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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

Regularization via f -Divergence: An Application to Multi-Oxide Spectroscopic Analysis

In this paper, we explore the application of convolutional neural networks (CNNs) for predicting the chemical composition of complex geologic samples in a simulated Martian atmospheric environment. Specifically, we aim to characterize oxide weight percentages (wt.%) of rock samples analyzed by remote Laser-Induced Breakdown Spectroscopy (LIBS), framing the problem as a multi-target regression task . Neural networks trained on LIBS spectra are prone to overfitting due to high spectral complexity, limited labeled data, and measurement noise. While regularization is critical for improving generalization, common methods (e.g., ℓ 2 regularization) impose constraints not directly tied to data distribution properties. We propose a novel regularization method based on a specific ƒ-divergence induced by a graph-based estimator, designed to constrain the distributional discrepancy between predictions and targets. This regularizer serves a dual purpose: (a) mitigating overfitting by enforcing a constraint on the distributional difference between predictions and noisy targets, and (b) acting as an auxiliary loss that penalizes large divergences. To enable backpropagation, we develop a differentiable approximation of this particular ƒ-divergence, making the method feasible for neural networks. Experiments on ChemCam and SuperCam LIBS calibration spectra show that mathematical equation-divergence regularization outperforms or matches standard regularization methods (ℓ 1 , ℓ 2 , dropout) and the classical baseline, partial least squares (PLS). Combining ƒ-divergence regularization with standard regularization yields further performance gains, indicating that distributional regularization is useful in this context giving a promising direction for robust model training in planetary science applications. Source code is publicly available at Klein and Li (2025), https://doi.org/10.11578/dc.20250530.7.

58 GEOSCIENCES↗
DOE OSTI2025

Improved Bayesian regularization of inverse problems in vibrations and acoustics using noise-only measurements

Here, this paper studies Tikhonov regularization (ridge regression) parameter selection for problems in vibrations and acoustics. The selection method is based on a popular Bayesian method, but it incorporates measurements of sensor noise. The regularization parameter is closely related to the ratio of system input energy to noise energy, so noise measurements inform the inference procedure and improve parameter identification. In cases where standard Bayesian regularization identifies zero as the optimal regularization parameter, noise measurements guarantee a unique nonzero optimum. Sufficient theoretical criteria are developed for this guarantee. The method is verified in even-determined and under-determined configurations in an acoustic source localization simulation and a vibration load identification experiment. It is shown to yield significant improvements over existing empirical Bayesian regularization. Improvements are larger in the even-determined case and smaller in the under-determined case, wherein the inverse solution is less sensitive to the regularization parameter.

42 ENGINEERING↗
DOE OSTI2025

Qubit Regularization of Quantum Field Theories

To study quantum field theories on a quantum computer, we must begin with Hamiltonians defined on a finite-dimensional Hilbert space and then take appropriate limits. This approach can be seen as a new type of regularization for quantum field theories, which we refer to as qubit regularization. A related finite-dimensional regularization, known as the D-theory approach, was proposed long ago as a general framework for all quantum field theories. In this framework, the dimensionality of the local Hilbert space at each spatial point can increase as needed through an additional flavor index. To reproduce asymptotically free QFTs, most studies assume that qubit-regularized theories require extending the local Hilbert space to infinity. However, contrary to this common belief, recent discoveries in (1+1) dimensions have revealed two examples where asymptotic freedom appears to emerge within a strictly finite-dimensional local Hilbert space through a novel renormalization group (RG) flow. These findings motivate further investigation into whether asymptotically free gauge theories could also emerge within a strictly finite-dimensional local Hilbert space. To support these explorations, we propose an orthonormal basis called the monomer-dimer-tensor-network (MDTN) basis and use it to construct new types of qubit-regularized lattice gauge theories.

Chandrasekharan, Shailesh [Duke Univ., Durham, NC ↗
DOE OSTI2025

3D mesh regularization within an ALE code using a weighted line sweeping method

The Lagrangian formalism is widely used to simulate hydrodynamic responses in complex engineering applications, particularly those involving strong shock waves. However, as the mesh moves with the fluid, it can become highly distorted, requiring a regularization step. This involves constructing a new grid and remapping conservative quantities onto it to restore mesh quality. This work introduces a regularization method for block-structured meshes within a 3D ALE (Arbitrary Lagrangian-Eulerian) code. The proposed approach prevents mesh tangling while preserving the anisotropic features of the initial Lagrangian mesh. This regularization technique incorporates aspect ratio-based weights to control mesh smoothing. Unlike uniform rezoning techniques, this weighted approach maintains proximity to the Lagrangian mesh while improving mesh quality. Here, the method effectively handles concave geometries by mitigating the grid attraction phenomenon, which typically leads to mesh concentration along concave edges. Numerical experiments demonstrate its efficiency in regularizing severely deformed meshes, and its integration within the ALE framework is validated on challenging hydrodynamic test cases, including the triple point problem.

42 ENGINEERING↗
NASA NTRS1974

Low thrust space vehicle trajectory optimization using regularized variables

Optimizing the trajectory of a low thrust space vehicle usually means solving a nonlinear two point boundary value problem. In general, accuracy requirements necessitate extensive computation times. In celestial mechanics, regularizing transformations of the equations of motion are used to eliminate computational and analytical problems that occur during close approaches to gravitational force centers. It was shown in previous investigations that regularization in the formulation of the trajectory optimization problem may reduce the computation time. In this study, a set of regularized equations describing the optimal trajectory of a continuously thrusting space vehicle is derived. The computational characteristics of the set are investigated and compared to the classical Newtonian unregularized set of equations. The comparison is made for low thrust, minimum time, escape trajectories and numerical calculations of Keplerian orbits. The comparison indicates that in the cases investigated for bad initial guesses of the known boundary values a remarkable reduction in the computation time was achieved. Furthermore, the investigated set of regularized equations shows high numerical stability even for long duration flights and is less sensitive to errors in the guesses of the unknown boundary values.

Schwenzfeger, K. J.↗
DOE OSTI2026

Emergence of complex-regular eutectic patterns in Al–Ge: Observations from correlative nano-imaging

Eutectic solidification exemplifies nonequilibrium pattern formation, making it a well-studied moving boundary problem. Yet the mechanisms behind the formation of complex-regular microstructures – particularly in highly anisotropic systems with a significant volume fraction of a faceted phase – remain poorly understood. Our understanding of such systems is made complicated by the nonlinear interface kinetics and unique growth dynamics characteristic of faceted phases. To address these challenges, we investigate a model Al–Ge eutectic system, where the faceted Ge phase constitutes a substantial volume fraction (~0.35) and where the two solid phases arrange into so-called “fishbone” or “feather” complex-regular patterns. Using synchrotron-based x-ray nano-imaging and nanotomography with high spatial resolution (22 nm per pixel), we capture in real-time the evolution of the solid–liquid interfaces and the resulting three-dimensional microstructures in this faceted/non-faceted eutectic system. By integrating these observations with electron backscattered diffraction, we elucidate the crystallographic biases on the solidification process and the mechanisms driving the formation of such complex-regular microstructures. These findings inform a new growth model for irregular eutectics in (near-)symmetrical phase diagrams, offering insight on advanced microstructural design and processing strategies. More broadly, we demonstrate how interfacial curvature is generated in irregular eutectic alloys and how it depends on the volume fraction of the faceted phase.

36 MATERIALS SCIENCE↗
DOE OSTI2026

RegularizedOptimization.jl: A Julia framework for regularized and nonsmooth optimization

RegularizedOptimization.jl is a Julia package that implements families of quadratic regularization and trust-region methods for solving the nonsmooth optimization problem $^{\textrm{minimize}}_{𝑥∈ℝ^𝑛}$ 𝑓(𝑥) + ℎ(𝑥) subject to 𝑐(𝑥) = 0, (1) where 𝑓 ∶ ℝ 𝑛 → ℝ and 𝑐 ∶ ℝ 𝑛 → ℝ 𝑚 are continuously differentiable, and ℎ ∶ ℝ 𝑛 → ℝ∪{+∞} is lower semi-continuous. The nonsmooth objective ℎ can be a regularizer, such as a sparsity inducing penalty, model simple constraints, such as 𝑥 belonging to a simple convex set, or can be a combination of both. All 𝑓, ℎ, and 𝑐 can be nonconvex. RegularizedOptimization.jl provides a modular and extensible framework for solving (1), and developing novel solvers. Currently, the following solvers are implemented: • Trust-region solvers TR and TRDH (Aravkin et al., 2022; Leconte & Orban, 2025) • Quadratic regularization solvers R2, R2DH and R2N (Aravkin et al., 2022; Diouane, Habiboullah, et al., 2024) • Levenberg-Marquardt solvers LM and LMTR (Aravkin et al., 2024) used when 𝑓 is a least-squares residual. • Augmented Lagrangian solver AL (De Marchi et al., 2023). All solvers rely on first derivatives of 𝑓 and 𝑐, and optionally on their second derivatives in the form of Hessian-vector products. If second derivatives are not available, quasi-Newton approximations can be used. In addition, the proximal mapping of the nonsmooth part ℎ, or adequate models thereof, must be evaluated. At each iteration, a step is computed by solving a subproblem of the form (1) inexactly, in which 𝑓, ℎ, and 𝑐 are replaced with appropriate models around the current iterate. The solvers R2, R2DH, and TRDH are particularly well suited to solve the subproblems, though they are general enough to solve (1). All solvers are allocation-free, so re-solves incur no additional allocations. To illustrate our claim of extensibility, a first version of the AL solver was implemented by an external contributor. Furthermore, a nonsmooth penalty approach, described in Diouane, Gollier, et al. (2024), is currently being developed, that relies on the library to efficiently solve the subproblems.

Gollier, Maxence [Polytechnique Montréal, QC (Cana↗
NASA NTRS1971

The topology of the regularized integral surfaces of the 3-body problem

Momentum, angular momentum, and energy of integral surfaces in the planar three-body problem are considered. The end points of orbits which cross an isolating block are identified. It is shown that this identification has a unique extension to an identification which pairs the end points of orbits entering the block and which end in a binary collision with the end points of orbits leaving the block and which come from a binary collision. The problem of regularization is that of showing that the identification of the end points of crossing orbits has a continuous, unique extension. The regularized phase space for the three-body problem was obtained, as were regularized integral surfaces for the problem on which the three-body equations of motion induce flows. Finally the topology of these surfaces is described.

Easton, R.↗
DOE OSTI2025

A Regularized Variance-Reduced Modified Extragradient Method for Stochastic Hierarchical Games

We consider an N -player hierarchical game in which the i th player’s objective comprises of an expectation-valued term, parametrized by rival decisions, and a hierarchical term. Such a framework allows for capturing a broad range of stochastic hierarchical optimization problems, Stackelberg equilibrium problems, and leader-follower games. We develop an iteratively regularized and smoothed variance-reduced modified extragradient framework for iteratively approaching hierarchical equilibria in a stochastic setting. We equip our analysis with rate statements, complexity guarantees, and almost-sure convergence results. We then extend these statements to settings where the lower-level problem is solved inexactly and provide the corresponding rate and complexity statements. Our model framework encompasses many game theoretic equilibrium problems studied in the context of power markets. We present a realistic application to the study of virtual power plants, emphasizing the role of hierarchical decision making and regularization. Preliminary numerics suggest that empirical behavior compares well with theoretical guarantees.

Tikhonov regularization↗
DOE OSTI2025

Structure-preserving neural networks for the regularized entropy-based closure of a linear, kinetic, radiative transport equation

The main challenge of large-scale numerical simulation of radiation transport is the high memory and computation time requirements of discretization methods for kinetic equations. In this work, we derive and investigate a neural network-based approximation to the entropy-based closure method to accurately compute the solution of the multi-dimensional moment system with a low memory footprint and competitive computational time. We extend methods developed for the standard entropy-based closure to the regularized entropy-based closures. The main idea is to interpret structure-preserving neural network approximations of the regularized entropy-based closure as a two-stage approximation to the original entropy-based closure. We conduct a numerical analysis of this approximation and investigate optimal parameter choices. Our numerical experiments demonstrate that the method has a much lower memory footprint than traditional methods with competitive computation times and simulation accuracy. The code and all trained networks are provided on GitHub.

entropy closure↗
DOE OSTI2026

Regularization by denoising diffusion models for solving inverse PDE problems with application to full waveform inversion

Partial differential equation (PDE)-governed inverse problems are fundamental across various scientific and engineering applications; yet they face significant challenges due to nonlinearity, ill-posedness, and sensitivity to noise. Here, we introduce a computational framework, regularization by denoising using diffusion models for partial differential equations (RED-DiffEq), by integrating physics-driven inversion and data-driven learning. RED-DiffEq leverages pretrained diffusion models as a regularization mechanism for PDE-governed inverse problems. We apply RED-DiffEq to solve the full waveform inversion problem in geophysics, a challenging seismic imaging technique that seeks to reconstruct high-resolution subsurface velocity models from seismic measurement data. Our method shows enhanced accuracy and robustness compared to benchmark methods. Additionally, it exhibits strong generalization and domain decomposition capacity, enabling the inversion of more complex velocity models with larger domains than those used in training the diffusion model. Our framework can also be directly applied to diverse PDE-governed inverse problems.

Shan, Siming [Yale University, New Haven, CT (Unit↗
DOE OSTI2025

Monomer-dimer tensor-network basis for qubit-regularized lattice gauge theories

Traditional SU⁡(𝑁) lattice gauge theories (LGTs) can be formulated using an orthonormal basis constructed from the irreducible representations (irreps) 𝑉 𝜆 of the SU⁡(𝑁) gauge symmetry. On a lattice, the elements of this basis are tensor networks comprising dimer tensors on the links labeled by a set of irreps {𝜆 ℓ } and monomer tensors on sites labeled by {𝜆 𝑠 }. These tensors naturally define a local site Hilbert space, ℋ$^𝑔_𝑠$, on which gauge transformations act. Gauss’s law introduces an additional index 𝛼 𝑠 =1,2,…,𝒟⁡(ℋ$^𝑔_𝑠$) that labels an orthonormal basis of the gauge-invariant subspace of ℋ$^𝑔_𝑠$. This monomer-dimer tensor-network (MDTN) basis, |{𝜆 𝑠 },{𝜆 ℓ },{𝛼 𝑠 }⟩, of the physical Hilbert space enables the construction of new qubit-regularized SU⁡(𝑁) gauge theories that are free of sign problems while preserving key features of traditional LGTs. Here, we investigate finite-temperature confinement-deconfinement transitions in a simple qubit-regularized SU(2) and SU(3) gauge theory in 𝑑 =2 and 𝑑 =3 spatial dimensions, formulated using the MDTN basis, and show that they reproduce the universal results of traditional LGTs at these transitions. Additionally, in 𝑑 =1, we demonstrate using a plaquette chain that the string tension at zero temperature can be continuously tuned to zero by adjusting a model parameter that plays the role of the gauge coupling in traditional LGTs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

Regularization prescription for the mixing between nonlocal gluon and quark operators

It is well known that in the study of mixing between nonlocal gluon and quark bilinear operators there exists an ambiguity when relating coordinate space and momentum space results. In this work, we show that this ambiguity is due to the lack of a proper regularization prescription of the singularity that arises when the separation between the gluon/quark fields approaches zero. We then demonstrate that dimensional regularization resolves this issue and yields consistent results in both coordinate and momentum space. This prescription is also compatible with lattice extractions of parton distributions from nonlocal operators.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Source function from two-particle correlation function through entropy-regularized Richardson-Lucy deblurring

Source functions are obtained from p – p and d – α correlation functions by applying the Richardson-Lucy (RL) deblurring to the Koonin-Pratt (KP) equation. To prevent fitting of noise in the correlation function, total-variation (TV) regularization is employed that has been effective in ordinary image restoration. TV alone cannot ensure normalization of the source functions. To ensure the latter, we propose a maximum-entropy regularized RL algorithm (MEM-RL). We outline the MEM-RL formalism and optimization strategy for the KP equation, demonstrating its effectiveness on both simulated and experimental data, including the p – p and d – α correlation functions.

62 RADIOLOGY AND NUCLEAR MEDICINE↗
DOE OSTI2026

Deep Neural Networks are Adaptive to Function Regularity and Data Distribution in Approximation and Estimation

Deep learning has exhibited remarkable results across diverse areas. To understand its success, substantial research has been directed towards its theoretical foundations. Nev- ertheless, the majority of these studies examine how well deep neural networks can model functions with uniform regularities. In this paper, we explore a different angle: how deep neural networks can adapt to varying degrees of smoothness in functions and nonuni- form data distributions across different locations and scales. More precisely, we focus on a broad class of functions defined by nonlinear tree-based approximation methods. This class encompasses a range of function types, such as functions with uniform regularities and discontinuous functions. We develop nonparametric approximation and estimation theories for this class using deep ReLU networks. Our results show that deep neural networks are adaptive to the nonuniform smoothness of functions and nonuniform data distributions at different locations and scales. We apply our results to several function classes, and derive the corresponding approximation and generalization errors. The validity of our results is demonstrated through numerical experiments.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1969

Trajectory optimization using regularized variables

Regularized equations for a particular optimal trajectory are compared with unregularized equations with respect to computational characteristics, using perturbation type numerical optimization. In the case of the three dimensional, low thrust, Earth-Jupiter rendezvous, the regularized equations yield a significant reduction in computer time.

Lewallen, J. M.↗
NASA NTRS1972

The topology of the regularized integral surfaces of the 3-body problem.

A method is described by which the integral surface can be modified in such a way that Newton's equations of motion actually give a flow. The process of regularization of vector fields by surgery, as described by the author (1971) is reviewed. The planar 3-body problem and its regularization, and the topology of the integral surfaces are considered. The Lagrange-Jacobi identity is used to show that there exists an isolating block such that any orbit which ends in a triple collision must enter and remain in this block.

Easton, R.↗
NASA NTRS1982

Application of the regular associated solution model to the Cd-Te and Hg-Te binary systems

The regular associated solution model is used to treat the phase diagrams of the binary II-VI semiconductor alloy systems Hg-Te and Cd-Te. The equations for the species activity coefficients are used without approximations regarding the magnitudes of the various binary interchange energies or the functional dependence on component mol fraction. The values of the four-adjustable parameters required for description of each system are fixed by fitting liquidus data, and the resulting activity coefficients are used to calculate component partial pressures, which are compared with experimental values as an indpendent check of the validity of the model. The results show that the regular associated solution model provides a usefully accurate, but not complete, description for both the Hg-Te and Cd-Te systems. The relationship of this work to previous investigations is discussed.

Kelley, J. D.↗