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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 1,621 records · Page 90
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

System and method for controlling an energy beam of an additive manufacturing system

An additive manufacturing system includes an energy beam generator that generates an energy beam to melt and fuse raw materials for a part and a computing device that controls operation of the energy beam generator. The computing device includes a memory element that stores or access a three-dimensional model of the part, and a processing element that receives at least a portion of the three-dimensional model and controls a parameter of the energy beam generator according to a gradient function so as to apply a variable amount of heat to the raw material that forms an overhang on the part.

42 ENGINEERING↗
DOE OSTI2020

Method and apparatus for two-layer copy-on-write

A system, apparatus and method are provided in which a range of virtual memory addresses and a copy of that range are mapped to the same first system address range in a data processing system until an address in the virtual memory address range, or its copy, is written to. The common system address range includes a number of divisions. Responsive to a write request to an address in a division of the common address range, a second system address range is generated. The second system address range is mapped to the same physical addresses as the first system address range, except that the division containing the address to be written to and its corresponding division in the second system address range are mapped to different physical addresses. First layer mapping data may be stored in a range table buffer and updated when the second system address range is generated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

An Entropy-Maximization Approach to Automated Training Set Generation for Interatomic Potentials

Machine learning-based interatomic potentials are currently garnering a lot of attention as they strive to achieve the accuracy of electronic structure methods at the computational cost of empirical potentials. Given their generic functional forms, the transferability of these potentials is highly dependent on the quality of the training set, the generation of which can be highly labor-intensive. Good training sets should at once contain a very diverse set of configurations while avoiding redundancies that incur cost without providing benefits. We formalize these requirements in a local entropy-maximization framework and propose an automated sampling scheme to sample from this objective function. We show that this approach generates much more diverse training sets than unbiased sampling and is competitive with hand-crafted training sets.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Reinforcement learning for block decomposition of planar CAD models

Abstract The problem of hexahedral mesh generation of general CAD models has vexed researchers for over 3 decades and analysts often spend more than 50% of the design-analysis cycle time decomposing complex models into simpler blocks meshable by existing techniques. The decomposed blocks are required for generating good quality meshes (tilings of quadrilaterals or hexahedra) suitable for numerical simulations of physical systems governed by conservation laws. We present a novel AI-assisted method for decomposing (segmenting) planar CAD (computer-aided design) models into well shaped rectangular blocks. Even though the simple examples presented here can also be meshed using many conventional methods, we believe this work is proof-of-principle of a AI-based decomposition method that can eventually be generalized to complex 2D and 3D CAD models. Our method uses reinforcement learning to train an agent to perform a series of optimal cuts on the CAD model that result in a good quality block decomposition. We show that the agent quickly learns an effective strategy for picking the location and direction of the cuts and maximizing its rewards. This paper is the first successful demonstration of an agent autonomously learning how to perform this block decomposition task effectively, thereby holding the promise of a viable method to automate this challenging process for more complex cases.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Adaptive Hybridizable Discontinuous Galerkin discretization of the Grad–Shafranov equation by extension from polygonal subdomains

In this work, we propose a high-order adaptive numerical solver for the semilinear elliptic boundary value problem modeling magnetic plasma equilibrium in axisymmetric confinement devices. In the fixed boundary case, the equation is posed on curved domains with piecewise smooth curved boundaries that may present corners. The solution method we present is based on the hybridizable discontinuous Galerkin method and sidesteps the need for geometry-conforming triangulations thanks to a transfer technique that allows to approximate the solution using only a polygonal subset as computational domain. Moreover, the solver features automatic mesh refinement driven by a residual-based a posteriori error estimator. As the mesh is locally refined, the computational domain is automatically updated in order to always maintain the distance between the actual boundary and the computational boundary of the order of the local mesh diameter. Numerical evidence is presented of the suitability of the estimator as an approximate error measure for physically relevant equilibria with pressure pedestals, internal transport barriers, and current holes on realistic geometries.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRSDate not supplied

Multi-Domain Routing in Delay Tolerant Networks

The goal of Delay Tolerant Networking (DTN) is to provide the missing ingredient for the ever-growing collection of communicating nodes in our solar system to become a Solar System Internet (SSI). Great strides have been made in modeling particular types of DTNs, such as schedule- or discovery-based. Now, analogously to the Internet, these smaller DTNs can be considered routing domains which must be stitched together to form the overall SSI. In this paper, we propose a framework for cross-domain routing in DTNs as well as methodologies for detecting these sub-domains. Example time-varying networks are given to demonstrate the techniques proposed. A basic component is the mathematical theory of sheaves, which unifies the underlying model of DTN routing algorithms, by giving rise to routing sheaves – these can be defined for the dynamic and scheduled networks as noted above, and can also be used to define the interfaces between these domains in order to route across them. An immediate application would be routing across discovery-based networks connected by scheduled networks. These DTN subdomains remain elusive, however, and need to become well-defined and properly sized for tractable computability. In particular, a balance must be determined between areas that are too large (i.e. large matrix computations) versus areas that are too small (i.e. “many” single-noded domains). Moreover, the connections between the domains should, at least locally, be chosen to optimize data flow and connectivity: we address this in three ways. First, tools from persistent homology are given to understand underlying structures, reminiscent of hierarchies in the Internet Protocol (IP) addressing. Second, we construct a notion of temporal graph curvature based on network geometry to analyze flows induced by dynamical processes on these networks. Finally, Schrodinger Bridges, a tool arising from statistical physics, are proposed as a method of constructing flows on time-evolving networks with desirable properties such as speed, robustness, and load sensitivity. We construct an approach to temporal hypergraphs to simultaneously model unicast, multicast, and broadcast, using the language of scheme theory, and then consider DTN network coding as a way to achieve network-level computation and organization. The paper concludes with a discussion and ideas for future work.

Alan Hylton↗
DOE OSTI2020

Where did the tumor start? An inverse solver with sparse localization for tumor growth models

In this work, we present a numerical scheme for solving an inverse problem for parameter estimation in tumor growth models for glioblastomas, a form of aggressive primary brain tumor. The growth model is a reaction–diffusion partial differential equation (PDE) for the tumor concentration. We use a PDE-constrained optimization formulation for the inverse problem. The unknown parameters are the reaction coefficient (proliferation), the diffusion coefficient (infiltration), and the initial condition field for the tumor PDE. Segmentation of magnetic resonance imaging (MRI) scans drive the inverse problem where segmented tumor regions serve as partial observations of the tumor concentration. Like most cases in clinical practice, we use data from a single time snapshot. Moreover, the precise time relative to the initiation of the tumor is unknown, which poses an additional difficulty for inversion. We perform a frozen-coefficient spectral analysis and show that the inverse problem is severely ill-posed. We introduce a biophysically motivated regularization on the structure and magnitude of the tumor initial condition. In particular, we assume that the tumor starts at a few locations (enforced with a sparsity constraint on the initial condition of the tumor) and that the initial condition magnitude in the maximum norm is equal to one. We solve the resulting optimization problem using an inexact quasi-Newton method combined with a compressive sampling algorithm for the sparsity constraint. Our implementation uses PETSc and AccFFT libraries. We conduct numerical experiments on synthetic and clinical images to highlight the improved performance of our solver over a previously existing solver that uses standard two-norm regularization for the calibration parameters. The existing solver is unable to localize the initial condition. Our new solver can localize the initial condition and recover infiltration and proliferation. In clinical datasets (for which the ground truth is unknown), our solver results in qualitatively different solutions compared to the two-norm regularized solver.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Composing preconditioners for multiphysics PDE systems with applications to Generalized MHD

New patch smoothers or relaxation techniques are developed for solving linear matrix equations coming from systems of discretized partial differential equations (PDEs). One key linear solver challenge for many PDE systems arises when the resulting discretization matrix has a near null space that has a large dimension, which can occur in generalized magnetohydrodynamic (GMHD) systems. Patch-based relaxation is highly effective for problems when the null space can be spanned by a basis of locally supported vectors. The patch-based relaxation methods that we develop can be used either within an algebraic multigrid (AMG) hierarchy or as stand-alone preconditioners. These patch-based relaxation techniques are a form of well-known overlapping Schwarz methods where the computational domain is covered with a series of overlapping sub-domains (or patches). Patch relaxation then corresponds to solving a set of independent linear systems associated with each patch. In the context of GMHD, we also reformulate the underlying discrete representation used to generate a suitable set of matrix equations. In general, deriving a discretization that accurately approximates the curl operator and the Hall term while also producing linear systems with physically meaningful near null space properties can be challenging. Unfortunately, many natural discretization choices lead to a near null space that includes non-physical oscillatory modes and where it is not possible to span the near null space with a minimal set of locally supported basis vectors. Further discretization research is needed to understand the resulting trade-offs between accuracy, stability, and ease in solving the associated linear systems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Methods and Results for Quantum Optimal Pulse Control on Superconducting Qubit Systems

The effective use of current Noisy Intermediate-Scale Quantum (NISQ) devices is often limited by the noise which is caused by interaction with the environment and affects the fidelity of quantum gates. In transmon qubit systems, the quantum gate fidelity can be improved by applying control pulses that can minimize the effects of the environmental noise. In this work, we employ physics-guided quantum optimal control strategies to design optimal pulses driving quantum gates on superconducting qubit systems. We test our results by conducting experiments on the IBM quantum hardware using their OpenPulse API. We compare the performance of our pulse-optimized quantum gates against the default quantum gates and show that the optimized pulses improve the fidelity of the quantum gates, in particular the single-qubit gates. Here we discuss the challenges we encountered in our work and point to possible future improvements.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Slip velocity boundary conditions for the lattice Boltzmann modeling of microchannel flows

Abstract Slip flows in ducts are important in numerous engineering applications, most notably in microchannel flows. Compared to the standard no‐slip Dirichlet condition, the case of slip formulates as a Robin‐type condition for the fluid tangential velocity. Such an increase in mathematical complexity is accompanied by a more challenging numerical transcription. The present work concerns with this topic, addressing the modeling of the slip velocity boundary condition in the lattice Boltzmann method (LBM) applied to steady slow viscous flows inside ducts of nontrivial shapes. As novelty, we extend the newly revised local second‐order boundary (LSOB) Dirichlet fluid flow method [ Philos. Trans. R. Soc. A 378, 20190404 (2020)] to implement the slip velocity condition within the two‐relaxation‐time (TRT) framework. The LSOB follows an in‐node philosophy where its operation principle seeks to explicitly reconstruct the unknown boundary populations in the form of a third‐order accurate Chapman–Enskog expansion, where the wall slip condition is built‐in as a normal Taylor‐type condition. The key point of this approach is that the required first‐ and second‐order momentum derivatives, rather than computed through nonlocal finite difference approximations, are locally determined through a simple local linear algebra procedure, whose formulation is particularly aided by the TRT symmetry argument. To express the obtained derivatives, two approaches are considered, called and , which operate with node and wall variables, respectively. These two formulations are developed to prescribe the physical slip condition over plane and curved walls, including the corners. Their consistency and accuracy characteristics are examined against alternative linkwise strategies to impose the wall slip velocity, such as the kinetic‐based diffusive bounce‐back scheme, the central linear interpolation slip scheme, and the multireflection slip scheme. The several slip schemes are tested over different 3D microchannel configurations, with walls not conforming with the LBM uniform mesh. Numerical tests confirm the advanced accuracy characteristics of the proposed LSOB slip boundary scheme, revealing the added challenge of the wall slip modeling, and that parabolic accuracy is a necessary requirement to reach second‐order accuracy within this problem class.

Silva, Goncalo↗
DOE OSTI2025

Defensive Cybersecurity Architecture Design Using Force-on-Force Cyber-Physical Modeling

Currently, nuclear power plant physical security systems are highly dependent on air-gaps as a protective measure against cyber-threats. Cyber-physical threats become more likely as advanced cyber-threat capabilities to jump air-gaps transition into common use. Defending against the emerging threat of cyber-enabled physical intrusions is poorly understood. The consequence of these cyber-physical attacks has no quantitative analysis method to inform risk-informed, performance-based cybersecurity approaches. By modifying the physical security simulation tool Dante, cyber-physical threat consequence was able to be analyzed on a notional facility. The results of this analysis are used to design a Defensive Cybersecurity Architecture (DCSA) for the physical security system to produce example resilience measures for this notional facility. A DCSA defines security levels to provide a graded approach for defending plant functions, and security zones for trusted communication between systems. This approach can be applied to real world systems to produce physical protection systems and response measures that are resilient to cyber-physical threats.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2022

Adaptive clipping‐and‐redistribution algorithms for bounded and conservative high‐order interpolations applied to discontinuous and reactive flows

Abstract A new adaptive clipping‐and‐redistribution method is presented which provides bounds‐preservation for multidimensional interpolation in the context of high‐order finite‐volume discretizations with adaptive mesh refinement (AMR). The underlying finite‐volume method (FVM) for the computational fluid dynamics applications is fourth‐order accurate for smooth solutions and utilizes AMR for computational efficiency in solving multiscale problems involving turbulence and combustion. High‐order interpolation between different AMR levels is required. However, this operation often leads to numerical issues because combustion species must have physical bounds preserved. The present study overcomes two major challenges in the development of the high‐order interpolation method. First, the method needs to be bound‐preserving near extrema or discontinuities to prevent the emergence of unphysical oscillations while maintaining fourth‐order accuracy in smooth flows. Second, the method needs to satisfy the conservation requirement in multiple dimensions, particularly in the context of curvilinear coordinate transformations. Additionally, the method is designed to be localized and computationally inexpensive. The new interpolation scheme is demonstrated by solving reacting flows, which are extremely sensitive to unphysical overshoots in conserved quantities. The test problems are shock‐induced ‐ combustion and a ‐air flame in a practical bluff‐body combustor. Results show the method prevents new extrema near discontinuities while maintaining high‐order accuracy in smooth regions. In particular, the method is extremely beneficial for combustion with stiff chemistry. With the proposed new method, even if flame fronts cross AMR interfaces or new grids are created in the vicinity of the flame, solution stability is retained.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

The moving target of visualization software for an increasingly complex world

Visualization has evolved into a mature scientific field and it has also become widely accepted as a standard approach in diverse fields, including physics, life sciences, and business intelligence. However, despite its successful development, there are still many open research questions that require customized implementations in order to explore and establish concepts, and to perform experiments and take measurements. Many methods and tools have been developed and published but most are stand-alone prototypes and have not reached a mature state that can be used in a reliable manner by collaborating domain scientists or a wider audience. In this study, we discuss the challenges, solutions, and open research questions that affect the development of sophisticated, relevant, and novel scientific visualization solutions with minimum overheads. Furthermore, we summarize and discuss the results of a recent National Institute of Informatics Shonan seminar on these topics.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

A novel implicit hybrid machine learning model and its application for reinforcement learning

A novel methodology to develop implicit hybrid models is presented. PyTorch is used to integrate physics-based equations with machine learning models. Automatic differentiation of the hybrid model is leveraged to solve the implicit equations. Iterative solving enables gradient based updates to the machine learning model. The novel methodology is compared to an explicit hybrid approach on a continuously stirred tank reactor (CSTR). The novel method results in a lower modelling error. Both hybrid models effectively train with noisy data. To test the implicit hybrid model, it is employed as a reinforcement learning (RL) training model. The RL algorithm trained on the hybrid model outperforms real time optimization of the CSTR and performs nearly as well as RL trained directly on the CSTR and a traditional gradient based approach. Training RL directly on the CSTR requires over 60,000 system interactions compared to 6000 historical data points for hybrid model development.

42 ENGINEERING↗
DOE OSTI2021

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this Letter, we present the first study of the convergence of eigenvector continuation. In order to perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between nonorthogonal vectors appearing at different orders in perturbation theory. From our analysis we can predict how eigenvector continuation converges both inside and outside the radius of convergence of perturbation theory. Further, while eigenvector continuation is a nonperturbative method, we show that its rate of convergence can be deduced from power series expansions of the eigenvectors. Our results also yield new insights into the nature of divergences in perturbation theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Hybrid (PDE+ML) models in the context of land ice modeling

Focal Area(s): Primary focal areas are: predictive modeling through the use of AI-derived model components; advanced methods including network design/optimization/deep learning. Science Challenge: The atmospheric, ocean and ice dynamics components of the Energy Exascale Earth System Model (E3SM) are governed by Partial Differential Equations (PDEs) and significant efforts have been made during the last decades to develop such computational models. Here we propose to fundamentally improve these PDE-based codes by enhancing them with Machine Learning (ML) sub-models for complex, poorly understood physical processes in the context of ice sheet modeling. We propose to train these models with a novel approach that allows the assimilation of the different sources of data available (direct/indirect observations and possibly simulation data), improving on existing simplified models. We also highlight computational challenges originating from the coexistence of PDE-based and ML-based models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Efficient Subset Simulation using Hamiltonian Neural Network enhanced Markov Chain Monte Carlo Methods

The Monte Carlo method delivers an unbiased estimate of the probability of failure. However, the variance of the estimate depends on the number of evaluated samples. This number must be very large for estimations of a low probability of failure. If the evaluation of each sample is computationally expensive, the crude Monte Carlo simulation strategy is impracticable. Therefore, subset simulations are used to reduce the required number of evaluations. Subset simulations require a Markov Chain Monte Carlo sampler, such as the random walk Metropolis-Hastings algorithm. The algorithm, however, struggles with sampling in low-probability regions, especially if they are narrow. As a consequence, advanced Markov Chain Monte Carlo simulations have been developed. In particular, the Hamiltonian Monte Carlo method explores the target distribution rapidly. Driven by the idea of Hamiltonian dynamics, this sampler provides a non-random walk through the target distribution. The incorporation of subset simulation and Hamiltonian Monte Carlo methods has shown promising results for reliability analysis. One downside of the Hamiltonian Monte Carlo method is that gradient evaluations are computationally expensive, especially when dealing with high-dimensional problems and evaluating long trajectories. We show that integrating Hamiltonian neural networks in Hamiltonian Monte Carlo simulations significantly speeds up the sampling task. Furthermore, the enhancement of adaptive trajectory length within the Hamiltonian Monte Carlo results in the efficient proposal of the following states. Based on this recent enhancement, we provide a fast sampling strategy for subset simulations using Hamiltonian neural networks to replace the evaluation of the gradient and significantly speed up the Hamiltonian Monte Carlo simulation.

97 MATHEMATICS AND COMPUTING↗