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Results for “mathematical regularization”

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

Complex optimization for big computational and experimental neutron datasets

Here, we present a framework to use high performance computing to determine accurate solutions to the inverse optimization problem of big experimental data against computational models. We demonstrate how image processing, mathematical regularization, and hierarchical modeling can be used to solve complex optimization problems on big data. We also demonstrate how both model and data information can be used to further increase solution accuracy of optimization by providing confidence regions for the processing and regularization algorithms. Finally, we use the framework in conjunction with the software package SIMPHONIES to analyze results from neutron scattering experiments on silicon single crystals, and refine first principles calculations to better describe the experimental data.

36 MATERIALS SCIENCE↗

Inverse Analysis with Variational Autoencoders: A Comparison of Shallow and Deep Networks

Inverse problems are applied to determine unknown properties by matching observational data with a physical model that often takes many parameters as input. To overcome the underconstrained nature of inverse problems and achieve good performance, an approach is presented involving regularization with a technique known as a variational autoencoder (VAE), which is trained to map a high-dimensional parameter space with a complex structure to a low-dimensional latent space with a simple structure. We apply this approach to unconditioned realizations of the parameters (heterogeneous hydraulic fields) for a hydrogeological inverse problem. Two types of hydraulic conductivity fields are used to evaluate the characterization for the different levels of heterogeneity complexity of the physical inputs. This approach keeps the computational cost of generating the training data low. The reason is unconditioned realizations neither rely on the observational data used to perform the inverse analysis nor require any groundwater flow model forward runs. In addition, this approach applies regularization on a low-dimensional latent space from the VAE and increases optimization efficiency through automatic differentiation. Furthermore, two different neural network (NN) structures are tested for their utility in using the VAE for inverse analysis. The performance of a deep, convolutional neural network strongly depends on the dimensionality of the latent space, which requires tuning. In contrast, a shallow, dense neural network provides consistently accurate characterization without tuning. Furthermore, our approach evaluates the advantages of the shallow, dense neural network over the deep, convolutional one and enables future application to a wide range of inverse problems.

97 MATHEMATICS AND COMPUTING↗

On Some New Properties of Quaternion Functions

Quaternions discovered by W. R. Hamilton made a great contribution to the progress in noncommutative algebra and vector analysis. However, the analysis of quaternion functions has not been duly developed. The matter is that the notion of a derivative of quaternion functions of a quaternion variable has not been known until recently. The author has succeeded in improving the situation. The present work contains an account of the results obtained by him in this direction. The notion of an ℍ-derivative is introduced for quaternion functions of a quaternion variable. The existence of an ℍ-derivative of elementary functions is established retaining the well-known formulas for the corresponding functions from complex (real) analysis. The rules on the ℍ-differentiation of a sum, a product, and an inverse function are formulated and proved. Necessary and sufficient conditions for the existence of an ℍ-derivative are established. The notions of ℂ{sup 2}-differentiation and ℂ{sup 2}-holomorphy are introduced for quaternion functions of a quaternion variable. Three equivalent conditions are found, each of them being a necessary and sufficient one for ℂ{sup 2}-differentiation. Representations by an integral and a power series are given for ℂ{sup 2}-holomorphic functions. It is proved that the harmonicity of functions f(z), z · f(z), and f(z) · z is the necessary and sufficient condition for a function f to be Fueter-regular.

97 MATHEMATICS AND COMPUTING↗

Identifying Topological Defects in Lamellar Phases through Contour Analysis of Complex Wave Fields

Lamellar phases frequently contain structural imperfections that significantly affect their behaviors and properties. Our previous research successfully reconstructed real-space configurations of defective lamellar phases from diffuse scattering patterns, indicating the presence of phase vortices as a potential method for identifying topological defects disrupting the smectic ordering. Here, this report presents a mathematical framework using regularized wave fields to represent defective lamellar structures in real space. Phase singularities, resulting from the interference of random waves and indicating lamellar order disruption, are identified through a contour integral. These wave fields, derived from coherent scattering in reciprocal space, were validated via computational benchmarks analyzing small-angle neutron scattering data from AOT surfactant solutions, facilitating further statistical analysis of the defects. Our study highlights the potential to extract meaningful information about topological defects in lyotropic phases by inversely analyzing experimentally measured two-point static correlations. Our method allows for detailed structural analysis of various lyotropic phases, both particulate and nonparticulate, in their quiescent states and facilitates quantitative investigation of defects’ role in phase transitions. By integrating small-angle scattering, deep learning, and vortex tangle analysis, our comprehensive approach shows promise in addressing complex challenges in the structural analysis of soft matter systems.

36 MATERIALS SCIENCE↗

Autonomous Operations for Advanced Reactors Utilizing Supervisory Control

Automation is a critical tenet of reactor plant operations as reliance on nuclear energy increases. Nuclear power plants require a large workforce which does not scale with output; that is, the cost per megawatt increases as reactor output becomes smaller. The economic viability of advanced reactors, particularly small modular reactors (SMRs) and microreactors, requires a significantly reduced onsite workforce. The logical solution is establishing a systematic process of elimination of reliance on human operators, and to the extent possible, replacing these actions with automated functions. In this paper, we propose a method for such transformation to establish a robust technical basis to enable transition to autonomy. Our method is based on finite state automata (FSA)—also known as finite state machines (FSMs). Relying on this method allows us to exploit the rich set of mathematical proofs available in the field of regular languages. FSA are one of the mathematical tools to model discrete event systems (DES). These properties are applied to produce an automated startup controller for the Massachusetts Institute of Technology Research Reactor (MITR). The startup procedure is captured in terms of discrete changes from one state to another while an independent supervisory control system directs the sequence of states and alerts a human in the event of an abnormal operation. First, the design and behavior of the MITR rod control system were modeled in Simulink. Then, the startup procedure was applied to the rod control system and the DES performed a startup by procedurally withdrawing rods to the subcritical position. The simulation also stops rod motion in response to an uncontrollable event and restarts rod motion once the event has been cleared.

46 - INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AN↗

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↗

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code

A passive yaw implementation is developed, validated, and explored for the WEC-Sim, an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01° was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than 1°, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

Development and Validation of Passive Yaw in the Open-Source WEC-Sim Code: Preprint

A passive yaw implementation is developed, validated, and explored for the Wave Energy Converter Simulator (WEC-Sim), an open-source wave energy converter modeling tool that works within MATLAB/Simulink. The Reference Model 5 (RM5) is selected for this investigation, and a WEC-Sim model of the device is modified to allow yaw motion. A boundary element method (BEM) code was used to calculate the excitation force coefficients for a range of wave headings. An algorithm was implemented in WEC-Sim to determine the equivalent wave heading from a body’s instantaneous yaw angle and interpolate the appropriate excitation coefficients to ensure the correct time-domain excitation force. This approach is able to determine excitation force for a body undergoing large yaw displacement. For the mathematically simple case of regular wave excitation, the dynamic equation was integrated numerically and found to closely approximate the results from this implementation in WEC-Sim. A case study is presented for the same device in irregular waves. In this case, computation time is increased by 32x when this interpolation is performed at every time step. To reduce this expense, a threshold yaw displacement can be set to reduce the number of interpolations performed. A threshold of 0.01 was found to increase computation time by only 22x without significantly affecting time domain results. Similar amplitude spectra for yaw force and displacements are observed for all threshold values less than or equal to 1, for which computation time is only increased by 2.2x.

50 EE - Wind and Water Power Program - Water (EE-4↗

Groups with Almost Regular and Almost Perfect Involutions

We establish the solubility of a group with Sylow 2-subgroup of the least order in the centralizer of an almost regular involution. We also study the structure of a group G with an almost perfect and almost regular involution a.

97 MATHEMATICS AND COMPUTING↗

Risk-averse optimal control of semilinear elliptic PDEs

In this paper, we consider the optimal control of semilinear elliptic PDEs with random inputs. These problems are often nonconvex, infinite-dimensional stochastic optimization problems for which we employ risk measures to quantify the implicit uncertainty in the objective function. In contrast to previous works in uncertainty quantification and stochastic optimization, we provide a rigorous mathematical analysis demonstrating higher solution regularity (in stochastic state space), continuity and differentiability of the control-to-state map, and existence, regularity and continuity properties of the control-to-adjoint map. Our proofs make use of existing techniques from PDE-constrained optimization as well as concepts from the theory of measurable multifunctions. We illustrate our theoretical results with two numerical examples motivated by the optimal doping of semiconductor devices.

97 MATHEMATICS AND COMPUTING↗

Sparse Recovery for Scientific Data

We have built build and analyzed fundamental mathematical tools that enable sparse recovery of scientific data for high performance computing, experimental facilities and sensor measurement. The proposed work will impact many areas of research across the DOE. We have designed, developed and analyzed fast scalable algorithms for the sparse recovery of scientific data sets that may be extremely large, generated very quickly and distributed across multiple storage devices. The algorithms we developed will be used to process the copious amounts of scientific data generated by the DOE supercomputer simulations and by DOE experimental and observational facilities. They leverage the fact that while the amount of data produced can be extremely large, the actual quantities of interest (QoI's) are often sparse, either in space time, or in some feature space. Mathematically, notions of compressive sensing, including l1 regularized and total variation regularized optimization have played an important part in this effort.

97 MATHEMATICS AND COMPUTING↗

A configurational force for adaptive re-meshing of gradient-enhanced poromechanics problems with history-dependent variables

Here, we introduce a mesh-adaption framework that employs a multi-physical configurational force and Lie algebra to capture multiphysical responses of fluid-infiltrating geological materials while maintaining the efficiency of the computational models. To resolve sharp gradients of both displacement and pore pressure, we introduce an energy-estimate-free re-meshing criterion by extending the configurational force theory to consider the energy dissipation due to the fluid diffusion and the gradient-dependent plastic flow. To establish new equilibria after remeshing, the local tensorial history-dependent variables at the integration points are first decomposed into spectral forms. Then, the principal values and directions are projected onto smooth fields interpolated by the basis function of the finite element space via the Lie-algebra mapping. Our numerical results indicate that this Lie algebra operator in general leads to a new trial state closer to the equilibrium than the ones obtained from the tensor component mapping approach. A new configurational force for dissipative fluid-infiltrating porous materials that exhibit gradient-dependent plastic flow is introduced such that the remeshing may accommodate the need to resolve the sharp pressure gradient as well as the strain localization. The predicted responses are found to be not influenced by the mesh size due to the micromorphic regularization, while the adaptive meshing enables us to capture the width of deformation bands without the necessity of employing fine mesh everywhere in the domain.

42 ENGINEERING↗

An Online Plug-and-Play Algorithm for Regularized Image Reconstruction

Plug-and-play priors (PnP) is a powerful framework for regularizing imaging inverse problems by using advanced denoisers within an iterative algorithm. Recent experimental evidence suggests that PnP algorithms achieve state-of-the-art performance in a range of imaging applications. Here, we introduce a new online PnP algorithm based on the proximal gradient method (PGM). The proposed algorithm uses only a subset of measurements at every iteration, which makes it scalable to very large datasets. We present a new theoretical convergence analysis, for both batch and online variants of PnP-PGM, for denoisers that do not necessarily correspond to proximal operators. We also present simulations illustrating the applicability of the algorithm to image reconstruction in diffraction tomography. Finally, the results in this paper have the potential to expand the applicability of the PnP framework to very large datasets.

97 MATHEMATICS AND COMPUTING↗

A Method of Parametric Solution of Convolution Equations

A method of moments is developed for the parametric form the solution of convolution equations of the first kind. Two models, the gamma model and the shifted gamma model, are studied in details and a non-parametric approach based on regularization is presented.

97 MATHEMATICS AND COMPUTING↗

Nonstationary Problem of Complex Heat Transfer in a System of Semitransparent Bodies with Boundary-Value Conditions of Diffuse Reflection and Refraction of Radiation

We consider a nonstationary initial boundary-value problem describing complex (radiative-conductive) heat transfer in a system of semitransparent bodies. To describe radiation propagation, we use the radiation transfer equation with boundary-value conditions of diffuse reflection and refraction of radiation. We take into account that the radiation intensity and optical properties of bodies depend on the radiation frequency. The unique solvability of a weak solution is established. The comparison theorem is proved. A priori estimates of a weak solution as well as its regularity are obtained.

97 MATHEMATICS AND COMPUTING↗

An interlaboratory comparison of mid-infrared spectra acquisition: Instruments and procedures matter

Diffuse reflectance spectroscopy has been extensively employed to deliver timely and cost-effective predictions of a number of soil properties. However, although several soil spectral laboratories have been established worldwide, the distinct characteristics of instruments and operations still hamper further integration and interoperability across mid-infrared (MIR) soil spectral libraries. In this study, we conducted a large-scale ring trial experiment to understand the lab-to-lab variability of multiple MIR instruments. By developing a systematic evaluation of different mathematical treatments with modeling algorithms, including regular preprocessing and spectral standardization, we quantified and evaluated instruments' dissimilarity and how this impacts internal and shared model performance. We found that all instruments delivered good predictions when calibrated internally using the same instruments' characteristics and standard operating procedures by solely relying on regular spectral preprocessing that accounts for light scattering and multiplicative/additive effects, e.g., using standard normal variate (SNV). When performing model transfer from a large public library (the USDA NSSCKSSL MIR library) to secondary instruments, good performance was also achieved by regular preprocessing (e. g., SNV) if both instruments shared the same manufacturer. However, significant differences between the KSSL MIR library and contrasting ring trial instruments responses were evident and confirmed by a semi-unsupervised spectral clustering. For heavily contrasting setups, spectral standardization was necessary before transferring prediction models. Non-linear model types like Cubist and memory-based learning delivered more precise estimates because they seemed to be less sensitive to spectral variations than global partial least square regression. In summary, the results from this study can assist new laboratories in building spectroscopy capacity utilizing existing MIR spectral libraries and support the recent global efforts to make soil spectroscopy universally accessible with centralized or shared operating procedures.

58 GEOSCIENCES↗

Relaxed Multibang Regularization for the Combinatorial Integral Approximation

Multibang regularization and combinatorial integral approximation decompositions are two actively researched techniques for integer optimal control. In this work, we consider a class of polyhedral functions that arise particularly as convex lower envelopes of multibang regularizers and show that they have beneficial properties with respect to regularization of relaxations of integer optimal control problems. We extend the algorithmic framework of the combinatorial integral approximation such that a subsequence of the computed discrete-valued controls converges to the infimum of the regularized integer control problem.

97 MATHEMATICS AND COMPUTING↗