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At least 595 records · Page 33

Learning constitutive relations using symmetric positive definite neural networks

In this work, we present a new neural-network architecture, called the Cholesky-factored symmetric positive definite neural network (SPD-NN), for modeling constitutive relations in computational mechanics. Instead of directly predicting the stress of the material, the SPD-NN trains a neural network to predict the Cholesky factor of the tangent stiffness matrix, based on which the stress is calculated in incremental form. As a result of this special structure, SPD-NN weakly imposes convexity on the strain energy function, satisfies the second order work criterion (Hill's criterion) and time consistency for path-dependent materials, and therefore improves numerical stability, especially when the SPD-NN is used in finite element simulations. Depending on the types of available data, we propose two training methods, namely direct training for strain and stress pairs and indirect training for loads and displacement pairs. We demonstrate the effectiveness of SPD-NN on hyperelastic, elasto-plastic, and multiscale fiber-reinforced plate problems from solid mechanics. The generality and robustness of SPD-NN make it a promising tool for a wide range of constitutive modeling applications.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Multi-variance replica exchange SGMCMC for inverse and forward problems via Bayesian PINN

Physics-informed neural network (PINN) has been successfully applied in solving a variety of nonlinear non-convex forward and inverse problems. However, the training is challenging because of the non-convex loss functions and the multiple optima in the Bayesian inverse problem. In this work, we propose a multi-variance replica exchange stochastic gradient Langevin dynamics method to tackle the challenge of the multiple local optima in the optimization and the challenge of the multiple modal posterior distribution in the inverse problem. Replica exchange methods are capable of escaping from the local traps and accelerating the convergence; two chains with different temperatures are designed where the low temperature chain aims for the local convergence, and the target of the high temperature chain is to travel globally and explore the whole loss function entropy landscape. However, it may not be efficient to solve mathematical inversion problems by using the vanilla replica method directly since the method doubles the computational cost in evaluating the forward solvers (likelihood functions) in the two chains. To address this issue, we propose to make different assumptions on the energy function estimation and this facilities one to use solvers of different fidelities in the likelihood function evaluation. More precisely, one can use a solver with low fidelity in the high temperature chain while using a solver with high fidelity in the low temperature chain. Our proposed method significantly lowers the computational cost in the high temperature chain, meanwhile preserving the accuracy and converging very fast. Here we give an unbiased estimate of the swapping rate and give an estimation of the discretization error of the scheme. To verify our idea, we design and solve four inverse problems which have multiple modes. The proposed method is also employed to train the Bayesian PINN to solve the forward and inverse problems; faster and more accurate convergence has been observed when compared to the stochastic gradient Langevin dynamics (SGLD) method and vanilla replica exchange methods.

97 MATHEMATICS AND COMPUTING↗

An optimization method for chaotic turbulent flow

Evidence indicates that quantities-of-interest in some turbulent flows can be controlled despite the overall chaotic dynamics. It is typically thought that this is via relatively deterministic, larger-scale components of the turbulence. However, finding such controls, if they exist, is challenging because chaos causes sensitivity gradients to explode and the search space to become intractably non-convex. This challenge is analyzed, and a penalty method is introduced to cope with it. In the new approach, the time domain is broken into segments approximately matching the chaos time scales, so that the solution within each segment is both physical and relatively deterministic. The initial condition of each segment is included in an adjoint-based gradient optimization, which temporarily introduces artificial Δq discontinuities in the overall solution. The optimization then proceeds in stages with increasing penalization of Δq. The method is developed and illustrated for a logistic map, the Lorenz Equation, and an advection augmented Kuramoto–Sivashinsky Equation. These examples show how the Δq temporarily increases the search scale prior to the strong Δq → 0 penalization that recovers a physical solution. It is then applied to turbulent Kolmogorov flow, for which it also far outperforms a standard adjoint-based gradient search. Finally, the utility of such an optimized chaotic solution is discussed.

97 MATHEMATICS AND COMPUTING↗

Phase Selection Rules of Multi‐Principal Element Alloys

Abstract Computational prediction of phase stability of multi‐principal element alloys (MPEAs) holds a lot of promise for rapid exploration of the enormous design space and autonomous discovery of superior structural and functional properties. Regardless of many plausible works that rely on phenomenological theory and machine learning, precise prediction is still limited by insufficient data and the lack of interpretability of some machine learning algorithms, e.g., convolutional neural network. In this work, a comprehensive approach is presented, encompassing the development of a complete dataset that contains 72 387 density functional theory calculations, as well as a predictive global phenomenological descriptor. The phase selection descriptor, based on atomic electronegativity and valence electron concentration, significantly outperforms the widely used valence electron concentration, excelling in both accuracy (with an f1 score of 63% compared to 47%) and its ability to predict the HCP phase (0.48 recall compared to 0). The comprehensive data mining on the global design space of 61 425 quaternary MPEAs made from 28 possible metals, together with the phenomenological theory and physical interpretation, will set up a solid computational science foundation for data‐driven exploration of MPEAs.

Chemistry↗

Measurements of W + W − production cross-sections in pp collisions at $\sqrt{s}=13$ TeV with the ATLAS detector

Measurements of W + W − → e ± νμ ∓ ν production cross-sections are presented, providing a test of the predictions of perturbative quantum chromodynamics and the electroweak theory. The measurements are based on data from pp collisions at $\sqrt{s}$ = 13 TeV recorded by the ATLAS detector at the Large Hadron Collider in 2015–2018, corresponding to an integrated luminosity of 140 fb −1 . The number of events due to top-quark pair production, the largest background, is reduced by rejecting events containing jets with b-hadron decays. An improved methodology for estimating the remaining top-quark background enables a precise measurement of W + W − cross-sections with no additional requirements on jets. The fiducial W + W − cross-section is determined in a maximum-likelihood fit with an uncertainty of 3.1%. The measurement is extrapolated to the full phase space, resulting in a total W + W − cross-section of 127 ± 4 pb. Differential cross-sections are measured as a function of twelve observables that comprehensively describe the kinematics of W + W − events. The measurements are compared with state-of-the-art theory calculations and excellent agreement with predictions is observed. A charge asymmetry in the lepton rapidity is observed as a function of the dilepton invariant mass, in agreement with the Standard Model expectation. A CP-odd observable is measured to be consistent with no CP violation. Limits on Standard Model effective field theory Wilson coefficients in the Warsaw basis are obtained from the differential cross-sections.

Accelerator Physics↗

Oppenheimer Science and Energy Leadership Program (OSELP) Software and Computing Strategy for the Future of Weapons Physics Applications [Slides]

Mission drivers at the national level are evolving to accommodate a broadening landscape. The U.S. faces a rapidly evolving, threat-based environment with an associated expansion of national-level priorities. Priorities continue to include all aspects of sustaining the existing, aging stockpile. Now, however, we must also include consideration of options for a future deterrent, including efficacy of the deterrent against new threats (threat assessment and response), capability needs associated with new materials and modern manufacturing and production processes, and efficiency requirements for a modern workflow for weapons design. Executing this complex strategy will come with challenges. We must execute our current mission, while we prepare for future missions and an increasingly uncertain future.

42 ENGINEERING↗

Center for Technology for Advanced Scientific Component Software (TASCS) (Final Technical Report)

This is a final technical report for the University of Maryland work in the SciDAC Center for Technology for Advanced Scientific Component Software (TASCS). The Maryland work focused on software tools for coupling parallel software components built using the Common Component Architecture (CCA) APIs. Those tools are based on the Maryland InterComm software framework that has been used in multiple computational science applications to build large-scale simulations of complex physical systems that employ multiple separately developed codes.

97 MATHEMATICS AND COMPUTING↗

Predictive Models for Semiconductor Device Design and Processing

The device feature size continues to be on a downward trend with a simultaneous upward trend in wafer size to 300 mm. Predictive models are needed more than ever before for this reason. At NASA Ames, a Device and Process Modeling effort has been initiated recently with a view to address these issues. Our activities cover sub-micron device physics, process and equipment modeling, computational chemistry and material science. This talk would outline these efforts and emphasize the interaction among various components. The device physics component is largely based on integrating quantum effects into device simulators. We have two parallel efforts, one based on a quantum mechanics approach and the second, a semiclassical hydrodynamics approach with quantum correction terms. Under the first approach, three different quantum simulators are being developed and compared: a nonequlibrium Green's function (NEGF) approach, Wigner function approach, and a density matrix approach. In this talk, results using various codes will be presented. Our process modeling work focuses primarily on epitaxy and etching using first-principles models coupling reactor level and wafer level features. For the latter, we are using a novel approach based on Level Set theory. Sample results from this effort will also be presented.

Meyyappan, Meyya↗

Learning robust parameter inference and density reconstruction in flyer plate impact experiments

Estimating physical parameters or material properties from experimental observations is a common objective in many areas of physics and material science. In many experiments, especially in shock physics, radiography is the primary means of observing the system of interest. However, radiography does not provide direct access to key state variables, such as density, which prevents the application of traditional parameter estimation approaches. Here we focus on flyer plate impact experiments on porous materials, and resolving the underlying parameterized equation of state (EoS) and crush porosity model parameters given radiographic observation(s). We use machine learning as a tool to demonstrate with high confidence that using only high impact velocity data does not provide sufficient information to accurately infer both EoS and crush model parameters, even with fully resolved density fields or a dynamic sequence of images. We thus propose an observable data set consisting of low and high impact velocity experiments/simulations that capture different regimes of compaction and shock propagation, and proceed to introduce a generative machine learning approach which produces a posterior distribution of physical parameters directly from radiographs. We demonstrate the effectiveness of the approach in estimating parameters from simulated flyer plate impact experiments, and show that the obtained estimates of EoS and crush model parameters can then be used in hydrodynamic simulations to obtain accurate and physically admissible density reconstructions. Finally, we examine the robustness of the approach to model mismatches, and find that the learned approach can provide useful parameter estimates in the presence of out-of-distribution radiographic noise and previously unseen physics, thereby promoting a potential breakthrough in estimating material properties from experimental radiographic images.

97 MATHEMATICS AND COMPUTING↗

Search for same-charge top-quark pair production in pp collisions at $\sqrt{s}$ = 13 TeV with the ATLAS detector

A search for the production of top-quark pairs with the same electric charge ($tt$ or $\overline{tt}$) is presented. The analysis uses proton-proton collision data at $\sqrt{s}$ = 13 TeV, recorded by the ATLAS detector at the Large Hadron Collider, corresponding to an integrated luminosity of 140 fb −1 . Events with two same-charge leptons and at least two b-tagged jets are selected. Neural networks are employed to define two selections sensitive to additional couplings beyond the Standard Model that would enhance the production rate of same-sign top-quark pairs. No significant signal is observed, leading to an upper limit on the total production cross-section of same-sign top-quark pairs of 1.6 fb at 95% confidence level. Corresponding limits on the three Wilson coefficients associated with the $\mathcal{O}^{(1)}_{tu}$, $\mathcal{O}^{(1)}_{Qu}$, and $\mathcal{O}^{(8)}_{Qu}$ operators in the Standard Model Effective Field Theory framework are derived.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Stage-parallel fully implicit Runge–Kutta solvers for discontinuous Galerkin fluid simulations

In this paper, we develop new techniques for solving the large, coupled linear systems that arise from fully implicit Runge–Kutta methods. This method makes use of the iterative preconditioned GMRES algorithm for solving the linear systems, which has seen success for fluid flow problems and discontinuous Galerkin discretizations. By transforming the resulting linear system of equations, one can obtain a method which is much less computationally expensive than the untransformed formulation, and which compares competitively with other time-integration schemes, such as diagonally implicit Runge–Kutta (DIRK) methods. We develop and test several ILU-based preconditioners effective for these large systems. We additionally employ a parallel-in-time strategy to compute the Runge–Kutta stages simultaneously. Numerical experiments are performed on the Navier–Stokes equations using Euler vortex and 2D and 3D NACA airfoil test cases in serial and in parallel settings. In conclusion, the fully implicit Radau IIA Runge–Kutta methods compare favorably with equal-order DIRK methods in terms of accuracy, number of GMRES iterations, number of matrix–vector multiplications, and wall-clock time, for a wide range of time steps.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Estimation of distributions via multilevel Monte Carlo with stratified sampling

We design and implement a novel algorithm for computing a multilevel Monte Carlo (MLMC) estimator of the joint cumulative distribution function (CDF) of a vector-valued quantity of interest in problems with random input parameters and initial conditions. Our approach combines MLMC with stratified sampling of the input sample space by replacing standard Monte Carlo at each level with stratified Monte Carlo initialized with proportionally allocated samples. We show that the resulting stratified MLMC (sMLMC) algorithm is more efficient than its standard MLMC counterpart due to the additional variance reduction provided by the stratification of the random parameter's domain, especially at the coarsest levels. Additional computational cost savings are obtained by smoothing the indicator function with a Gaussian kernel, which proves to be an efficient and robust alternative to recently developed polynomial-based techniques.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Open data set of live cyanobacterial cells imaged using an X-ray laser

Structural studies on living cells by conventional methods are limited to low resolution because radiation damage kills cells long before the necessary dose for high resolution can be delivered. X-ray free-electron lasers circumvent this problem by outrunning key damage processes with an ultra-short and extremely bright coherent X-ray pulse. Diffraction-before-destruction experiments provide high-resolution data from cells that are alive when the femtosecond X-ray pulse traverses the sample. This paper presents two data sets from micron-sized cyanobacteria obtained at the Linac Coherent Light Source, containing a total of 199,000 diffraction patterns. Utilizing this type of diffraction data will require the development of new analysis methods and algorithms for studying structure and structural variability in large populations of cells and to create abstract models. Such studies will allow us to understand living cells and populations of cells in new ways. New X-ray lasers, like the European XFEL, will produce billions of pulses per day, and could open new areas in structural sciences.

59 BASIC BIOLOGICAL SCIENCES↗

SYMBA: symbolic computation of squared amplitudes in high energy physics with machine learning

The cross section is one of the most important physical quantities in high-energy physics and the most time consuming to compute. While machine learning has proven to be highly successful in numerical calculations in high-energy physics, analytical calculations using machine learning are still in their infancy. In this work, we use a sequence-to-sequence model, specifically, a transformer, to compute a key element of the cross section calculation, namely, the squared amplitude of an interaction. We show that a transformer model is able to predict correctly 97.6% and 99% of squared amplitudes of quantum chromodynamics and quantum electrodynamics processes, respectively, at a speed that is up to orders of magnitude faster than current symbolic computation frameworks. We discuss the performance of the current model, its limitations and possible future directions for this work.

97 MATHEMATICS AND COMPUTING↗

Preface to Special Topic: New Physics and Materials for Neuromorphic Computation

Artificial Intelligence is a topic that is pervasive in many modern developments and not just confined to science anymore. Many practical applications are based on performing classification tasks inspired by how the natural brain processes information. This current Special Topic on New Physics and Materials for Neuromorphic Computation looks toward solutions for such computational processes that go beyond the currently well-established semiconducting digital computation paradigm.

36 MATERIALS SCIENCE↗

Physics constrained unsupervised deep learning for rapid, high resolution scanning coherent diffraction reconstruction

By circumventing the resolution limitations of optics, coherent diffractive imaging (CDI) and ptychography are making their way into scientific fields ranging from X-ray imaging to astronomy. Yet, the need for time consuming iterative phase recovery hampers real-time imaging. While supervised deep learning strategies have increased reconstruction speed, they sacrifice image quality. Furthermore, these methods’ demand for extensive labeled training data is experimentally burdensome. Here, we propose an unsupervised physics-informed neural network reconstruction method, PtychoPINN, that retains the factor of 100-to-1000 speedup of deep learning-based reconstruction while improving reconstruction quality by combining the diffraction forward map with real-space constraints from overlapping measurements. In particular, PtychoPINN gains a factor of 4 in linear resolution and an 8 dB improvement in PSNR while also accruing improvements in generalizability and robustness. This blend of performance and computational efficiency offers exciting prospects for high-resolution real-time imaging in high-throughput environments such as X-ray free electron lasers (XFELs) and diffraction-limited light sources.

97 MATHEMATICS AND COMPUTING↗

Recipes for when physics fails: recovering robust learning of physics informed neural networks

Abstract Physics-informed neural networks (PINNs) have been shown to be effective in solving partial differential equations by capturing the physics induced constraints as a part of the training loss function. This paper shows that a PINN can be sensitive to errors in training data and overfit itself in dynamically propagating these errors over the domain of the solution of the PDE. It also shows how physical regularizations based on continuity criteria and conservation laws fail to address this issue and rather introduce problems of their own causing the deep network to converge to a physics-obeying local minimum instead of the global minimum. We introduce Gaussian process (GP) based smoothing that recovers the performance of a PINN and promises a robust architecture against noise/errors in measurements. Additionally, we illustrate an inexpensive method of quantifying the evolution of uncertainty based on the variance estimation of GPs on boundary data. Robust PINN performance is also shown to be achievable by choice of sparse sets of inducing points based on sparsely induced GPs. We demonstrate the performance of our proposed methods and compare the results from existing benchmark models in literature for time-dependent Schrödinger and Burgers’ equations.

97 MATHEMATICS AND COMPUTING↗