Engineering Papers⌕ Search

SEARCH · Engineering Papers

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 1,585 records · Page 88

Large-Scale Welding Process Simulation by GPU Parallelized Computing

The computational design of industrially relevant welded structures is extremely time consuming due to coupled physics and high nonlinearity. Previously, most welding distortion and residual stress simulations have been limited to small coupons and reduced order (from three-dimensional [3D] to two-dimensional [2D]), or inherent strain approximations were used for large structures. In this current study, an explicit finite element code based on a graphics processing unit was utilized to perform 3D transient thermomechanical simulation of structural components during welding. Laser brazing of aluminum alloy panels as representative of automotive manufacturing scenarios was simulated to predict out-of-plane distortion under different clamping conditions. The predicted deformation pattern and magnitude were validated by laser scanning data of physical assemblies. In addition, the code was used to investigate residual stresses developed during multipass arc welding of a nuclear industry pressurizer surge nozzle and subsequent welding repair where a 3D simulation was necessary. Taking the experimental data as reference, the 3D model predicted better residual stress distribution than a typical 2D asymmetrical model. Stress evolution in welding repair was also presented and discussed in this study. Furthermore, the efficient numerical model made it feasible to use integrated computational welding engineering to simulate welding processes for large-scale structures.

97 MATHEMATICS AND COMPUTING↗

Shadow Lagrangian dynamics for superfluidity

Motivated by a similar approach for Born-Oppenheimer molecular dynamics, this paper proposes an extended "shadow" Lagrangian density for quantum states of superfluids. The extended Lagrangian contains an additional field variable that is forced to follow the wave function of the quantum state through a rapidly oscillating extended harmonic oscillator. By considering the adiabatic limit for large frequencies of the harmonic oscillator, we can derive the two equations of motions, a Schrödinger-type equation for the quantum state and a wave equation for the extended field variable. The equations are coupled in a nonlinear way, but each equation individually is linear with respect to the variable that it defines. The computational advantage of this new system is that it can be easily discretized using linear time stepping methods, where we propose to use a Crank-Nicolson-type approach for the Schrödinger equation and an extended leapfrog scheme for the wave equation. Furthermore, the difference between the quantum state and the extended field variable defines a consistency error that should go to zero if the frequency tends to infinity. By coupling the time-step size in our discretization to the frequency of the harmonic oscillator we can extract an easily computable consistency error indicator that can be used to estimate the numerical error without additional costs. The findings are illustrated in numerical experiments.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

Identifying and classifying localized states in gapless systems using pseudospectral methods

For decades, band theory has been used to understand the physical properties of crystals by leveraging these systems’ translational symmetries to determine the spectral range and distribution of their Bloch eigenstates. However, many important phenomena only manifest at a crystal’s defects or boundaries where this translational symmetry is broken, such as defect-localized states that appear at color centers, or boundary-localized states whose existence is guaranteed by topology. Although it is possible to extend band theoretic approaches to study these classes of states, these extensions are only applicable in gapped systems, where any localized states are spectrally isolated from the crystal’s bulk states.

97 MATHEMATICS AND COMPUTING↗

Expanding the Domain of Applicability of Machine Learning Models with Limited Data for Drug Property Prediction

Accurate machine learning models for predicting small molecule interactions with biological targets are essential for therapeutic discovery, biothreat response, and computational drug design, but their performance is often limited for understudied targets with sparse experimental data. To address this challenge, we developed and evaluated methods to improve molecular property prediction under low-data conditions, using the NimA-related kinase (NEK) family as a proof-of-concept. This work focused on two complementary goals within the ATOM Modeling PipeLine (AMPL) and the Generative Molecular Design (GMD) loop: expanding model applicability through transfer learning, representation learning, feature scaling, sampling strategies, and active-learning-inspired compound selection; and enabling efficient virtual screening to prioritize compounds that balance predicted activity, design objectives, and synthetic accessibility.

organic↗

PAGOSA Mesh Block Calculator

A method for automatically generating the “mesh namelist block” portion of a PAGOSA input file, which specifies the boundaries and zone sizes of the computational mesh, has been developed. This application standardizes the mesh block for 2-, and 3-dimensional problems and is computed after the user specifies the extent and resolution of the mesh and the number of processors which will be used to run the problem. The inputs may be provided directly through a series of command-line guided questions, or a separate input file. The mesh block is written to both standard output and to disk.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Advanced Modeling and Simulation Methods for Evaluation of Thermal Neutron Scattering Materials

With the rise of interest in thermal neutron scattering data for advanced reactor, criticality safety, and shielding applications, new experimental data are required for evaluation of new materials or for re-evaluation (or validations) of previously evaluated materials. New experimental data are evaluated in a three-step process: (1) computing the phonon characteristics, (2) computing the dynamic structure factor (DSF) from the data, and (3) using the experimental setup to simulate the experimental data. All three steps have challenges, ranging from the need for a sufficiently general material simulation code—a processing code that can compute the corresponding DSF—to having a detailed layout of the instrument/beamline/facility where the data were measured. Whereas phonon characteristics of materials can be computed using various methods (molecular dynamics, density functional theory, etc.), a high-fidelity computation of the DSF and the simulation of the experiment based on the DSF is vital to the accuracy of the evaluation. The latter two steps can be achieved by using the two corresponding code systems developed by instrument scientists at the Spallation Neutron Source (SNS) at Oak Ridge National Laboratory: (1) OCLIMAX, a program that calculates the dynamic structure factor from DFT and MD simulation results, and (2) MCViNE, a Monte Carlo neutron ray-tracing program designed to simulate neutron scattering experiments. Recently, polyethylene and yttrium hydride were measured at the Wide Angular-Range Chopper (ARCS) and SEQUOIA instrument stations of the SNS. These experiments are simulated using the density functional theory code, the Cambridge Serial Total Energy Package (CASTEP), to compute its phonon characteristics (eigenvalues/vectors and PDOS), which is then processed using OCLIMAX to yield the DSF, and finally the data at each instrument station are simulated by the MCViNE for comparison to the measured data for evaluation. For comparison to conventional evaluation methods, the scattering data processed from OCLIMAX are compared against those processed from the LEAPR module of NJOY, and the results from MCViNE simulations are compared against previously used simplified beamline models implemented in the Monte Carlo N-Particle (MCNP) code.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

A Tailored Convolutional Neural Network for Nonlinear Manifold Learning of Computational Physics Data Using Unstructured Spatial Discretizations

In this work, we propose a nonlinear manifold learning technique based on deep convolutional autoencoders that is appropriate for model order reduction of physical systems in complex geometries. Convolutional neural networks have proven to be highly advantageous for compressing data arising from systems demonstrating a slow-decaying Kolmogorov n-width. However, these networks are restricted to data on structured meshes. Unstructured meshes are often required for performing analyses of real systems with complex geometry. Our custom graph convolution operators based on the available differential operators for a given spatial discretization effectively extend the application space of deep convolutional autoencoders to systems with arbitrarily complex geometry that are typically discretized using unstructured meshes. We propose sets of convolution operators based on the spatial derivative operators for the underlying spatial discretization, making the method particularly well suited to data arising from the solution of partial differential equations. We demonstrate the method using examples from heat transfer and fluid mechanics and show better than an order of magnitude improvement in accuracy over linear methods.

97 MATHEMATICS AND COMPUTING↗

Polyhedral Relaxations for Optimal Pump Scheduling of Potable Water Distribution Networks

The classic pump scheduling or optimal water flow (OWF) problem for water distribution networks (WDNs) minimizes the cost of power consumption for a given WDN over a fixed time horizon. In its exact form, the OWF is a computationally challenging mixed-integer nonlinear program (MINLP). It is complicated by nonlinear equality constraints that model network physics, discrete variables that model operational controls, and intertemporal constraints that model changes to storage devices. To address the computational challenges of the OWF, this paper develops tight polyhedral relaxations of the original MINLP, derives novel valid inequalities (or cuts) using duality theory, and implements novel optimization-based bound tightening and cut generation procedures. The efficacy of each new method is rigorously evaluated by measuring empirical improvements in OWF primal and dual bounds over 45 literature instances. The evaluation suggests that our relaxation improvements, model strengthening techniques, and a thoughtfully selected polyhedral relaxation partitioning scheme can substantially improve OWF primal and dual bounds, especially when compared with similar relaxation-based techniques that do not leverage these new methods.

bound tightening↗

An efficient reconstruction algorithm for diffusion on triangular grids using the nodal discontinuous Galerkin method

High-energy-density (HED) hydrodynamics studies such as those relevant to inertial confinement fusion and astrophysics require highly disparate densities, temperatures, viscosities, and other diffusion parameters over relatively short spatial scales. This presents a challenge for high-order accurate methods to effectively resolve the hydrodynamics at these scales, particularly in the presence of highly disparate diffusion. A significant volume of engineering and physics applications use an unstructured discontinuous Galerkin (DG) method developed based on the finite element mesh generation and algorithmic framework. This work discusses the application of an affine reconstructed nodal DG method for unstructured grids of triangles. Solving the diffusion terms in the DG method is non-trivial due to the solution representations being piecewise continuous. Hence, the diffusive flux is not defined on the interface of elements. The proposed numerical approach reconstructs a smooth solution in a parallelogram that is enclosed by the quadrilateral formed by two adjacent triangle elements. The interface between these two triangles is the diagonal of the enclosed parallelogram. Similar to triangles, the mapping of parallelograms from a physical domain to a reference domain is an affine mapping, which is necessary for an accurate and efficient implementation of the numerical algorithm. Thus, all computations can still be performed on the reference domain, which promotes efficiency in computation and storage. This reconstruction does not make assumptions on choice of polynomial basis. Reconstructed DG algorithms have previously been developed for modal implementations of the convection–diffusion equations. However, to the best of the authors’ knowledge, this is the first practical guideline that has been proposed for applying the reconstructed algorithm on a nodal discontinuous Galerkin method with a focus on accuracy and efficiency. As a result, the algorithm is demonstrated on a number of benchmark cases as well as a challenging substantive problem in HED hydrodynamics with highly disparate diffusion parameters.

Computational efficiency↗

PyApprox: Enabling efficient model analysis

PyApprox is a Python-based one-stop-shop for probabilistic analysis of scientific numerical models. 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 the most popular 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. Simple interfaces are provided for the most commonly-used algorithms to limit a user’s need to tune the various hyper-parameters of each algorithm. However, more advanced work flows that require customization of hyper-parameters is also supported. An extensive set of Benchmarks from the literature is also provided to facilitate the easy comparison of different algorithms for a wide range of model analyses. 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 ground water.

97 MATHEMATICS AND COMPUTING↗

Parallelized domain decomposition for multi-dimensional Lagrangian random walk mass-transfer particle tracking schemes

Lagrangian particle tracking schemes allow a wide range of flow and transport processes to be simulated accurately, but a major challenge is numerically implementing the inter-particle interactions in an efficient manner. This article develops a multi-dimensional, parallelized domain decomposition (DDC) strategy for mass-transfer particle tracking (MTPT) methods in which particles exchange mass dynamically. We show that this can be efficiently parallelized by employing large numbers of CPU cores to accelerate run times. In order to validate the approach and our theoretical predictions we focus our efforts on a well-known benchmark problem with pure diffusion, where analytical solutions in any number of dimensions are well established. In this work, we investigate different procedures for “tiling” the domain in two and three dimensions (2-D and 3-D), as this type of formal DDC construction is currently limited to 1-D. An optimal tiling is prescribed based on physical problem parameters and the number of available CPU cores, as each tiling provides distinct results in both accuracy and run time. We further extend the most efficient technique to 3-D for comparison, leading to an analytical discussion of the effect of dimensionality on strategies for implementing DDC schemes. Increasing computational resources (cores) within the DDC method produces a trade-off between inter-node communication and on-node work. For an optimally subdivided diffusion problem, the 2-D parallelized algorithm achieves nearly perfect linear speedup in comparison with the serial run-up to around 2700 cores, reducing a 5 h simulation to 8 s, while the 3-D algorithm maintains appreciable speedup up to 1700 cores.

97 MATHEMATICS AND COMPUTING↗

Gaussian Mixture Model Solvers for the Boltzmann Equation

This report documents our experience constructing a numerical method for the collisional Boltzmann equation that is capable of accurately capturing the collisionless through strongly collisional limits. We explore three different functional representations and present a detailed account of a numerical method based on a spatially dependent Gaussian mixture model (GMM). The Kullback-Leibler divergence is used as a closeness measure and various expectation maximization (EM) solution algorithms are implemented to find a compact representation in velocity space for distribution functions that exhibit significant non-Maxwellian character. We discuss issues that appear with this representation over a range of Knudsen numbers for a prototypical test problem and demonstrate that the strongly collisional limit recovers a solution to Euler's equations. Looking forward, this approach is broadly applicable to the non-relativistic and relativistic collisional Vlasov equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Moving Target Defense Routing for SDN-enabled Smart Grid

The increasing attack surface area in the smart grid communication networks is making the grid more susceptible to cyber attacks that can lead to instability of the grid and even blackouts. While there are multiple types of cyber attacks that can impact the grid, Denial of Service (DoS) attacks are relatively easier to inject as they require lesser knowledge about the system as compared to data integrity attacks. Various research works showcase methods to prevent or mitigate the impacts of DoS attacks in the smart grid but the research still lacks in demonstrating the feasibility and efficacy of the solutions in a real-world environment. In this paper, we propose a Moving Target Defense (MTD)-enabled Software Defined Network (SDN) for the Smart Grid communication implemented on a Hardwarein- the-Loop (HIL) Testbed. We showcase the implementation of the proposed architecture of MTD-enabled SDN using Mininet 2.3.0 which enables communication between the physical grid and the control center. The results show the advantages of using MTD based on SDN for the wide-area network (WAN) with much lower packet drop percentages in the case of MTD-based routing in the SDN WAN. Index Terms—SDN,

97 MATHEMATICS AND COMPUTING↗

Using density functional theory to construct multiphase equations of state: tin as an example

We present a general methodology for using density functional theory (DFT) calculations as a basis for constructing multiphase equations of state (EOS). Focusing on tin as an example, we discuss the full process of generating a tabular EOS, starting from first-principles calculations and arriving at a full EOS in agreement with existing experimental data. We begin by describing DFT calculations for the five solid phases and liquid phase of tin, including cold curve, phonon, and DFT-based molecular dynamics calculations. We then discuss methods for incorporating DFT results into materials models used in OpenSesame, the program used to create a full tabular multiphase EOS. Next, we outline a general strategy for adjusting model parameters in OpenSesame to fit to a variety of experimental data, including isobaric data, isothermal data, shock data, solid-solid phase boundary measurements, and measurements of the melt curve. We end with a discussion of the advantages of using DFT data as a foundation for EOS generation and discuss potential strategies for automated EOS generation based on the fitting process highlighted in this work.

74 ATOMIC AND MOLECULAR PHYSICS↗

Recurrent neural network-based multiaxial plasticity model with regularization for physics-informed constraints

We report a recurrent neural network (RNN) based model is developed as a surrogate to predict nonlinear plastic response under multiaxial loading. The RNN-based model is trained and tested on stress versus strain curves generated using a numerical solution based on the classical radial return method. Besides simply learning the basic constitutive relationship, a novel approach is taken to enforce certain physical conditions. Specifically, regularization is employed to maintain non-negative plastic power density throughout the loading history thereby ensuring monotonically increasing plastic work and thermodynamic consistency. Enforcing physics in this manner permits coupling of the data-driven RNN approach with physics-based knowledge and laws. This has the effect of reducing the necessary amount of data and ensuring known physical laws are not violated. Since, once trained, the model need not perform the expensive task of solving nonlinear equations, its efficiency is orders of magnitude greater than its numerical counterpart. The RNN-based model has been trained on varied sets of data and the accuracy on test datasets validated. The developed model is general and robust and has widespread application such as in the simulation of metal forming, large scale plasticity, and part life prediction.

42 ENGINEERING↗

A detailed study of interpretability of deep neural network based top taggers

Abstract Recent developments in the methods of explainable artificial intelligence (XAI) allow researchers to explore the inner workings of deep neural networks (DNNs), revealing crucial information about input–output relationships and realizing how data connects with machine learning models. In this paper we explore interpretability of DNN models designed to identify jets coming from top quark decay in high energy proton–proton collisions at the Large Hadron Collider. We review a subset of existing top tagger models and explore different quantitative methods to identify which features play the most important roles in identifying the top jets. We also investigate how and why feature importance varies across different XAI metrics, how correlations among features impact their explainability, and how latent space representations encode information as well as correlate with physically meaningful quantities. Our studies uncover some major pitfalls of existing XAI methods and illustrate how they can be overcome to obtain consistent and meaningful interpretation of these models. We additionally illustrate the activity of hidden layers as neural activation pattern diagrams and demonstrate how they can be used to understand how DNNs relay information across the layers and how this understanding can help to make such models significantly simpler by allowing effective model reoptimization and hyperparameter tuning. These studies not only facilitate a methodological approach to interpreting models but also unveil new insights about what these models learn. Incorporating these observations into augmented model design, we propose the particle flow interaction network model and demonstrate how interpretability-inspired model augmentation can improve top tagging performance.

97 MATHEMATICS AND COMPUTING↗

DeepGRN: prediction of transcription factor binding site across cell-types using attention-based deep neural networks

Abstract Background Due to the complexity of the biological systems, the prediction of the potential DNA binding sites for transcription factors remains a difficult problem in computational biology. Genomic DNA sequences and experimental results from parallel sequencing provide available information about the affinity and accessibility of genome and are commonly used features in binding sites prediction. The attention mechanism in deep learning has shown its capability to learn long-range dependencies from sequential data, such as sentences and voices. Until now, no study has applied this approach in binding site inference from massively parallel sequencing data. The successful applications of attention mechanism in similar input contexts motivate us to build and test new methods that can accurately determine the binding sites of transcription factors. Results In this study, we propose a novel tool (named DeepGRN) for transcription factors binding site prediction based on the combination of two components: single attention module and pairwise attention module. The performance of our methods is evaluated on the ENCODE-DREAM in vivo Transcription Factor Binding Site Prediction Challenge datasets. The results show that DeepGRN achieves higher unified scores in 6 of 13 targets than any of the top four methods in the DREAM challenge. We also demonstrate that the attention weights learned by the model are correlated with potential informative inputs, such as DNase-Seq coverage and motifs, which provide possible explanations for the predictive improvements in DeepGRN. Conclusions DeepGRN can automatically and effectively predict transcription factor binding sites from DNA sequences and DNase-Seq coverage. Furthermore, the visualization techniques we developed for the attention modules help to interpret how critical patterns from different types of input features are recognized by our model.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

AI for Science: Report on the Department of Energy (DOE) Town Halls on Artificial Intelligence (AI) for Science

The report documents the DOE Town Halls held during 2019 at Argonne National Laboratory, Oak Ridge National Laboratory, Lawrence Berkeley National Laboratory, and in Washington, DC. From July to October 2019, the Argonne, Oak Ridge, and Berkeley National Laboratories hosted a series of four town hall meetings attended by more than 1,000 U.S. scientists and engineers. The goal of the town hall series was to examine scientific opportunities in the areas of artificial intelligence (AI), Big Data, and high-performance computing (HPC) in the next decade, and to capture the big ideas, grand challenges, and next steps to realizing these opportunities. In this report and in the Department of Energy (DOE) laboratory community, we use the term “AI for Science” to broadly represent the next generation of methods and scientific opportunities in computing, including the development and application of AI methods (e.g., machine learning, deep learning, statistical methods, data analytics, automated control, and related areas) to build models from data and to use these models alone or in conjunction with simulation and scalable computing to advance scientific research. The AI for Science town hall discussions focused on capturing the transformational uses of AI that employ HPC and/or data analysis, leveraging data sets from HPC simulations or instruments and user facilities, and addressing scientific challenges unique to DOE user facilities and the agency’s wide-ranging fundamental and applied science enterprise.

36 MATERIALS SCIENCE↗