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Results for “Mathematical physics methods”

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 1,135 records · Page 63
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Interpenetrating Plasma Simulations

This project investigated multifluid models for simulating interpenetrating plasmas. These models solve the Euler equations for each plasma stream along with an appropriate model for electron dynamics. The project developed a novel code, Euclid, that simulates these models using high-order conservative spatial discretization methods and explicit and semi-implicit time integration methods. Euclid was used to solve several multifluid test cases representative of plasma dynamics in high-energy density physics experiments. Kinetic simulations of interpenetrating flows using the LOKI code revealed novel physical effects of the ion-ion streaming instability. A new multi-flow collision operator was developed for the LOKI code. A simple model of the ion-ion streaming instability was also developed. Several presentations were given on the project results; three journal articles have been published, one has been submitted, and two are planned.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

PyApprox: A software package for sensitivity analysis, Bayesian inference, optimal experimental design, and multi-fidelity uncertainty quantification and surrogate modeling

PyApprox is a Python-based one-stop-shop for probabilistic analysis of numerical models such as those used in the earth, environmental and engineering sciences. Easy to use and extendable tools are provided for constructing surrogates, sensitivity analysis, Bayesian inference, experimental design, and forward uncertainty quantification. The algorithms implemented represent a wide range of methods for model analysis developed over the past two decades, including recent advances in multi-fidelity approaches that use multiple model discretizations and/or simplified physics to significantly reduce the computational cost of various types of analyses. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of new or existing algorithms for a wide range of model analyses. Here, this paper introduces PyApprox and its various features, and presents results demonstrating the utility of PyApprox on a benchmark problem modeling the advection of a tracer in groundwater.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Limitations of Hartree–Fock with quantum resources

The Hartree–Fock problem provides the conceptual and mathematical underpinning of a large portion of quantum chemistry. As efforts in quantum technology aim to enhance computational chemistry algorithms, the Hartree–Fock method, central to many other numerical approaches, is a natural target for quantum enhanced algorithms. While quantum computers and quantum simulation offer many prospects for the future of modern chemistry, the non-deterministic polynomial-complete Hartree–Fock problem is not a likely candidate. Here, we highlight this fact from a number of perspectives including computational complexity, practical examples, and the full characterization of energy landscapes for simple systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Characterization and thermometry of dissipatively stabilized steady states

In this work we study the properties of dissipatively stabilized steady states of noisy quantum algorithms, exploring the extent to which they can be well approximated as thermal distributions, and proposing methods to extract the effective temperature T. We study an algorithm called the relaxational quantum eigensolver (RQE), which is one of a family of algorithms that attempt to find ground states and balance error in noisy quantum devices. In RQE, we weakly couple a second register of auxiliary ‘shadow’ qubits to the primary system in Trotterized evolution, thus engineering an approximate zero-temperature bath by periodically resetting the auxiliary qubits during the algorithm’s runtime. Balancing the infinite temperature bath of random gate error, RQE returns states with an average energy equal to a constant fraction of the ground state. We probe the steady states of this algorithm for a range of base error rates, using several methods for estimating both T and deviations from thermal behavior. In particular, we both confirm that the steady states of these systems are often well-approximated by thermal distributions, and show that the same resources used for cooling can be adopted for thermometry, yielding a fairly reliable measure of the temperature. These methods could be readily implemented in near-term quantum hardware, and for stabilizing and probing Hamiltonians where simulating approximate thermal states is hard for classical computers.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Framework for an adaptive integrated observation system using a hierarchy of machine learning approaches

Focal Area(s): 1. Data acquisition enabled by machine learning, AI, and advanced methods including experimental/network design/optimization, and hardware-related efforts involving AI. 2. Insight gleaned from complex measurements using AI, big data analytics, and other advanced methods, including explainable AI and physics- or knowledge-guided AI Science Challenge and Rationale: Atmospheric processes are stochastic, occur at scales from the micrometer to many kilometers, and are constantly changing over time. Characterizing these interactions and associated environmental conditions using traditional measurement techniques is difficult and can take years to build statistics on atmospheric phenomena that occurs episodically. Developing new innovative approaches to modify sampling strategies in real-time would enable the routine collection of targeted measurements focused on a specific set of science questions.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Graph-based featurization methods for classifying small molecule compounds

For over a decade, drug-induced liver injury (DILI) has posed significant drawbacks in the synthesis and development of drugs and remains a consequential concern. With finite success within the existing preclinical models, DILI is one of the main causes of drug withdrawal or termination from the market. Particularly, this withdrawal occurs during the late stages of drug development (Kullak-Ublick, 2017). Since DILI is difficult to diagnose and treat, it has become an obstacle in the drug production market that in turn affects clinicians, pharmaceutical companies, and consumers. We propose a method for learning features of DILI-positive drugs based on the graphical relationships and patterns they possess within a network of biological databases. We also train various statistical and machine learning models on these learned features in order to classify the drugs as DILI-positive or negative. Our methods include Random Forest, Neural networks, and logistic regression classification. We utilize labeled DILI-positive and DILI-negative datasets, which were developed by the FDA and the National center for toxicological research, as well as additional literature datasets (Thakkar, 2020) in order to validate our results and assess our featurization and model accuracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Quantum random number generator

A system and method are provided to yield a QRNG based on homodyne detection of quantum noise (e.g., vacuum noise measured as shot noise) generated from a local oscillator, such as an LED. In one embodiment, a QRNG may be provided that is adjustable based on a control input to produce a random output that can be translated to one or more random data bits.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Optimization and supervised machine learning methods for fitting numerical physics models without derivatives

Here, we address the calibration of a computationally expensive nuclear physics model for which derivative information with respect to the fit parameters is not readily available. Of particular interest is the performance of optimization-based training algorithms when dozens, rather than millions or more, of training data are available and when the expense of the model places limitations on the number of concurrent model evaluations that can be performed. As a case study, we consider the Fayans energy density functional model, which has characteristics similar to many model fitting and calibration problems in nuclear physics. We analyze hyperparameter tuning considerations and variability associated with stochastic optimization algorithms and illustrate considerations for tuning in different computational settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

SymbolNet: neural symbolic regression with adaptive dynamic pruning for compression

Abstract Compact symbolic expressions have been shown to be more efficient than neural network (NN) models in terms of resource consumption and inference speed when implemented on custom hardware such as field-programmable gate arrays (FPGAs), while maintaining comparable accuracy (Tsoi et al 2024 EPJ Web Conf. 295 09036). These capabilities are highly valuable in environments with stringent computational resource constraints, such as high-energy physics experiments at the CERN Large Hadron Collider. However, finding compact expressions for high-dimensional datasets remains challenging due to the inherent limitations of genetic programming (GP), the search algorithm of most symbolic regression (SR) methods. Contrary to GP, the NN approach to SR offers scalability to high-dimensional inputs and leverages gradient methods for faster equation searching. Common ways of constraining expression complexity often involve multistage pruning with fine-tuning, which can result in significant performance loss. In this work, we propose S y m b o l N e t , a NN approach to SR specifically designed as a model compression technique, aimed at enabling low-latency inference for high-dimensional inputs on custom hardware such as FPGAs. This framework allows dynamic pruning of model weights, input features, and mathematical operators in a single training process, where both training loss and expression complexity are optimized simultaneously. We introduce a sparsity regularization term for each pruning type, which can adaptively adjust its strength, leading to convergence at a target sparsity ratio. Unlike most existing SR methods that struggle with datasets containing more than O ( 10 ) inputs, we demonstrate the effectiveness of our model on the LHC jet tagging task (16 inputs), MNIST (784 inputs), and SVHN (3072 inputs).

Tsoi, Ho Fung (ORCID:0000000225502184)↗
DOE OSTI2022

Subcell limiting strategies for discontinuous Galerkin spectral element methods

Here, we present a general family of subcell limiting strategies to construct robust high-order accurate nodal discontinuous Galerkin (DG) schemes. The main strategy is to construct compatible low order finite volume (FV) type discretizations that allow for convex blending with the high-order variant with the goal of guaranteeing additional properties, such as bounds on physical quantities and/or guaranteed entropy dissipation. For an implementation of this main strategy, four main ingredients are identified that may be combined in a flexible manner: (i) a nodal high-order DG method on Legendre–Gauss–Lobatto nodes, (ii) a compatible robust subcell FV scheme, (iii) a convex combination strategy for the two schemes, which can be element-wise or subcell-wise, and (iv) a strategy to compute the convex blending factors, which can be either based on heuristic troubled-cell indicators, or using ideas from flux-corrected transport methods. By carefully designing the metric terms of the subcell FV method, the resulting methods can be used on unstructured curvilinear meshes, are locally conservative, can handle strong shocks efficiently while directly guaranteeing physical bounds on quantities such as density, pressure or entropy. We further show that it is possible to choose the four ingredients to recover existing methods such as a provably entropy dissipative subcell shock-capturing approach or a sparse invariant domain preserving approach. We test the versatility of the presented strategies and mix and match the four ingredients to solve challenging simulation setups, such as the KPP problem (a hyperbolic conservation law with non-convex flux function), turbulent and hypersonic Euler simulations, and MHD problems featuring shocks and turbulence.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

High-fidelity parallel entangling gates on a neutral-atom quantum computer

The ability to perform entangling quantum operations with low error rates in a scalable fashion is a central element of useful quantum information processing. Neutral-atom arrays have recently emerged as a promising quantum computing platform, featuring coherent control over hundreds of qubits and any-to-any gate connectivity in a flexible, dynamically reconfigurable architecture. The main outstanding challenge has been to reduce errors in entangling operations mediated through Rydberg interactions. Here we report the realization of two-qubit entangling gates with 99.5% fidelity on up to 60 atoms in parallel, surpassing the surface-code threshold for error correction. Our method uses fast, single-pulse gates based on optimal control, atomic dark states to reduce scattering and improvements to Rydberg excitation and atom cooling. We benchmark fidelity using several methods based on repeated gate applications, characterize the physical error sources and outline future improvements. Finally, we generalize our method to design entangling gates involving a higher number of qubits, which we demonstrate by realizing low-error three-qubit gates. By enabling high-fidelity operation in a scalable, highly connected system, these advances lay the groundwork for large-scale implementation of quantum algorithms, error-corrected circuits and digital simulations.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

(U) Calculating First-Order Sensitivities to Material Density and Composition in Fixed-Source Problems Using the MCNP6 Perturbation Capability

The Taylor series (differential operator) perturbation method, as implemented in the PERT capability in MCNP6 (Ref. 1), can be used for first-order sensitivity analyses in fixed-source problems.2 Sensitivities of a response with respect to material and nuclide densities can be used for efficient first-order uncertainty quantification. This report discusses how to compute sensitivities of material densities and compositions in order to propagate uncertainties using the standard uncertainty propagation formula.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Physics-preserving enriched Galerkin method for a fully-coupled thermo-poroelasticity model

This paper proposes a new numerical method for a fully-coupled, quasi-static thermo-poroelasticity model in a unified enriched Galerkin (EG) method framework. In our method, the mechanics sub-problem is solved using a locking-free EG method, and the flow and heat sub-problems are solved using a locally-conservative EG method. The proposed method offers mass and energy conservation properties with much lower costs than other methods with the same properties, including discontinuous Galerkin methods and mixed finite element methods. The well-posedness and optimal a priori error estimates are carefully derived. Here, several numerical tests confirm the theoretical optimal convergence rates and the mass and energy conservation properties of the new method.

15 GEOTHERMAL ENERGY↗
DOE OSTI2024

Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition

Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Revealing the Chemical Bonding in Adatom Arrays via Machine Learning of Hyperspectral Scanning Tunneling Spectroscopy Data

The adatom arrays on surfaces offer an ideal playground to explore the mechanisms of chemical bonding via changes in the local electronic tunneling spectra. While this information is readily available in hyperspectral scanning tunneling spectroscopy data, its analysis has been considerably impeded by a lack of suitable analytical tools. Here we develop a machine learning based workflow combining supervised feature identification in the spatial domain and unsupervised clustering in the energy domain to reveal the details of structure-dependent changes of the electronic structure in adatom arrays on the Co 3 Sn 2 S 2 cleaved surface. This approach, in combination with first-principles calculations, provides insight for using artificial neural networks to detect adatoms and classifies each based on their local neighborhood comprised of other adatoms. These structurally classified adatoms are further spectrally deconvolved. The unexpected inhomogeneity of electronic structures among adatoms in similar configurations is unveiled using this method, suggesting there is not a single atomic species of adatoms, but rather multiple types of adatoms on the Co 3 Sn 2 S 2 surface. This is further supported by a slight contrast difference in the images (or slight size variation) of the topography of the adatoms.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

Preparing for the next pandemic via transfer learning from existing diseases with hierarchical multi-modal BERT: a study on COVID-19 outcome prediction

Abstract Developing prediction models for emerging infectious diseases from relatively small numbers of cases is a critical need for improving pandemic preparedness. Using COVID-19 as an exemplar, we propose a transfer learning methodology for developing predictive models from multi-modal electronic healthcare records by leveraging information from more prevalent diseases with shared clinical characteristics. Our novel hierarchical, multi-modal model ( $${\textsc {TransMED}}$$ T R A N S MED ) integrates baseline risk factors from the natural language processing of clinical notes at admission, time-series measurements of biomarkers obtained from laboratory tests, and discrete diagnostic, procedure and drug codes. We demonstrate the alignment of $${\textsc {TransMED}}$$ T R A N S MED ’s predictions with well-established clinical knowledge about COVID-19 through univariate and multivariate risk factor driven sub-cohort analysis. $${\textsc {TransMED}}$$ T R A N S MED ’s superior performance over state-of-the-art methods shows that leveraging patient data across modalities and transferring prior knowledge from similar disorders is critical for accurate prediction of patient outcomes, and this approach may serve as an important tool in the early response to future pandemics.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2022

Local Lagrangian reduced-order modeling for the Rayleigh-Taylor instability by solution manifold decomposition

The Rayleigh-Taylor instability is a classical hydrodynamic instability of great interest in various disciplines of science and engineering, including astrophysics, atmospheric sciences and climate, geophysics, and fusion energy. Analytical methods cannot be applied to explain the long-time behavior of the Rayleigh-Taylor instability, and therefore, numerical simulation of the full problem is required. However, in order to capture the growth of amplitude of perturbations accurately, both the spatial and temporal discretizations need to be extremely fine for traditional numerical methods, and long-time simulation may become prohibitively expensive. In this paper, we propose efficient reduced order model techniques to accelerate the simulation of the Rayleigh-Taylor instability in compressible gas dynamics. Here, we introduce a general framework for decomposing the solution manifold to construct the temporal domain partition and temporally-local reduced order model construction with varying Atwood number. We propose two practical approaches in this framework, namely decomposition by physical time and by penetration distance. Numerical results are presented to examine the performance of the proposed approaches.

97 MATHEMATICS AND COMPUTING↗