We introduce a new training algorithm for deep neural networks that utilize random complex exponential activation functions. Our approach employs a Markov chain Monte Carlo sampling procedure to iteratively train network layers, avoiding global and gradient-based optimization while maintaining error control. It consistently attains the theoretical approximation rate for residual networks with complex exponential activation functions, determined by network complexity. Additionally, it enables efficient learning of multiscale and high-frequency features, producing interpretable parameter distributions. Despite using sinusoidal basis functions, we do not observe Gibbs phenomena in approximating discontinuous target functions.
Legacy and modern-day ablation codes typically assume equilibrium pyrolysis gas chemistry. Yet, experimental data suggest that speciation from resin decomposition is far from equilibrium. A thermal and chemical kinetic study was performed on pyrolysis gas advection through a porous char, using the Theoretical Ablative Composite for Open Testing (TACOT) as a demonstrator material. The finite-element tool SIERRA/ Aria simulated the ablation of TACOT under various conditions. Temperature and phenolic decomposition rates generated from Aria were applied as inputs to a simulated network of perfectly stirred reactors (PSRs) in the chemical solver Cantera. A high-fidelity combustion mechanism computed the gas composition and thermal properties of the advecting pyrolyzate. The results indicate that pyrolysis gases do not rapidly achieve chemical equilibrium while traveling through the simulated material. Instead, a highly chemically reactive zone exists in the ablator between 1400 and 2500 K, wherein the modeled pyrolysis gases transition from a chemically frozen state to chemical equilibrium. These finite-rate results demonstrate a significant departure in computed pyrolysis gas properties from those derived from equilibrium solvers. Under the same conditions, finite-rate-derived gas is estimated to provide up to 50% less heat absorption than equilibrium-derived gas. This discrepancy suggests that nonequilibrium pyrolysis gas chemistry could substantially impact ablator material response models.
Traditional Monte Carlo methods for particle transport utilize source iteration to express the solution, the flux density, of the transport equation as a Neumann series. Our contribution is to show that the particle paths simulated within source iteration are associated with the adjoint flux density and the adjoint particle paths are associated with the flux density. We make our assertion rigorous through the use of stochastic calculus by representing the particle path used in source iteration as a solution to a stochastic differential equation (SDE). The solution to the adjoint Boltzmann equation is then expressed in terms of the same SDE, and the solution to the Boltzmann equation is expressed in terms of the SDE associated with the adjoint particle process. An important consequence is that the particle paths used within source iteration simultaneously provide Monte Carlo samples of the flux density and adjoint flux density in the detector and source regions, respectively. The significant practical implication is that particle trajectories can be reused to obtain both forward and adjoint quantities of interest. To the best our knowledge, the reuse of entire particles paths has not appeared in the literature. Monte Carlo simulations are presented to support the reuse of the particle paths.
In [R. J. Baraldi and D. P. Kouri, Mathematical Programming, (2022), pp. 1-40], we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex and nonsmooth convex function. The principle expense of this method is in computing a trial iterate that satisfies the so-called fraction of Cauchy decrease condition—a bound that ensures the trial iterate produces sufficient decrease of the subproblem model. In this paper, we expound on various proximal trust-region subproblem solvers that generalize traditional trust-region methods for smooth unconstrained and convex-constrained problems. We introduce a simplified spectral proximal gradient solver, a truncated nonlinear conjugate gradient solver, and a dogleg method. We compare algorithm performance on examples from data science and PDE-constrained optimization.
Water security and climate change are important priorities for communities and regions worldwide. The intersections between water and climate change extend across many environmental and human activities. This Primer is intended as an introduction, grounded in examples, for students and others considering the interactions between climate, water, and society. In this Primer, we summarize key intersections between water and climate across four sectors: environment; drinking water, sanitation, and hygiene; food and agriculture; and energy. We begin with an overview of the fundamental water dynamics within each of these four sectors, and then discuss how climate change is impacting water and society within and across these sectors. Emphasizing the relationships and interconnectedness between water and climate change can encourage systems thinking, which can show how activities in one sector may influence activities or outcomes in other sectors. We argue that to achieve a resilient and sustainable water future under climate change, proposed solutions must consider the water–climate nexus to ensure the interconnected roles of water across sectors are not overlooked. Toward that end, we offer an initial set of guiding questions that can be used to inform the development of more holistic climate solutions. This article is categorized under: Science of Water > Water and Environmental Change Engineering Water > Water, Health, and Sanitation Human Water > Value of Water.
Carbon capture, utilization, and storage (CCUS) is an important pathway for meeting climate mitigation goals. While the economic viability of CCUS is well understood, previous studies do not evaluate the economic feasibility of carbon capture and storage (CCS) in the Permian Basin specifically regarding the new Section 45Q tax credits. We developed a technoeconomic analysis method, evaluated the economic feasibility of CCS at the acid gas injection (AGI) wells, and assessed the implication of Section 45Q tax credits for CCS at the AGIs. We find that the compressors, well depth, and the permit and monitoring costs drive the facility costs. Compressors are the predominant contributors to capital and operating expenditure driving the levelized cost of CO2 storage. Strategic cost reduction measures identified include 1) sourcing of low-cost electricity and 2) optimizing operational efficiency in well operations. In evaluating the impact of the tax credits on CCS projects, facility scale proved decisive. We found that facilities with an annual injection rate exceeding 10,000 MT storage capacity demonstrate economic viability contingent upon the procurement of inputs at the least cost. The new construction of AGI wells were found to be economically viable at a storage capacity of 100,000 MT. The basin is heavily focused on CCUS (tax credit – $65/MT CO2), which overshadows CCS ($85/MT CO2) opportunities. Balancing the dual objectives of CCS and CCUS requires planning and coordination for optimal resource and pore space utilization to attain the basin's decarbonization potential. We also found that CCS on AGI is a lower cost CCS option as compared to CCS on other industries.
Legacy and modern-day ablation codes typically assume equilibrium pyrolysis gas chemistry. Yet, experimental data suggest that speciation from resin decomposition is far from equilibrium. A thermal and chemical kinetic study was performed on pyrolysis gas advection through a porous char, using the Theoretical Ablative Composite for Open Testing (TACOT) as a demonstrator material. The finite-element tool SIERRA/ Aria simulated the ablation of TACOT under various conditions. Temperature and phenolic decomposition rates generated from Aria were applied as inputs to a simulated network of perfectly stirred reactors (PSRs) in the chemical solver Cantera. A high-fidelity combustion mechanism computed the gas composition and thermal properties of the advecting pyrolyzate. The results indicate that pyrolysis gases do not rapidly achieve chemical equilibrium while traveling through the simulated material. Instead, a highly chemically reactive zone exists in the ablator between 1400 and 2500 K, wherein the modeled pyrolysis gases transition from a chemically frozen state to chemical equilibrium. These finite-rate results demonstrate a significant departure in computed pyrolysis gas properties from those derived from equilibrium solvers. Under the same conditions, finite-rate-derived gas is estimated to provide up to 50% less heat absorption than equilibrium-derived gas. This discrepancy suggests that nonequilibrium pyrolysis gas chemistry could substantially impact ablator material response models.
The sensitivity analysis algorithms that have been developed by the radiation transport community in multiple neutron transport codes, such as MCNP and SCALE, are extensively used by fields such as the nuclear criticality community. However, these techniques have seldom been considered for electron transport applications. In the past, the differential-operator method with the single scatter capability has been implemented in Sandia National Laboratories’ Integrated TIGER Series (ITS) coupled electron-photon transport code. This work is meant to extend the available sensitivity estimation techniques in ITS by implementing an adjoint-based sensitivity method, GEAR-MC, to strengthen its sensitivity analysis capabilities. To ensure the accuracy of this method being extended to coupled electron-photon transport, it is compared against the central-difference and differential-operator methodologies to estimate sensitivity coefficients for an experiment performed by McLaughlin and Hussman. Energy deposition sensitivities were calculated using all three methods, and the comparison between them has provided confidence in the accuracy of the newly implemented method. Unlike the current implementation of the differential-operator method in ITS, the GEAR-MC method was implemented with the option to calculate the energy-dependent energy deposition sensitivities, which are the sensitivity coefficients for energy deposition tallies to energy-dependent cross sections. The energy-dependent cross sections could be the cross sections for the material, elements in the material, or reactions of interest for the element. These sensitivities were compared to the energy-integrated sensitivity coefficients and exhibited a maximum percentage difference of 2.15%.
The Direct Simulation Monte Carlo (DSMC) method is utilized to numerically simulate test conditions in the Sandia Hypersonic Shock Tunnel (HST) facility. The setup consists of a hypersonic flow over a cylinder with the freestream at flow speeds of 4-5 km/s in a state of thermal non-equilibrium. We present comparisons of temperatures derived from spectrographic measurements of Nitric Oxide (NO) emission in the ultraviolet (UV) region with predictions from the DSMC solver. Furthermore, we present differences between spectrally banded imaging measurements taken during experiments in the infrared (IR) and UV regions with those obtained from numerical simulations.
There is growing interest to extend low-rank matrix decompositions to multi-way arrays, or tensors. One fundamental low-rank tensor decomposition is the canonical polyadic decomposition (CPD). The challenge of fitting a low-rank, nonnegative CPD model to Poisson-distributed count data is of particular interest. Several popular algorithms use local search methods to approximate the maximum likelihood estimator (MLE) of the Poisson CPD model. This work presents two new algorithms that extend state-of-the-art local methods for Poisson CPD. Hybrid GCP-CPAPR combines Generalized Canonical Decomposition (GCP) with stochastic optimization and CP Alternating Poisson Regression (CPAPR), a deterministic algorithm, to increase the probability of converging to the MLE over either method used alone. Restarted CPAPR with SVDrop uses a heuristic based on the singular values of the CPD model unfoldings to identify convergence toward optimizers that are not the MLE and restarts within the feasible domain of the optimization problem, thus reducing overall computational cost when using a multi-start strategy. We provide empirical evidence that indicates our approaches outperform existing methods with respect to converging to the Poisson CPD MLE.
This work introduces a comprehensive simulation tool that provides a robust 1D Schrödinger - Poisson solver for modeling the electrostatics of heterostructures with an arbitrary number of layers, and non-uniform doping profiles along with the treatment of partial ionization of dopants at low temperatures. The effective masses are derived from the first-principles calculations. The solver is used to characterize three Ge1-xSnx/Ge heterostructures with non-uniform doping profiles and determine the subband structure at various temperatures. The simulation results of the sheet carrier densities show excellent agreement with the experimentally extracted data, thus demonstrating the capabilities of the solver.
The impact of high-altitude electromagnetic pulse events on the electric grid is not fully understood, and validated modeling of mitigations, such as lightning surge arresters (LSAs) is necessary to predict the propagation of very fast transients on the grid. Experimental validation of high frequency models for surge arresters is an active area of research. This article serves to experimentally validate a previously defined ZnO LSA model using four metal-oxide varistor pucks and nanosecond scale pulses to measure voltage and current responses. The SPICE circuit models of the pucks showed good predictability when compared to the measured arrester response when accounting for a testbed inductance of approximately 100 nH. Additionally, the comparatively high capacitance of low-profile arresters show a favorable response to high-speed transients that indicates the potential for effective electromagnetic pulse mitigation with future materials design.
Vertical-axis wind turbines (VAWTs) have been the subject of research and development for nearly a century. However, this turbine architecture has fallen in and out of favor on multiple occasions. Beginning in the late 1970s, the U.S. Department of Energy sponsored an extensive experimental program through Sandia National Laboratories which produced a mass of experimental data from several highly instrumented turbines. Turbines designed, built, and tested include the 2 meter, 5 meter, 17 meter, and 34 meter and their respective configurations. This program kicked off a commercial collaboration and resulted in the FloWind turbines. The FloWind turbines had several notable design changes from the experimental turbines that, in conjunction with a general lack of understanding regarding predicting fatigue at the time, led to the majority of the turbines failing prematurely during the late 80s.
As quantum computing hardware becomes more complex with ongoing design innovations and growing capabilities, the quantum computing community needs increasingly powerful techniques for fabrication failure root-cause analysis. This is especially true for trapped-ion quantum computing. As trapped-ion quantum computing aims to scale to thousands of ions, the electrode numbers are growing to several hundred, with likely integrated photonic components also adding to the electrical and fabrication complexity, making faults even harder to locate. In this work, we used a high-resolution quantum magnetic imaging technique, based on nitrogen-vacancy centers in diamond, to investigate short-circuit faults in an ion trap chip. We imaged currents from these short-circuit faults to ground and compared them to intentionally created faults, finding that the root cause of the faults was failures in the on-chip trench capacitors. This work, where we exploited the performance advantages of a quantum magnetic sensing technique to troubleshoot a piece of quantum computing hardware, is a unique example of the evolving synergy between emerging quantum technologies to achieve capabilities that were previously inaccessible.
Stochastic collocation (SC) is a well-known non-intrusive method of constructing surrogate models for uncertainty quantification. In dynamical systems, SC is especially suited for full-field uncertainty propagation that characterizes the distributions of the high-dimensional solution fields of a model with stochastic input parameters. However, due to the highly nonlinear nature of the parameter-to-solution map in even the simplest dynamical systems, the constructed SC surrogates are often inaccurate. This work presents an alternative approach, where we apply the SC approximation over the dynamics of the model, rather than the solution. By combining the data-driven sparse identification of nonlinear dynamics framework with SC, we construct dynamics surrogates and integrate them through time to construct the surrogate solutions. We demonstrate that the SC-over-dynamics framework leads to smaller errors, both in terms of the approximated system trajectories as well as the model state distributions, when compared against full-field SC applied to the solutions directly. We present numerical evidence of this improvement using three test problems: a chaotic ordinary differential equation, and two partial differential equations from solid mechanics.
Statistical analysis of tensor-valued data has largely used the tensor-variate normal (TVN) distribution that may be inadequate for data arising from distributions with heavier or lighter tails. We study a general family of elliptically contoured (EC) TV distributions and derive its characterizations, moments, marginal, and conditional distributions. We describe procedures for maximum likelihood estimation from data that are (1) uncorrelated draws from an EC distribution, (2) from a scale mixture of the TVN distribution, and (3) from an underlying but unknown EC distribution, for which we extend Tyler’s robust estimator. A detailed simulation study highlights the benefits of choosing an EC distribution over the TVN for heavier-tailed data. We develop TV classification rules using discriminant analysis and EC errors and show that they better predict cats and dogs from images in the Animal Faces-HQ dataset than the TVN-based rules. A novel tensor-on-tensor regression and TV analysis of variance (TANOVA) framework under EC errors is also demonstrated to better characterize gender, age, and ethnic origin than the usual TVN-based TANOVA in the celebrated labeled faces of the wild dataset.
Ab initio molecular dynamics (AIMD) simulations were carried out to investigate the equation of state of Nb2O5 and its pressure-density relationship under shock conditions. The focus of this study is on the monoclinic B−Nb2O5 (C2/c) polymorph. Enthalpy calculations from AIMD trajectories at 300 K show that the pressure-induced transformation between the thermodynamically most stable crystalline monoclinic parent phase H−Nb2O5 (P2/m) and B−Nb2O5 occurs at ∼1.9 GPa. This H→B transition is energetically more favorable than the H→L(Pmm2) pressure-induced transition recently observed at ∼5.9−9.0 GPa. The predicted shock properties of Nb2O5 polymorphs are also compared to their Nb and NbO2 counterparts to assess the impact of niobium oxidation on shock response.
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. In this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
Entropy is a state variable that may be obtained from any thermodynamically complete equation of state (EOS). However, hydrocode calculations that output the entropy often contain numerical errors; this is not because of the EOS, but rather the solution techniques that are used in hydrocodes (especially Eulerian) such as convection, remapping, and artificial viscosity. Here, in this work, empirical correlations are investigated to reduce the errors in entropy without altering the solution techniques for the conservation of mass, momentum, and energy. Specifically, these correlations are developed for the function of entropy ZS, and they depend upon the net artificial viscous work, as determined via Sandia National Laboratories’ shock physics hydrocode CTH. These results are a continuation of a prior effort to implement the entropy-based CREST reactive burn model in CTH, and they are presented here to stimulate further interest from the shock physics community. Future work is planned to study higher-dimensional shock waves, shock wave interactions, and possible ties between the empirical correlations and a physical law.
The spatial distribution of electric field due to an imposed electric charge density profile in an infinite slab of dielectric material is derived analytically by integrating Gauss's law. Various charge density distributions are considered, including exponential and power-law forms. The Maxwell stress tensor is used to compute a notional static stress in the material due to the charge density and its electric field. Characteristics of the electric field and stress distributions are computed for example cases in polyethylene, showing that field magnitudes exceeding the dielectric strength would be required in order to achieve a stress exceeding the ultimate tensile strength.
Composite materials with different microstructural material symmetries are common in engineering applications where grain structure, alloying and particle/fiber packing are optimized via controlled manufacturing. In fact these microstructural tunings can be done throughout a part to achieve functional gradation and optimization at a structural level. To predict the performance of particular microstructural configuration and thereby overall performance, constitutive models of materials with microstructure are needed. In this work we provide neural network architectures that provide effective homogenization models of materials with anisotropic components. These models satisfy equivariance and material symmetry principles inherently through a combination of equivariant and tensor basis operations. We demonstrate them on datasets of stochastic volume elements with different textures and phases where the material undergoes elastic and plastic deformation, and show that the these network architectures provide significant performance improvements.
Modern lens designs are capable of resolving greater than 10 gigapixels, while advances in camera frame-rate and hyperspectral imaging have made data acquisition rates of Terapixel/second a real possibility. The main bottlenecks preventing such high data-rate systems are power consumption and data storage. In this work, we show that analog photonic encoders could address this challenge, enabling high-speed image compression using orders-of-magnitude lower power than digital electronics. Our approach relies on a silicon-photonics front-end to compress raw image data, foregoing energy-intensive image conditioning and reducing data storage requirements. The compression scheme uses a passive disordered photonic structure to perform kernel-type random projections of the raw image data with minimal power consumption and low latency. A back-end neural network can then reconstruct the original images with structural similarity exceeding 90%. This scheme has the potential to process data streams exceeding Terapixel/second using less than 100 fJ/pixel, providing a path to ultra-high-resolution data and image acquisition systems.
Using coarse graining, the upscaled mechanical properties of a solid with small scale heterogeneities are derived. The method maps internal forces at the small scale onto peridynamic bond forces in the coarse grained mesh. These upscaled bond forces are used to calibrate a peridynamic material model with position-dependent parameters. These parameters incorporate mesoscale variations in the statistics of the small scale system. The upscaled peridynamic model can have a much coarser discretization than the original small scale model, allowing larger scale simulations to be performed efficiently. The convergence properties of the method are investigated for representative random microstructures. A bond breakage criterion for the upscaled peridynamic material model is also demonstrated.
We present a machine-learning strategy for finite element analysis of solid mechanics wherein we replace complex portions of a computational domain with a data-driven surrogate. In the proposed strategy, we decompose a computational domain into an “outer” coarse-scale domain that we resolve using a finite element method (FEM) and an “inner” fine-scale domain. We then develop a machine-learned (ML) model for the impact of the inner domain on the outer domain. In essence, for solid mechanics, our machine-learned surrogate performs static condensation of the inner domain degrees of freedom. This is achieved by learning the map from displacements on the inner-outer domain interface boundary to forces contributed by the inner domain to the outer domain on the same interface boundary. We consider two such mappings, one that directly maps from displacements to forces without constraints, and one that maps from displacements to forces by virtue of learning a symmetric positive semi-definite (SPSD) stiffness matrix. We demonstrate, in a simplified setting, that learning an SPSD stiffness matrix results in a coarse-scale problem that is well-posed with a unique solution. We present numerical experiments on several exemplars, ranging from finite deformations of a cube to finite deformations with contact of a fastener-bushing geometry. We demonstrate that enforcing an SPSD stiffness matrix drastically improves the robustness and accuracy of FEM–ML coupled simulations, and that the resulting methods can accurately characterize out-of-sample loading configurations with significant speedups over the standard FEM simulations.
In this study we present a replication method to determine surface roughness and to identify surface features when a sample cannot be directly analyzed by conventional techniques. As a demonstration, this method was applied to an unused spent nuclear fuel dry storage canister to determine variation across different surface features. In this study, an initial material down-selection was performed to determine the best molding agent and determined that non-modified Polytek PlatSil23-75 provided the most accurate representation of the surface while providing good usability. Other materials that were considered include Polygel Brush-On 35 polyurethane rubber (with and without Pol-ease 2300 release agent), Polytek PlatSil73-25 silicone rubber (with and without PlatThix thickening agent and Pol-ease 2300 release agent), and Express STD vinylpolysiloxane impression putty. The ability of PlatSil73-25 to create an accurate surface replica was evaluated by creating surface molds of several locations on surface roughness standards representing ISO grade surfaces N3, N5, N7, and N8. Overall, the molds were able to accurately reproduce the expected roughness average (Ra) values, but systematically over-estimated the peak-valley maximum roughness (Rz) values. Using a 3D printed sample cell, several locations across the stainless steel spent nuclear fuel canister were sampled to determine the surface roughness. These measurements provided information regarding variability in normal surface roughness across the canister as well as a detailed evaluation on specific surface features (e.g., welds, grind marks, etc.). The results of these measurements can support development of dry storage canister ageing management programs, as surface roughness is an important factor for surface dust deposition and accumulation. This method can be applied more broadly to different surfaces beyond stainless steel to provide rapid, accurate surface replications for analytical evaluation by profilometry.