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At least 1,099 records · Page 61

Explicit block encodings of boundary value problems for many-body elliptic operators

Simulation of physical systems is one of the most promising use cases of future digital quantum computers. In this work we systematically analyze the quantum circuit complexities of block encoding the discretized elliptic operators that arise extensively in numerical simulations for partial differential equations, including high-dimensional instances for many-body simulations. When restricted to rectangular domains with separable boundary conditions, we provide explicit circuits to block encode the many-body Laplacian with separable periodic, Dirichlet, Neumann, and Robin boundary conditions, using standard discretization techniques from low-order finite difference methods. To obtain high-precision, we introduce a scheme based on periodic extensions to solve Dirichlet and Neumann boundary value problems using a high-order finite difference method, with only a constant increase in total circuit depth and subnormalization factor. We then present a scheme to implement block encodings of differential operators acting on more arbitrary domains, inspired by Cartesian immersed boundary methods. We then block encode the many-body convective operator, which describes interacting particles experiencing a force generated by a pair-wise potential given as an inverse power law of the interparticle distance. This work provides concrete recipes that are readily translated into quantum circuits, with depth logarithmic in the total Hilbert space dimension, that block encode operators arising broadly in applications involving the quantum simulation of quantum and classical many-body mechanics.

Kharazi, Tyler [University of California, Berkeley↗

Graph-based quantum response theory and shadow Born–Oppenheimer molecular dynamics

Graph-based linear scaling electronic structure theory for quantum-mechanical molecular dynamics simulations [A. M. N. Niklasson et al., J. Chem. Phys. 144, 234101 (2016)] is adapted to the most recent shadow potential formulations of extended Lagrangian Born–Oppenheimer molecular dynamics, including fractional molecular-orbital occupation numbers [A. M. N. Niklasson, J. Chem. Phys. 152, 104103 (2020) and A. M. N. Niklasson, Eur. Phys. J. B 94, 164 (2021)], which enables stable simulations of sensitive complex chemical systems with unsteady charge solutions. The proposed formulation includes a preconditioned Krylov subspace approximation for the integration of the extended electronic degrees of freedom, which requires quantum response calculations for electronic states with fractional occupation numbers. For the response calculations, we introduce a graph-based canonical quantum perturbation theory that can be performed with the same natural parallelism and linear scaling complexity as the graph-based electronic structure calculations for the unperturbed ground state. Further, the proposed techniques are particularly well-suited for semi-empirical electronic structure theory, and the methods are demonstrated using self-consistent charge density-functional tight-binding theory both for the acceleration of self-consistent field calculations and for quantum-mechanical molecular dynamics simulations. Graph-based techniques combined with the semi-empirical theory enable stable simulations of large, complex chemical systems, including tens-of-thousands of atoms.

74 ATOMIC AND MOLECULAR PHYSICS↗

Measuring thermal profiles in high explosives using neural networks

We present a new method for calculating the temperature profile of high explosive (HE) material using a Convolutional Neural Network (CNN). To train/test the CNN, we have developed a hybrid experiment/simulation method for collecting acoustic and temperature data. We experimentally heat cylindrical containers of HE material until detonation/deflagration, where we continuously measure the acoustic bursts through the HE using multiple acoustic transducers lined around the exterior container circumference. However, measuring the temperature profile in the HE in an experiment would require inserting a large number of thermal probes, which would disrupt the heating process. Thus, we use two thermal probes, one at the HE center and one at the wall. We then use numerical simulation of the heating process to calculate the temperature distribution and correct the simulated temperatures based on the experimental center and wall temperatures. We calculate temperature errors on the order of 15 °C, which is ~12% of the range of temperatures in the experiment. We also investigate how the algorithm’s accuracy is affected by the number of acoustic receivers used to collect each measurement and the resolution of the temperature prediction. This work provides a means of assessing the safety status of HE material, which cannot be achieved using existing temperature measurement methods. In addition, it has implications for a range of other applications where internal temperature profile measurements would provide critical information. These applications include detecting chemical reactions, observing thermodynamic processes such as combustion, monitoring metal or plastic casting, determining the energy density in thermal storage capsules, and identifying abnormal battery operations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Efficacy of the Method of Four Coefficients to Determine Charge-Carrier Scattering

The investigation of the electronic properties of semiconductors from transport measurements (i.e., resistivity, Hall, and Seebeck coefficient measurements) is challenging due to the averaging of charge-carrier dynamics inherent in such measurements. Here, we investigate the incorporation of a fourth measurement of electronic transport, the Nernst coefficient, into the analysis, termed the method of four coefficients. This approach yields the Fermi level, effective mass, scattering exponent, and relaxation time prefactor. We begin with a review of the underlying mathematics and investigate the mapping between the four-dimensional material property and transport coefficient spaces. We then investigate how the traditional single-parabolic band method yields a single, potentially incorrect point on the solution subspace. This uncertainty can be resolved through Nernst coefficient measurements and we map the span of the ensuing subspace. We conclude with an investigation of how sensitive the analysis of transport coefficients is to experimental error for different sample types.

charge carriers↗

Adaptive Uncertainty Quantification for Stochastic Hyperbolic Conservation Laws

Here, we propose a predictor-corrector adaptive method for the study of hyperbolic partial differential equations (PDEs) under uncertainty. Constructed around the framework of stochastic finite volume (SFV) methods, our approach circumvents sampling schemes or simulation ensembles while also preserving fundamental properties, in particular hyperbolicity of the resulting systems and conservation of the discrete solutions. Furthermore, we augment the existing SFV theory with a priori convergence results for statistical quantities, in particular push-forward densities, which we demonstrate through numerical experiments. By linking refinement indicators to regions of the physical and stochastic spaces, we drive anisotropic refinements of the discretizations, introducing new degrees of freedom where deemed profitable. To illustrate our proposed method, we consider a series of numerical examples for nonlinear hyperbolic PDEs based on Burgers’ and Euler’s equations.

97 MATHEMATICS AND COMPUTING↗

Two-Scale Neural Networks for Partial Differential Equations with Small Parameters

We propose a two-scale neural network method for solving partial differential equations (PDEs) with small parameters using physics-informed neural networks (PINNs). We directly incorporate the small parameters into the architecture of neural networks. The proposed method enables solving PDEs with small parameters in a simple fashion, without adding Fourier features or other computationally taxing searches of truncation parameters. Various numerical examples demonstrate reasonable accuracy in capturing features of large derivatives in the solutions caused by small parameters.

97 MATHEMATICS AND COMPUTING↗

Modeling protected species distributions and habitats to inform siting and management of pioneering ocean industries: A case study for Gulf of Mexico aquaculture

Marine Spatial Planning (MSP) provides a process that uses spatial data and models to evaluate environmental, social, economic, cultural, and management trade-offs when siting (i.e., strategically locating) ocean industries. Aquaculture is the fastest-growing food sector in the world. The United States (U.S.) has substantial opportunity for offshore aquaculture development given the size of its exclusive economic zone, habitat diversity, and variety of candidate species for cultivation. However, promising aquaculture areas overlap many protected species habitats. Aquaculture siting surveys, construction, operations, and decommissioning can alter protected species habitat and behavior. Additionally, aquaculture-associated vessel activity, underwater noise, and physical interactions between protected species and farms can increase the risk of injury and mortality. In 2020, the U.S. Gulf of Mexico was identified as one of the first regions to be evaluated for offshore aquaculture opportunities as directed by a Presidential Executive Order. We developed a transparent and repeatable method to identify aquaculture opportunity areas (AOAs) with the least conflict with protected species. First, we developed a generalized scoring approach for protected species that captures their vulnerability to adverse effects from anthropogenic activities using conservation status and demographic information. Next, we applied this approach to data layers for eight species listed under the Endangered Species Act, including five species of sea turtles, Rice’s whale, smalltooth sawfish, and giant manta ray. Next, we evaluated four methods for mathematically combining scores (i.e., Arithmetic mean, Geometric mean, Product, Lowest Scoring layer) to generate a combined protected species data layer. The Product approach provided the most logical ordering of, and the greatest contrast in, site suitability scores. Finally, we integrated the combined protected species data layer into a multi-criteria decision-making modeling framework for MSP. This process identified AOAs with reduced potential for protected species conflict. These modeling methods are transferable to other regions, to other sensitive or protected species, and for spatial planning for other ocean-uses.

54 ENVIRONMENTAL SCIENCES↗

Plasma Surface Interactions: Predicting the Performance and Impact of Dynamic PFC Surfaces

The objective of this project is to develop, and integrate, high-performance simulation tools capable of predicting plasma-facing component (PFC) operating lifetime and the impact of the evolving surface morphology of tungsten-based PFCs on plasma contamination, including the dynamic recycling of fuel species and tritium retention, in future magnetic fusion devices. Establishing a fundamental physical understanding and developing predictive capabilities of plasma-surface interactions (PSI) requires simultaneously addressing complex and diverse physics occurring over a wide range of length (Angstroms to meters) and time (femtoseconds to years) scales, as well as integrating extensive physical processes across the plasma–surface interface. This requires development of not only detailed physics models and computational strategies at each scale, but also algorithms and methods to couple them effectively in a way that can be robustly validated. Deploying these tools requires the continued development and coupling of leadership-scale computational codes to describe the boundary plasma and the evolving PFC surface, as well as a host of simulations that bridge disparate scales to address complex physical and computational issues at the plasma–surface interface in multi-component materials systems for magnetic fusion energy development beyond ITER.

36 MATERIALS SCIENCE↗

Scattering Calorimeter FY24 Deliverable Report

A simulation-based method has been developed to prototype new detector designs for nuclear data measurements utilizing neutron scattering. This method uses representative physics inputs for signal and background generation, full detector resolution smearing benchmarked by experimental data, and a neutron beam timing simulation to produce analyzable output like a physical measurement. A test case has been studied using a hybrid time-of-flight calorimeter detector for scattering cross-section measurements on 239 Pu with 1-5 MeV incident monoenergetic neutrons. Data analysis methods have been developed to perform event-level particle reconstruction and reaction channel discrimination. This analysis has been used to estimate the capability of the test detector to perform simultaneous scattering and fission cross section measurements, as well as its ability to provide neutron spectra and particle angular information.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Accelerating transients with NekRS: GPU overlapping domain implementation and multi-rate timestepping

The simulation of nuclear transients using Computational Fluid Dynamics (CFD) presents significant computational challenges due to the inherent complexity and the wide separation in temporal scales between various flow physical phenomena. These disparities lead to high computational costs, often making the simulation of transients impractical without advanced techniques. Consequently, multiple research initiatives are being pursued by the NEAMS thermal-hydraulic area, some driven by academic institutions and some by national laboratories. Overall, they are exploring novel methods to make transient simulations more feasible and efficient. This report delves into recent advancements within the CFD code NekRS, specifically those achieved in Fiscal Year 2024 under the CONNECT effort, aimed at improving the performance and feasibility of transient simulations. The first major advancement involves the porting of NekRS to Aurora, one of the Department of Energy’s (DOE) most powerful supercomputers. Additionally, the report discusses the implementation of an overlapping domain capability within NekRS. This novel GPU-accelerated capability allows different spatial regions of the domain to be solved independently, enhancing the code’s efficiency, particularly when running large-scale simulations in complex domains. The scalability of this approach is demonstrated, highlighting its potential to transform how transients are approached in CFD simulations. Lastly, the report focuses on how this overlapping domain capability specifically accelerates transient simulations through multi-rate timestepping. By decoupling different regions and facilitating faster computations, this method offers a promising pathway to making nuclear transient simulations more computationally feasible, addressing one of the critical bottlenecks in the field. Together, these advancements represent a significant leap forward in transient simulation technology, bringing closer the possibility of handling highly complex nuclear scenarios with greater efficiency and accuracy.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Advancements in Validation of TSLs through Inelastic Neutron Scattering and Transmission Measurements [Abstract]

Historically, the free gas approximation has been used to treat the thermal scattering of neutrons with energies below a few electron-volts (eV) in unevaluated materials. However, this method inadequately reproduces neutron scattering at these energies. Until recently, only a limited number of materials had available thermal scattering law (TSL) files/libraries in the ENDF nuclear data libraries in this energy range. With advancements in atomistic modeling techniques, such as molecular dynamics, ab-initio molecular dynamics, and density functional theory, TSL libraries have become available for many more materials. This is particularly relevant due to the rising interest in several advanced reactor systems that require novel moderator and reflector materials. While quasi-integral and integral benchmarks have been designed to validate historically important moderator materials (such as light water and polyethylene), there is currently a lack of standard validation methods for TSLs, especially when multiple conflicting TSLs exist. To address this issue, the Oak Ridge National Lab Nuclear Data group has been working on utilizing inelastic neutron scattering (INS) measurements combined with transmission (i.e., total cross section) measurements to evaluate and validate TSLs for different materials. We plan to demonstrate how this method has worked on materials such as polyethylene, lucite, and polystyrene. In addition, we will compare the newly created libraries to ENDF libraries for these materials and explain why integral benchmarks should not be used for validation when multiple TSLs exist.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

Optimization Through Multi-Fidelity Modeling

We present a novel method for optimizing parameter selection for simulations with an evaluation budget. We start with an existing method for building a multi-fidelity model out of many low-fidelity simulations and few high-fidelity simulations. We propose a novel method to simplify parameter selection without sacrificing performance. We verify these results and compare with existing literature. Next, we propose a novel algorithm which uses this difference model to suggest new points in the parameter design space to simulate. We add each point we simulate to the model to improve its quality for the next iteration. The algorithm trades off reducing the uncertainty of the existing model with optimization of the objective. The first is more useful when a large fraction of the computation budget remains. The second is more useful when a small fraction of the computation budget remains. Our method converges to the optimum by using a high-fidelity evaluation for just 16 of the 427 points. Our method is general enough to work if there is no low-fidelity model. Furthermore, it is agnostic to the underlying physics of the problem. Therefore, both the low-fidelity and high-fidelity models can be generated by any arbitrary function, including simulations and physical experiments.

97 MATHEMATICS AND COMPUTING↗

Variational deep learning of equilibrium transition path ensembles

Here, we present a time-dependent variational method to learn the mechanisms of equilibrium reactive processes and efficiently evaluate their rates within a transition path ensemble. This approach builds off of the variational path sampling methodology by approximating the time-dependent commitment probability within a neural network ansatz. The reaction mechanisms inferred through this approach are elucidated by a novel decomposition of the rate in terms of the components of a stochastic path action conditioned on a transition. This decomposition affords an ability to resolve the typical contribution of each reactive mode and their couplings to the rare event. The associated rate evaluation is variational and systematically improvable through the development of a cumulant expansion. We demonstrate this method in both over- and under-damped stochastic equations of motion, in low-dimensional model systems, and in the isomerization of a solvated alanine dipeptide. In all examples, we find that we can obtain quantitatively accurate estimates of the rates of the reactive events with minimal trajectory statistics and gain unique insights into transitions through the analysis of their commitment probability.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Improve wildfire predictability driven by extreme water cycle with interpretable physically-guided ML/AI

Focal Area(s): Predictive modeling using AI techniques and AI-derived model components; use of AI and other tools to design a prediction system comprising of a hierarchy of models (Primary); insight gleaned from complex data (both observed and simulated) using AI, big data analytics, and other advanced methods, including explainable AI and physics or knowledge-guided AI (Secondary). Science Challenge: Wildfires modify land surface characteristics, such as vegetation composition, soil and litter carbon stocks, and surface albedo, with significant consequences for the regional carbon cycle. For example, tropical regions (i.e., African and South America) are particularly vulnerable to wildfire, account for more than 80% of the global burned area, and emit ~1.4 PgC y -1 into the atmosphere together with other dust and aerosols that strongly affect regional climate.

54 ENVIRONMENTAL SCIENCES↗

Numerical Solution of the Steady-State Network Flow Equations for a Non-Ideal Gas

Herein we formulate a steady-state network flow problem for non-ideal gas that relates injection rates and nodal pressures in the network to flows in pipes. For this problem, we present and prove a theorem on uniqueness of generalized solution for a broad class of non-ideal pressure-density relations that satisfy a monotonicity property. Further, we develop a Newton-Raphson algorithm for numerical solution of the steady-state problem, which is made possible by a systematic non-dimensionalization of the equations. The developed algorithm has been extensively tested on benchmark instances and shown to converge robustly to a generalized solution. Previous results [1]-[4], indicate that the steady-state network flow equations for an ideal gas are difficult to solve by the Newton-Raphson method because of its extreme sensitivity to the initial guess. In contrast, we find that non-dimensionalization of the steady-state problem is key to robust convergence of the Newton-Raphson method. We identify criteria based on the uniqueness of solutions under which the existence of a non-physical generalized solution found by a non-linear solver implies non-existence of a physical solution, i.e., infeasibility of the problem. Finally, we compare pressure and flow solutions based on ideal and non-ideal equations of state to demonstrate the need to apply the latter in practice. The solver developed in this article is open-source and is made available for both the academic and research communities as well as the industry.

97 MATHEMATICS AND COMPUTING↗

Accelerating Combustion and Surface Chemistry Simulations

Design of modern combustion systems relies on computer models to predict how changes in design will affect performance. These models have largely displaced previous methods that rely on the designer’s intuition or costly and time-consuming physical testing. By using improved models, design cycles can be shortened, and cleaner and more efficient combustion devices can be created. This project aims to improve computer simulations of transportation fuels with the goal of making these simulations faster and more accurate for predicting combustion in vehicles.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

Capturing many-body correlation effects with quantum and classical computing

Theoretical descriptions of excited states of molecular systems in high-energy regimes are crucial for supporting and driving many experimental efforts at light source facilities. However, capturing their complicated correlation effects requires formalisms that provide a hierarchical infrastructure of approximations. These approximations lead to an increased overhead in classical computing methods and, therefore, decisions regarding the ranking of approximations and the quality of results must be made on purely numerical grounds. The emergence of quantum computing methods has the potential to change this situation. Here, in this study, we demonstrate the efficiency of the quantum phase estimator (QPE) in identifying core-level states relevant to x-ray photoelectron spectroscopy. We compare and validate the QPE predictions with exact diagonalization and real-time equation-of-motion coupled-cluster formulations, which are some of the most accurate methods for states dominated by collective correlation effects.

74 ATOMIC AND MOLECULAR PHYSICS↗

Better together: Elements of successful scientific software development in a distributed collaborative community

Many scientific disciplines rely on computational methods for data analysis, model generation, and prediction. Implementing these methods is often accomplished by researchers with domain expertise but without formal training in software engineering or computer science. This arrangement has led to underappreciation of sustainability and maintainability of scientific software tools developed in academic environments. Some software tools have avoided this fate, including the scientific library Rosetta. We use this software and its community as a case study to show how modern software development can be accomplished successfully, irrespective of subject area. Rosetta is one of the largest software suites for macromolecular modeling, with 3.1 million lines of code and many state-of-the-art applications. Since the mid 1990s, the software has been developed collaboratively by the RosettaCommons, a community of academics from over 60 institutions worldwide with diverse backgrounds including chemistry, biology, physiology, physics, engineering, mathematics, and computer science. Developing this software suite has provided us with more than two decades of experience in how to effectively develop advanced scientific software in a global community with hundreds of contributors. Here we illustrate the functioning of this development community by addressing technical aspects (like version control, testing, and maintenance), community-building strategies, diversity efforts, software dissemination, and user support. We demonstrate how modern computational research can thrive in a distributed collaborative community. The practices described here are independent of subject area and can be readily adopted by other software development communities

97 MATHEMATICS AND COMPUTING↗