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DOE OSTI2024

Spinbox: tools for many-body quantum systems in a Monte Carlo context

Spinbox is a piece of software that facilitates quantum mechanical calculations relevant to Monte Carlo simulation of atomic nuclei. At the front lines of research on the nuclear many-body problem are a large number of supercomputer-scale simulation codes. These codes produce valuable results but can be hard to understand, especially for those without intimate knowledge of the relevant theoretical methods. Thus, tools that fill pedagogical roles are extremely valuable. Spinbox makes it easy for one to replicate and analyze the computational processes relevant to a Quantum Monte Carlo (QMC) simulation that may be difficult to understand/debug/analyze due to the scale of the corresponding simulation software. Spinbox is written in Python using other state-of-the-art Python modules for numerical calculations. While a number of Python libraries exist that are suited to general quantum many-body calculations, the motivation of Spinbox is quite particular. In Diffusion Monte Carlo methods (DMC, GFMC, AFDMC), the central calculation is the imaginary-time propagation of individual samples of the many-body wavefunction. Although quantum wavefunctions generally must be described by a probability distribution over a basis, DMC imbues particles (within one sample) with classical spatial coordinates. This method is unusual, so other Python packages are typically not set up to do this easily. Furthermore, the software has built-in options for nuclear systems assuming isospin symmetry, which can be set up with other libraries but is a nontrivial process to do so. Features: - numerical representation of samples of the many-body wavefunctions, including tensor-product states (used in AFDMC) - numerical representation of many-body operators, including tensor-product operators: general, spin, imaginary-time propagation, etc. - the correct associated arithmetic and algebra, implemented as class methods - classes for representing realistic nuclear two- and three-body Hamiltonians (e.g. Argonne V18, Illinois NNN) - large-scale parallel integration over random variables, crucial for the AFDMC method My goal is to make this package open source so that anyone may use it and contribute to it, particularly other researchers doing AFDMC calculations

Fox, Jordan↗

DOE OSTI2022

GenMod: A generative modeling approach for spectral representation of PDEs with random inputs

Here, we propose a method for quantifying uncertainty in high-dimensional PDE systems with random parameters, where the number of solution evaluations is small. Parametric PDE solutions are often approximated using a spectral decomposition based on polynomial chaos expansions. For the class of systems we consider (i.e., high dimensional with limited solution evaluations) the coefficients are given by an underdetermined linear system in a regression formulation. This implies additional assumptions, such as sparsity of the coefficient vector, are needed to approximate the solution. Here, we present an approach where we assume the coefficients are close to the range of a generative model that maps from a low to a high dimensional space of coefficients. Our approach is inspired be recent work examining how generative models can be used for compressed sensing in systems with random Gaussian measurement matrices. Using results from PDE theory on coefficient decay rates, we construct an explicit generative model that predicts the polynomial chaos coefficient magnitudes. The algorithm we developed to find the coefficients, which we call GenMod, is composed of two main steps. First, we predict the coefficient signs using Orthogonal Matching Pursuit. Then, we assume the coefficients are within a sparse deviation from the range of a sign-adjusted generative model. This allows us to find the coefficients by solving a nonconvex optimization problem, over the input space of the generative model and the space of sparse vectors. We obtain theoretical recovery results for a Lipschitz continuous generative model and for a more specific generative model, based on coefficient decay rate bounds. We examine three high-dimensional problems and show that, for all three examples, the generative model approach outperforms sparsity promoting methods at small sample sizes.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2025

Nonparametric extensions of nuclear equations of state: Probing the breakdown scale of relativistic mean-field theory

Phenomenological calculations of the properties of dense matter, such as relativistic mean-field theories, represent a pathway to predicting the microscopic and macroscopic properties of neutron stars. However, such theories do not generically have well-controlled uncertainties and may break down within neutron stars. To faithfully represent the uncertainty in this breakdown scale, we develop a hybrid representation of the dense-matter equation of state, which assumes the form of a relativistic mean-field theory at low densities, while remaining agnostic to any nuclear theory at high densities. To achieve this, we use a nonparametric equation of state model to incorporate the correlations of the underlying relativistic mean-field theory equation of state at low pressures and transition to more flexible correlations above some chosen pressure scale. We perform astrophysical inference under various choices of the transition pressure between the theory-informed and theory-agnostic models. Here, we further study whether the chosen relativistic mean-field theory breaks down above some particular pressure and find no such evidence. Using simulated data for future astrophysical observations at about two-to-three times the precision of current constraints, we show that our method can identify the breakdown pressure associated with a potential strong phase transition.

Equations of state of nuclear matter↗

DOE OSTI2021

MB-Fit: Software infrastructure for data-driven many-body potential energy functions

Many-body potential energy functions (MB-PEFs), which integrate data-driven representations of many-body short-range quantum mechanical interactions with physics-based representations of many-body polarization and long-range interactions, have recently been shown to provide high accuracy in the description of molecular interactions from the gas to the condensed phase. Here, we present MB-Fit, a software infrastructure for the automated development of MB-PEFs for generic molecules within the TTM-nrg (Thole-type model energy) and MB-nrg (many-body energy) theoretical frameworks. Besides providing all the necessary computational tools for generating TTM-nrg and MB-nrg PEFs, MB-Fit provides a seamless interface with the MBX software, a many-body energy and force calculator for computer simulations. Given the demonstrated accuracy of the MB-PEFs, particularly within the MB-nrg framework, we believe that MB-Fit will enable routine predictive computer simulations of generic (small) molecules in the gas, liquid, and solid phases, including, but not limited to, the modeling of quantum isomeric equilibria in molecular clusters, solvation processes, molecular crystals, and phase diagrams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Effect of causality constraints on Bayesian analyses of heavy-ion collisions

There have long been questions about the limits to the validity of relativistic fluid dynamics and whether it is being used outside its regime of validity in modern simulations of relativistic heavy-ion collisions. An important new tool for answering this question is a causality analysis in the nonlinear regime—if the solutions of the evolution equations do not respect relativistic causality, then they are not a faithful representation of the underlying relativistic theory (in this case, quantum chromodynamics). Using this nonlinear criterion, it has recently been shown that hydrodynamics is indeed being used outside its regime of validity in simulations, at least sometimes. Here we explore the phenomenological implications, particularly the quantitative effects of demanding limits on acausality in modern Bayesian parameter estimation. We find that, while typically only a small fraction of the system's energy is initially in an acausal regime, placing strict limits on the allowed energy fraction significantly changes the preferred properties of the initial condition, which in turn alters the extracted medium properties such as bulk viscosity, where large values are no longer favored. Furthermore, these findings highlight the importance of developing better theoretical descriptions of the early-time, out-of-equilibrium dynamics of relativistic heavy-ion collisions.

Bayesian methods↗

DOE OSTI2025

Benders Decomposition Using Graph Modeling and Multi-Parametric Programming

Benders decomposition is a widely used method for solving large and structured optimization problems, but its performance is affected by the repeated solution of subproblems. We propose a flexible and modular algorithmic framework for accelerating Benders decomposition. Specifically, we express the problem structure by using a graph-theoretic modeling abstraction in which nodes represent optimization subproblems and edges represent connectivity between subproblems. A key innovation of our approach is that we embed multiparametric programming (mp) surrogates for node subproblems, which maps the exact analytical map of the subproblem solution space. The use of mp surrogates allows us to replace subproblem solves with fast look-ups and function evaluations for primal and dual variables during the iterative Benders process. We formally show the equivalence between classical Benders cuts and those derived from the mp solution. We implement our framework in the open-source PlasmoBenders.jl software package. To demonstrate the capabilities of the proposed framework, we apply it to a two-stage stochastic programming problem, which aims to make optimal capacity expansion decisions under market uncertainty. We evaluate both single-cut and multicut variants of Benders decomposition and show that the use of mp surrogates achieves substantial speedups in subproblem solve time, while preserving the convergence guarantees of Benders decomposition. We highlight advantages in solution analysis and interpretability that is enabled by mp critical region tracking; specifically, we show that these reveal how decisions evolve geometrically across the Benders search. Our results aim to demonstrate that combining surrogate modeling with graph modeling offers a promising and extensible foundation for structure-exploiting decomposition. In addition, by decomposing the problem into more tractable subproblems, the proposed approach also aims to overcome scalability issues of mp. Finally, the use of mp surrogates provides a unifying and modular optimization framework that enables the representation of heterogeneous node subproblems as modeling objects with a homogeneous structure.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

Numerical modelling of impact seismic sources using the stress glut theory

SUMMARY Meteorite impacts have proved to be a significant source of seismic signal on the Moon, and have now been recorded on Mars by InSight seismometers. Understanding how impacts produce seismic signal is key to the interpretation of this unique data, and to improve their identification in continuous seismic records. Here, we use the seismic Representation Theorem, and particularly the stress glut theory, to model the seismic motion resulting from impact cratering. The source is described by equivalent forces, some resulting from the impactor momentum transfer, and others from the stress glut, which represents the mechanical effect of plasticity and non linear processes in the source region. We condense these equivalent forces into a point-source with a time-varying single force and nine-component moment tensor. This analytical representation bridges the gap between the complex dynamics of crater formation, and the linear point-source representation classically used in seismology. Using the multiphysics modelling software HOSS, we develop a method to compute the stress glut of an impact, and the associated point-source from hypervelocity impact simulations. For a vertical and an oblique impact at 1000 m s−1, we show that the moment tensor presents a significant deviatoric component. Hence, the source is not an ideal isotropic explosion contrary to previous assumptions, and draws closer to a double couple for the oblique impact. The contribution of the point force to the seismic signal appears negligible. We verify this model by comparing two signals: (1) HOSS is coupled to SPECFEM3D to propagate the near-source signal elastically to remote seismic stations; (2) the point-source model derived from the stress-glut theory is used to generate displacements at the same distance. The comparison shows that the point-source model is accurately simulating the low-frequency impact seismic waveform, and its seismic moment is in trend with Lunar and Martian impact data. High-frequencies discrepancies exist, which are partly related to finite-source effects, but might be further explained by the difference in mathematical framework between classical seismology and HOSS’ numerical modelling.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Light Water Sustainability Program: Optimizing Information Automation Using a New Method Based on System-Theoretic Process Analysis

This report describes the interim progress for research supporting the design and optimization of information automation systems for nuclear power plants. Much of the domestic nuclear fleet is currently focused on modernizing technologies and processes, including transitioning toward digitalization in the control room and elsewhere throughout the plant, along with a greater use of automation, artificial intelligence, robotics, and other emerging technologies. While there are significant opportunities to apply these technologies toward greater plant safety, efficiency, and overall cost-effectiveness, optimizing their design and avoiding potential safety and performance risks depends on ensuring that human-performance-related organizational and technical design issues are identified and addressed. This report describes modeling tools and techniques, based on sociotechnical system theory, to support these design goals and their application in the current research effort. The report is intended for senior nuclear energy stakeholders, including regulators, corporate management, and senior plant management. We have developed and employed a method to design an optimized information automation ecosystem (IAE) based on the systems-theoretic constructs underlying sociotechnical systems theory in general and the Systems-Theoretic Accident Modeling and Processes (STAMP) approach in particular. We argue that an IAE can be modeled as an interactive information control system whose behavior can be understood in terms of dynamic control and feedback relationships amongst the system’s technical and organizational components. Up to this point, we have employed a Causal Analysis based on STAMP (CAST) technique to examine a performance- and safety-related incident at an industry partner’s plant that involved the unintentional activation of an emergency diesel generator. This analysis provided insight into the behavior of the plant’s current information control structure within the context of a specific, significant event. Our ongoing analysis is focused on identifying near-term process improvements and longer-term design requirements for an optimized IAE system. The latter analyses will employ a second STAMP-derived technique, System-Theoretic Process Analysis (STPA). STPA is a useful modeling tool for generating and analyzing actual or potential information control structures. Finally, we have begun modeling plantwide organizational relationships and processes. Organizational system modeling will supplement our CAST and STPA findings and provide a basis for mapping out a plantwide information control architecture. CAST analysis findings indicate an important underlying contributor to the incident under investigation, and a significant risk to information automation system performance, was perceived schedule pressure, which exposed weaknesses in interdepartmental coordination between and within responsible plant organizations and challenged the resilience of established plant processes, until a human caused the initiating event. These findings are discussed in terms of their risk to overall system performance and their implications for information automation system resilience and brittleness. We present two preliminary information automation models. The proactive issue resolution model is a test case of an information automation concept with significant near-term potential for application and subsequent reduction in significant plant events. The IAE model is a more general representation of a broader, plantwide information automation system. From our results, we have generated a set of preliminary system-level requirements and safety constraints. These requirements will be further developed over the remainder of our project in collaboration with nuclear industry subject matter experts and specialists in the technical systems under consideration. Additionally, we will continue to pursue the system analyses initiated in the first part of our effort, with a particular emphasis on STPA as the main tool to identify weak or weakening control structures that affect the resilience of organizations and programs. Our intent is to broaden the scope of the analysis from an individual use case to a related set of use cases (e.g., maintenance tasks, compliance tasks) with similar human-system performance challenges. This will enable more generalized findings to refine the Proactive Issue Resolution and IAE models, as well as their system-level requirements and safety constraints. We will use organizational system modeling analyses to supplement STPA findings and model development. We conclude the report with a set of summary recommendations and an initial draft list of system-level requirements and safety constraints for optimized information automation systems.

99 GENERAL AND MISCELLANEOUS↗

DOE OSTI2023

Optimizing Information Automation Using a New Method Based on System-Theoretic Process Analysis: Tool Development and Method Evaluation

This report is an update to a prior report that describes progress and findings for a program of research supporting the design and optimization of information automation systems for nuclear power plants. Much of the domestic nuclear fleet is currently focused on modernizing technologies and processes, including transitioning toward digitalization in the control room and throughout the plant, along with a greater interest in the use of automation, artificial intelligence, robotics, and other emerging technologies. While there are significant opportunities to apply these technologies toward greater plant safety, efficiency, and overall cost-effectiveness, optimizing their design and avoiding potential safety and performance risks depends on ensuring that human performance-related organizational and technical design issues are identified and addressed early in the design process. This report describes modeling tools and techniques, based on sociotechnical systems theory, to support these design goals and their application in the current research effort. The report is primarily intended for senior nuclear energy stakeholders, including regulators, corporate management, and senior plant management. We have developed and employed a method to design an optimized information automation ecosystem (IAE) based on the systems-theoretic constructs underlying sociotechnical systems theory in general and the Systems-Theoretic Accident Modeling and Processes (STAMP) approach in particular. We argue that an IAE can be modeled as an interactive information control system whose behavior can be understood in terms of dynamic control, feedback, and communication relationships amongst the system’s technical and organizational components. We have employed two STAMP-based tools in this effort. The first is Causal Analysis based on STAMP (CAST), an accident and incident analysis technique that was used to examine a performance- and safety-related incident at an industry partner’s plant involving the unintentional activation of an emergency diesel generator. This analysis provided insight into the behavior of the plant’s current information control structure within the context of a specific, significant event. The second tool is Systems Theoretic Process Analysis (STPA) which is a proactive risk analysis tool used to examine existing and potential, planned sociotechnical systems. STPA was used to identify risk factors in the current design of a generic nuclear power plant (NPP) preventive maintenance system. Our analyses focused on identifying near-term system improvements and longer-term design requirements for an optimized IAE system. CAST analysis findings indicate an important underlying contributor to the incident under investigation, and a significant risk to information automation system performance, was perceived time and schedule pressure, which exposed weaknesses in interdepartmental coordination between and within responsible plant organizations and challenged the resilience of established plant processes, until a human caused the eventual event. These findings are discussed in terms of their risk to overall system performance and their implications for information automation system resilience and brittleness. STPA findings exposed several areas of concern in the design of current preventive maintenance systems. We also present two preliminary information automation models. The proactive issue resolution (PIR) model is a test case of an information automation concept with significant near-term potential for application and subsequent reduction in significant plant events. The IAE model is a more general representation of a broader, plantwide information automation system and represents an end-state vision for our work. From our results, we have generated an initial set of preliminary system-level requirements and safety constraints for these models. We have also focused on early development of easy to learn, easy to use “transportable” tools for sociotechnical systems analysis. We intend these to be used by NPP personnel as a means of gaining reliable and relatively quick insight into (1) sociotechnical systems factors impacting incidents and accidents, (2) potential sociotechnical risk factors in existing or planned system designs, and (3) potential weaknesses in a system’s safety and/or information control structure. We conclude the report with a set of summary recommendations, a discussion of planned and potential follow-on research and development, and a draft list of system-level requirements and safety constraints for optimized information automation systems.

99 GENERAL AND MISCELLANEOUS↗