a single-phase SST connected to a single voltage source on a long transmission line on the one side and a single linear resistor on the other. The control law is specifically developed for the late-time, low-frequency portion of a HEMP insult, namely the 𝐸 3𝐴 components. The Hamiltonian error-based converter ratio control law is compared with nonlinear optimal feedforward controls to show that the HSSPFC is an external energy storage optimal controller.

HEMP mitigation↗
DOE OSTI2024

High speed vibration compensation using magnetic fiducials via NIMBLE

Additive manufacturing (AM) technology, specifically 3D printing, holds great promise for in-orbit manufacturing. In-space printing can significantly reduce the mass, cost, and risk of long-term space exploration by enabling replacement parts to be made as needed and reducing dependence on Earth. However, printing in a zero-gravity environment poses challenges due to the absence of a rigid ground for the print platform, which can result in vibrational and rotational forces that may impact printing integrity. Here, to address this issue, this paper proposes a novel linear magnetic position tracking algorithm, named Navigation Integrating Magnets By Linear Estimation (NIMBLE), for dynamic vibration compensation during 3D printing of truss structures in space. Compared to the most commonly used nonlinear optimization method, the NIMBLE algorithm is more than two orders of magnitude faster. With only a single 3-axis magnet sensor and a small NdFeB magnet, the NIMBLE algorithm provides a simple and easily implemented tracking solution for in-orbit 3D printing.

3D printing in space↗
DOE OSTI2025

Automated Resonance Fitting for Nuclear Data Evaluation

Global and national efforts to deliver high-quality nuclear data to users have a wide-ranging impact, affecting applications in national security, reactor operations, basic science, medicine, and more. Cross section evaluation is a major part of this effort, combining theory and experimentation to produce recommended values and uncertainties for reaction probabilities. Resonance region evaluation is a specialized type of nuclear data evaluation that can require significant manual effort and months of time from expert scientists. In this article, non-convex non-linear optimization methods are combined with concepts of inferential statistics to infer a resonance model from experimental data in an automated manner that is not dependent on prior evaluation(s). This methodology aims to enhance the workflow of a resonance evaluator by minimizing time, effort, and the potential for bias from prior assumptions, while enhancing reproducibility and documentation, thereby addressing well-known challenges in the field.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2026

Discovery of Probabilistic Dirichlet-to-Neumann Maps on Graphs

Dirichlet-to-Neumann maps enable the coupling of multiphysics simulations across computational subdomains by ensuring continuity of state variables and fluxes at artificial interfaces. We present a novel method for learning Dirichlet-to-Neumann maps on graphs using Gaussian processes, specifically for problems where the data obey a conservation law arising from an underlying partial differential equation. Our approach combines discrete exterior calculus and nonlinear optimal recovery to infer relationships between vertex and edge values. This framework yields data-driven predictions with uncertainty quantification across the entire graph, even when observations are limited to a subset of vertices and edges. By minimizing the reproducing kernel Hilbert space norm while penalizing kernel complexity through maximum likelihood estimation, our method ensures that the resulting surrogate strictly enforces conservation laws without overfitting. We demonstrate our method on two representative applications: subsurface flow in fracture networks and arterial blood flow. Finally, the results demonstrate that the method maintains high accuracy and well-calibrated uncertainty estimates even under severe data scarcity, highlighting its potential for scientific applications where limited data and reliable uncertainty quantification are critical.

Dirichlet-to-Neumann map↗
DOE OSTI2025

Technical Report on Subsurface Monitoring of the Brady Hot Spring Geothermal Site, Nevada, based upon Full Waveform Inversion

Abilities to accurately characterize the subsurface in a geothermal setting is key to assess and support production. An important element of geothermal reservoir monitoring is also the ability to investigate fluid transport within fracture network. This report focuses on improving subsurface imaging and monitoring in geothermal settings using full waveform inversion based on the adjoint method and time-lapse imaging. To assess our method, we rely on a dense seismic dataset collected in 2016 at the Brady Hot Springs geothermal site in Nevada for the DOE-funded project Poroelastic Tomography by Adjoint Inverse Modeling of Data from Seismology, Geodesy, and Hydrology. This dataset captures subsurface changes across four stages of geothermal power plant operations, which involve varying rates of fluid injection and extraction. Two velocity models were previously derived from this dataset using different methods: one based on travel times and another on sweep interferometry. Our first step is to refine these models using adjoint tomography, which has been applied successfully at global and regional-scales but is less common at the reservoir-scale. Two approaches are then explored for time-lapse analysis: directly comparing refined tomographic models from different stages or backpropagating waveform differences relative to a baseline tomographic model. The main take away is that both approaches highlight similar reservoir behaviors, but the latter approach is more computationally effective in capturing small-scale changes in subsurface properties. For this work, we leverage the use of Salvus (www.mondaic.com), an end-to-end seismic imaging solution, relying on the spectral element method to compute forward and adjoint simulations, and developed by Mondaic Ltd. It includes integrated workflow management that handles waveform and metadata, launches simulations, computes waveform misfits and adjoint sources, and iterates for model updates by nonlinear optimization.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Analysis of the Trusted Inertial Terrain-Aided Navigation Measurement Function

The trusted inertial terrain-aided navigation (TITAN) algorithm leverages an airborne vertical synthetic aperture radar to measure the range to the closest ground points along several prescribed iso-Doppler contours. These TITAN minimum-range, prescribed-Doppler measurements are the result of a constrained nonlinear optimization problem whose optimization function and constraints both depend on the radar position and velocity. Owing to the complexity of this measurement definition, analysis of the TITAN algorithm is lacking in prior work. This publication offers such an analysis, making the following three contributions: (1) an analytical solution to the TITAN constrained optimization measurement problem, (2) a derivation of the TITAN measurement function Jacobian, and (3) a derivation of the Cramér-Rao lower bound on the estimated position and velocity error covariance. These three contributions are verified via Monte Carlo simulations over synthetic terrain, which further reveal two remarkable properties of the TITAN algorithm: (1) the along-track positioning errors tend to be smaller than the cross-track positioning errors, and (2) the cross-track positioning errors are independent of the terrain roughness.

TITAN↗
DOE OSTI2025

A unified funnel restoration SQP algorithm

We consider nonlinearly constrained optimization problems and discuss a generic double-loop framework consisting of basic algorithmic ingredients that unifies a broad range of nonlinear optimization solvers. This framework has been implemented in the open-source solver Uno, a Swiss Army knife-like C++ optimization framework that unifies many nonlinearly constrained nonconvex optimization solvers. We illustrate the framework with a sequential quadratic programming (SQP) algorithm that maintains an acceptable upper bound on the constraint violation, called a funnel, that is monotonically decreased to control the feasibility of the iterates. Infeasible quadratic subproblems are handled by a feasibility restoration strategy. Globalization is controlled by a line search or a trust-region method. We prove global convergence of the trust-region funnel SQP method, building on known results from filter methods. We implement the algorithm in Uno, and we provide extensive test results for the trust-region line-search funnel SQP on small CUTEst instances.

Kiessling, David [Katholieke Univ. Leuven, Heverle↗
DOE OSTI2024

Riemannian Optimization Applied to AC Optimal Power Flow

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. This is done by using the Julia programming language and the Julia packages PowerModels.jl and Manopt.jl.

AC optimal power flow↗
DOE OSTI2024

Riemannian Optimization Applied to AC Optimal Power Flow: Preprint

The nonlinear, nonconvex AC optimal power flow problem is of growing importance as the nature of the power grid evolves. This problem can be difficult to solve for interior point methods. However, the advent of optimization algorithms over smooth Riemannian manifolds presents an alternative approach. The nonlinear, nonconvex constraints in the AC power flow problem form an embedded submanifold of Euclidean space. In this paper, the authors explore the performance of Riemannian optimization algorithms for the ACOPF problem where the optimization is performed directly on the AC power flow manifold. They demonstrate that these are viable computational alternatives to interior point methods. This is done by using Julia and the packages PowerModels.jl and Manopt.jl.

manifold optimization↗
DOE OSTI2024

Investigating nonlinear magnetohydrodynamics in an optimized, reactor-scale quasi-axisymmetric stellarator

We use the new simulation capabilities of the extended-magnetohydrodynamic (MHD) code, M3D-C1, to investigate the nonlinear MHD properties of a reactor-scale quasisymmetric stellarator equilibrium. Our model captures the self-consistent evolution of the magnetic field, temperature, density, and flow profiles without imposing restrictions on the structure of the first. We include the effects of resistivity using a realistic temperature-dependent Spitzer model, along with a model for heat transport that captures the key physical characteristic, namely, strongly anisotropic diffusion in directions perpendicular and parallel to the magnetic field. We consider a quasi-axisymmetric, finite-pressure equilibrium that was optimized for self-consistent bootstrap current, quasi-symmetry, and energetic particle confinement. Our assessment finds that the equilibrium is highly unstable to interchange-like pressure-driven instabilities near the plasma edge. The initially unstable modes rapidly destabilize other modes in the direction of the N-fold rotational symmetry (toroidal, in this case). For this equilibrium, N = 2, meaning destabilization of a large number of even-numbered toroidal Fourier modes. Thus, field-periodicity is likely to be an important factor in the nonlinear MHD stability characteristics of optimized stellarators.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2024

Sparse Cholesky factorization for solving nonlinear PDEs via Gaussian processes

In recent years, there has been widespread adoption of machine learning-based approaches to automate the solving of partial differential equations (PDEs). Among these approaches, Gaussian processes (GPs) and kernel methods have garnered considerable interest due to their flexibility, robust theoretical guarantees, and close ties to traditional methods. They can transform the solving of general nonlinear PDEs into solving quadratic optimization problems with nonlinear, PDE-induced constraints. However, the complexity bottleneck lies in computing with dense kernel matrices obtained from pointwise evaluations of the covariance kernel, and its partial derivatives, a result of the PDE constraint and for which fast algorithms are scarce. The primary goal of this paper is to provide a near-linear complexity algorithm for working with such kernel matrices. We present a sparse Cholesky factorization algorithm for these matrices based on the near-sparsity of the Cholesky factor under a novel ordering of pointwise and derivative measurements. The near-sparsity is rigorously justified by directly connecting the factor to GP regression and exponential decay of basis functions in numerical homogenization. We then employ the Vecchia approximation of GPs, which is optimal in the Kullback-Leibler divergence, to compute the approximate factor. This enables us to compute ϵ-approximate inverse Cholesky factors of the kernel matrices with complexity O(N log d (N/ϵ)) in space and O(N log 2d (N/ϵ)) in time. We integrate sparse Cholesky factorizations into optimization algorithms to obtain fast solvers of the nonlinear PDE. We numerically illustrate our algorithm’s near-linear space/time complexity for a broad class of nonlinear PDEs such as the nonlinear elliptic, Burgers, and Monge-Ampère equations. In summary, we provide a fast, scalable, and accurate method for solving general PDEs with GPs and kernel methods.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Robust Optimal Experimental Design of Infinite-Dimensional Bayesian Nonlinear Inverse Problems

Abstract. We consider robust optimal experimental design (ROED) for nonlinear Bayesian inverse problems governed by partial differential equations (PDEs). An optimal design is one that maximizes some utility quantifying the quality of the solution of an inverse problem. However, the optimal design is dependent on elements of the inverse problem such as the simulation model, the prior, or the measurement error model. ROED aims to produce an optimal design that is aware of the additional uncertainties encoded in the inverse problem and remains optimal even after variations in them. We follow a worst-case scenario approach to develop a new framework for robust optimal design of nonlinear Bayesian inverse problems. The proposed framework (a) is scalable and designed for infinite-dimensional Bayesian nonlinear inverse problems constrained by PDEs; (b) develops efficient approximations of the utility, namely the expected information gain; (c) employs eigenvalue sensitivity techniques to develop analytical forms and efficient evaluation methods of the gradient of the utility with respect to the uncertainties against which we wish to be robust; and (d) employs a probabilistic optimization paradigm that properly defines and efficiently solves the resulting combinatorial max-min optimization problem. The effectiveness of the proposed approach is illustrated for optimal sensor placement problem in an inverse problem governed by an elliptic PDE.

Chowdhary, Abhijit↗
DOE OSTI2025

Optimal Power Management for Large-Scale Battery Energy Storage Systems via Bayesian Inference

Large-scale battery energy storage systems (BESS) have found ever-increasing use across industry and society to accelerate clean energy transition and improve energy supply reliability and resilience. However, their optimal power management poses significant challenges: the underlying high-dimensional nonlinear nonconvex optimization lacks computational tractability in real-world implementation, and the uncertainty of the exogenous power demand makes exact optimization difficult. This paper presents a new solution framework to address these bottlenecks. The solution pivots on introducing power-sharing ratios to specify each cell’s power quota from the output power demand. To find the optimal power-sharing ratios, we formulate a nonlinear model predictive control (NMPC) problem to achieve power-loss-minimizing BESS operation while complying with safety, cell balancing, and power supply-demand constraints. We then propose a parameterized control policy for the power-sharing ratios, which utilizes only three parameters, to reduce the computational demand in solving the NMPC problem. This policy parameterization allows us to translate the NMPC problem into a Bayesian inference problem for the sake of 1) computational tractability, and 2) overcoming the nonconvexity of the optimization problem. We leverage the ensemble Kalman inversion technique to solve the parameter estimation problem. Concurrently, a low-level control loop is developed to seamlessly integrate our proposed approach with the BESS to ensure practical implementation. This low-level controller receives the optimal power-sharing ratios, generates output power references for the cells, and maintains a balance between power supply and demand despite uncertainty in output power. We conduct extensive simulations and experiments on a 20-cell prototype to validate the proposed approach.

Battery energy storage systems (BESSs)↗
DOE OSTI2025

A mixed-integer PDE-constrained optimization formulation for constructing electromagnetic cloaks with multiple materials

We study the design of an electromagnetic cloak from multiple materials with an additional constraint on the mass of the cloak. Our problem is an example of a topology optimization problem, and we formulate this problem as a mixed-integer partial-differential equation constrained optimization (MIPDECO) problem, where Maxwell’s equation models the propagation of the wave through the cloak and surrounding medium. We use binary variables to model the assignment of the different materials, and their relevant properties (permittivity and density). The mass constraint adds a nontrivial constraint to this problem. We propose a two-phase strategy to solve this problem. In the first phase, we solve a continuous relaxation, and then propose a new variant of the feasibility pump that exploits the structure of the PDE to obtain an initial integral solution candidate. In the second phase, we use a trust-region approach to improve this incumbent. We also consider a continuation or mesh-sequencing approach to find better solutions faster on consecutively finer meshes. We present detailed numerical results to illustrate the effectiveness of our approaches for constructing multi-material cloaks with a mass constraint.

Calculus of Variations and Optimization↗
DOE OSTI2025

Efficient proximal subproblem solvers for a nonsmooth trust-region method

In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. Finally, we compare algorithm performance on examples from data science and PDE-constrained optimization.

97 MATHEMATICS AND COMPUTING↗