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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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Data supporting manuscript submitted to PNAS: Video-Rate Raman-based Metabolic Imaging by Airy Light-Sheet Illumination and Photon-Sparse Detection. The data set includes: [1] raw data and [2] related images used in the analyses described within the manuscript.
Tensor algebra is a powerful tool for computing, but writing optimized codes that operate on sparse tensors can be very complex. This project enables a Tensor Algebra Compiler (TACO) that simplifies this task from man-years to man-days and extends TACO to support complex and large distributed systems. This report details the hypotheses, approaches used, and findings in this project.
Accurate self-motion estimation is critical for various navigational tasks in mobile robotics. Optic flow provides a means to estimate self-motion using a camera sensor and is particularly valuable in GPS- and radio-denied environments. The present study investigates the influence of different activation functions—ReLU, leaky ReLU, GELU, and Mish—on the accuracy, robustness, and encoding properties of convolutional neural networks (CNNs) and multi-layer perceptrons (MLPs) trained to estimate self-motion from optic flow. Our results demonstrate that networks with ReLU and leaky ReLU activation functions not only achieved superior accuracy in self-motion estimation from novel optic flow patterns but also exhibited greater robustness under challenging conditions. The advantages offered by ReLU and leaky ReLU may stem from their ability to induce sparser representations than GELU and Mish do. Our work characterizes the encoding of optic flow in neural networks and highlights how the sparseness induced by ReLU may enhance robust and accurate self-motion estimation from optic flow.
Small metal clusters are of fundamental scientific interest and of tremendous significance in catalysis. These nanoscale clusters display diverse geometries and structural motifs depending on the cluster size; a knowledge of this size-dependent structural motifs and their dynamical evolution has been of longstanding interest. Given the high computational cost of first-principles calculations, molecular modeling and atomistic simulations such as molecular dynamics (MD) has proven to be an important complementary tool to aid this understanding. Classical MD typically employ predefined functional forms which limits their ability to capture such complex size-dependent structural and dynamical transformation. Neural Network (NN) based potentials represent flexible alternatives and in principle, well-trained NN potentials can provide high level of flexibility, transferability and accuracy on-par with the reference model used for training. A major challenge, however, is that NN models are interpolative and requires large quantities (similar to 10 4 or greater) of training data to ensure that the model adequately samples the energy landscape both near and far-from-equilibrium. A highly desirable goal is minimize the number of training data, especially if the underlying reference model is first-principles based and hence expensive. In this work, we introduce an active learning (AL) scheme that trains a NN model on-the-fly with minimal amount of first-principles based training data. Our AL workflow is initiated with a sparse training dataset (similar to 1 to 5 data points) and is updated on-the-fly via a Nested Ensemble Monte Carlo scheme that iteratively queries the energy landscape in regions of failure and updates the training pool to improve the network performance. Using a representative system of gold clusters, we demonstrate that our AL workflow can train a NN with similar to 500 total reference calculations. Using an extensive DFT test set of similar to 1100 configurations, we show that our AL-NN is able to accurately predict both the DFT energies and the forces for clusters of a myriad of different sizes. Our NN predictions are within 30 meV/atom and 40 meV/angstrom of the reference DFT calculations. Moreover, our AL-NN model also adequately captures the various size-dependent structural and dynamical properties of gold clusters in excellent agreement with DFT calculations and available experiments. We finally show that our AL-NN model also captures bulk properties reasonably well, even though they were not included in the training data.
We investigate the spectral form factor of the sparse Sachdev-Ye-Kitaev model. We use numerical methods to establish that at intermediate times the connected part of the spectral form factor is the dominant one. These connected contributions arise from fluctuations around the disconnected geometry, not from a new saddle point. A similar effect was previously conjectured in SYK but required a value of N out of reach of current numerical simulations.
This paper applies an idea of adaptive momentum for the nonlinear conjugate gradient to accelerate optimization problems in sparse recovery. Specifically, we consider two types of minimization problems: a (single) differentiable function and the sum of a non-smooth function and a differentiable function. In the first case, we adopt a fixed step size to avoid the traditional line search and establish the convergence analysis of the proposed algorithm for a quadratic problem. This acceleration is further incorporated with an operator splitting technique to deal with the non-smooth function in the second case. As a result, we use the convex ι 1 and the nonconvex ι 1 – ι 2 functionals as two case studies to demonstrate the efficiency of the proposed approaches over traditional methods.
Traditional probabilistic methods for the simulation of advection-diffusion equations (ADEs) often overlook the entropic contribution of the discretization, e.g., the number of particles, within associated numerical methods. Many times, the gain in accuracy of a highly discretized numerical model is outweighed by its associated computational costs or the noise within the data. Herein, we address the question of how many particles are needed in a simulation to best approximate and estimate parameters in one-dimensional advective-diffusive transport. To do so, we use the well-known Akaike Information Criterion (AIC) and a recently-developed correction called the Computational Information Criterion (COMIC) to guide the model selection process. Random-walk and mass-transfer particle tracking methods are employed to solve the model equations at various levels of discretization. Numerical results demonstrate that the COMIC provides an optimal number of particles that can describe a more efficient model in terms of parameter estimation and model prediction compared to the model selected by the AIC even when the data is sparse or noisy, the sampling volume is not uniform throughout the physical domain, or the error distribution of the data is non-IID Gaussian.
NMR relaxation dispersion measurements report on conformational changes occurring on the μs-ms timescale. Chemical shift information derived from relaxation dispersion can be used to generate structural models of weakly populated alternative conformational states. Current methods to obtain such models rely on determining the signs of chemical shift changes between the conformational states, which are difficult to obtain in many situations. Here, we use a “sample and select” method to generate relevant structural models of alternative conformations of the C-terminal-associated region of Escherichia coli dihydrofolate reductase (DHFR), using only unsigned chemical shift changes for backbone amides and carbonyls ( 1 H, 15 N, and 13 C'). We find that CS-Rosetta sampling with unsigned chemical shift changes generates a diversity of structures that are sufficient to characterize a minor conformational state of the C-terminal region of DHFR. The excited state differs from the ground state by a change in secondary structure, consistent with previous predictions from chemical shift hypersurfaces and validated by the x-ray structure of a partially humanized mutant of E. coli DHFR (N23PP/G51PEKN). The results demonstrate that the combination of fragment modeling with sparse chemical shift data can determine the structure of an alternative conformation of DHFR sampled on the μs-ms timescale. Such methods will be useful for characterizing alternative states, which can potentially be used for in silico drug screening, as well as contributing to understanding the role of minor states in biology and molecular evolution.
In this paper, we develop high-order nodal discontinuous Galerkin (DG) methods for hyperbolic conservation laws that satisfy invariant domain preserving properties using subcell flux corrections and convex limiting. These methods are based on a subcell flux corrected transport (FCT) methodology that involves blending a high-order target scheme with a robust, low-order invariant domain preserving method that is obtained using a graph viscosity technique. Furthermore, the new low-order discretizations are based on sparse stencils which do not increase with the polynomial degree of the high-order DG method. As a result, the accuracy of the low-order method does not degrade when used with high-order target methods. The method is applied to both scalar conservation laws, for which the discrete maximum principle is naturally enforced, and to systems of conservation laws such as the Euler equations, for which positivity of density and a minimum principle for specific entropy are enforced. Numerical results are presented on a number of benchmark test cases.
Deep neural operators can learn nonlinear mappings between infinite-dimensional function spaces via deep neural networks. As promising surrogate solvers of partial differential equations (PDEs) for real-time prediction, deep neural operators such as deep operator networks (DeepONets) provide a new simulation paradigm in science and engineering. Pure data-driven neural operators and deep learning models, in general, are usually limited to interpolation scenarios, where new predictions utilize inputs within the support of the training set. However, in the inference stage of real-world applications, the input may lie outside the support, i.e., extrapolation is required, which may result to large errors and unavoidable failure of deep learning models. Here, we address this challenge of extrapolation for deep neural operators. First, we systematically investigate the extrapolation behavior of DeepONets by quantifying the extrapolation complexity, via the 2-Wasserstein distance between two function spaces and propose a new strategy of bias–variance trade-off for extrapolation with respect to model capacity. Subsequently, we develop a complete workflow, including extrapolation determination, and we propose five reliable learning methods that guarantee a safe prediction under extrapolation by requiring additional information—the governing PDEs of the system or sparse new observations. The proposed methods are based on either fine-tuning a pre-trained DeepONet or multifidelity learning. We demonstrate the effectiveness of the proposed framework for various types of parametric PDEs. Furthermore, our systematic comparisons provide practical guidelines for selecting a proper extrapolation method depending on the available information, desired accuracy, and required inference speed.
Hypothesis Small-Angle Neutron Scattering (SANS) is a powerful technique for studying soft matter systems such as colloids, polymers, and lyotropic phases, providing nanoscale structural insights. However, its effectiveness is limited by low neutron flux, leading to long acquisition times and noisy data. Here, we hypothesize that Bayesian statistical inference using Gaussian Process Regression (GPR) can reconstruct high-fidelity scattering data from sparse measurements by leveraging intensity smoothness and continuity. Experiments and Simulations The method was benchmarked computationally and validated through SANS experiments on various soft matter systems, including wormlike micelles, colloidal suspensions, polymeric structures, and lyotropic phases. GPR-based inference was applied to both experimental and synthetic data to evaluate its effectiveness in noise reduction and intensity reconstruction. Findings GPR significantly enhances SANS data quality and therefore reducing measurement times by up to two orders of magnitude. This cost-effective approach maximizes experimental efficiency, enabling high-throughput studies and real-time monitoring of dynamic systems. It is particularly beneficial for weakly scattering and time-sensitive studies. Beyond SANS, this framework applies to other low-SNR techniques, including laboratory-based small-angle X-ray scattering and various dynamical scattering methods. Furthermore, it offers transformative potential for compact neutron sources, enhancing their viability for structural analysis in resource-limited settings.
Deep neural networks (DNN) have been used to model nonlinear relations between physical quantities. Those DNNs are embedded in physical systems described by partial differential equations (PDE) and trained by minimizing a loss function that measures the discrepancy between predictions and observations in some chosen norm. This loss function often includes the PDE constraints as a penalty term when only sparse observations are available. As a result, the PDE is only satisfied approximately by the solution. However, the penalty term typically slows down the convergence of the optimizer for stiff problems. We present a new approach that trains the embedded DNNs while numerically satisfying the PDE constraints. We develop an algorithm that enables differentiating both explicit and implicit numerical solvers in reverse-mode automatic differentiation. This allows the gradients of the DNNs and the PDE solvers to be computed in a unified framework. We demonstrate that our approach enjoys faster convergence and better stability in relatively stiff problems compared to the penalty method. Furthermore, our approach allows for the potential to solve and accelerate a wide range of data-driven inverse modeling, where the physical constraints are described by PDEs and need to be satisfied accurately.
The mercury constitutive model predicting the strain and stress in the target vessel plays a central role in improving the lifetime prediction and future target designs of the mercury targets at the Spallation Neutron Source. We leverage the experiment strain data collected over multiple years to improve the mercury constitutive model through a combination of large scale simulations of the target behavior and the use of machine learning tools for parameter estimation. We present two interdisciplinary approaches for surrogate-based model calibration of expensive simulations using evolutionary neural networks and sparse polynomial expansions. The newly calibrated simulations achieve 7% average improvement on the prediction accuracy and 8% reduction in mean absolute error compared to previously reported reference parameters, with some individual sensors experiencing up to 30% improvement. The calibrated simulations can aid in fatigue analysis to estimate the mercury target lifetime, which reduces abrupt failure and saves tremendous amount of costs.
Systems subjected to dynamic loads often require monitoring of their vibrational response, but limitations on the total number and placement of the measurement sensors can hinder the data-collection process. Here, we present an indirect approach to estimate a system’s full-field dynamic response, including all uninstrumented locations, using response measurements from sensors sparsely located on the system. This approach relies on Bayesian inference that utilizes a system model to estimate the full-field response and quantify the uncertainty in these estimates. By casting the estimation problem in the frequency domain, this approach utilizes the modal frequency response functions as a natural, frequency-dependent weighting scheme for the system mode shapes to perform the expansion. This frequency-dependent weighting scheme enables an accurate expansion, even with highly correlated mode shapes that may arise from spatial aliasing due to the limited number of sensors, provided these correlated modes do not have natural frequencies that are closely spaced. Furthermore, the inherent regularization mechanism that arises in this Bayesian-based procedure enables the utilization of the full set of system mode shapes for the expansion, rather than any reduced subset. This approach can produce estimates when considering a single realization of the measured responses, and with some modification, it can also produce estimates for power spectral density matrices measured from many realizations of the responses from statistically stationary random processes. A simply supported beam provides an initial numerical validation, and a cylindrical test article excited by acoustic loads in a reverberation chamber provides experimental validation.
Physics-informed neural networks (PINNs) were recently proposed in [18] as an alternative way to solve partial differential equations (PDEs). A neural network (NN) represents the solution, while a PDE-induced NN is coupled to the solution NN, and all differential operators are treated using automatic differentiation. Here, we first employ the standard PINN and a stochastic version, sPINN, to solve forward and inverse problems governed by a non-linear advection–diffusion–reaction (ADR) equation, assuming we have some sparse measurements of the concentration field at random or pre-selected locations. Subsequently, we attempt to optimise the hyper-parameters of sPINN by using the Bayesian optimisation method (meta-learning) and compare the results with the empirically selected hyper-parameters of sPINN. In particular, for the first part in solving the inverse deterministic ADR, we assume that we only have a few high-fidelity measurements, whereas the rest of the data is of lower fidelity. Hence, the PINN is trained using a composite multi-fidelity network, first introduced in [12], that learns the correlations between the multi-fidelity data and predicts the unknown values of diffusivity, transport velocity and two reaction constants as well as the concentration field. For the stochastic ADR, we employ a Karhunen–Loève (KL) expansion to represent the stochastic diffusivity, and arbitrary polynomial chaos (aPC) to represent the stochastic solution. Correspondingly, we design multiple NNs to represent the mean of the solution and learn each aPC mode separately, whereas we employ a separate NN to represent the mean of diffusivity and another NN to learn all modes of the KL expansion. For the inverse problem, in addition to stochastic diffusivity and concentration fields, we also aim to obtain the (unknown) deterministic values of transport velocity and reaction constants. The available data correspond to 7spatial points for the diffusivity and 20 space–time points for the solution, both sampled 2000 times. We obtain good accuracy for the deterministic parameters of the order of 1–2% and excellent accuracy for the mean and variance of the stochastic fields, better than three digits of accuracy. In the second part, we consider the previous stochastic inverse problem, and we use Bayesian optimisation to find five hyper-parameters of sPINN, namely the width, depth and learning rate of two NNs for learning the modes. Here, we obtain much deeper and wider optimal NNs compared to the manual tuning, leading to even better accuracy, i.e., errors less than 1% for the deterministic values, and about an order of magnitude less for the stochastic fields.
Crystalline materials used in technological applications are often complex assemblies composed of multiple phases and differently oriented grains. Robust identification of the phases and orientation relationships from these samples is crucial, but the information extracted from the diffraction condition probed by an electron beam is often incomplete. We have developed an automated crystal orientation mapping (ACOM) procedure which uses a converged electron probe to collect diffraction patterns from multiple locations across a complex sample. We provide an algorithm to determine the orientation of each diffraction pattern based on a fast sparse correlation method. We demonstrate the speed and accuracy of our method by indexing diffraction patterns generated using both kinematical and dynamical simulations. We have also measured orientation maps from an experimental dataset consisting of a complex polycrystalline twisted helical AuAgPd nanowire. From these maps we identify twin planes between adjacent grains, which may be responsible for the twisted helical structure. All of our methods are made freely available as open source code, including tutorials which can be easily adapted to perform ACOM measurements on diffraction pattern datasets.
Here we extend our recently developed sparse-stochastic fragmented exchange formalism for ground-state near-gap hybrid DFT to calculate absorption spectra within linear-response time-dependent generalized Kohn-Sham DFT (LR-GKS-TDDFT) for systems consisting of thousands of valence electrons within a grid-based/plane-wave representation. A mixed deterministic/fragmented-stochastic compression of the exchange kernel, here using long-range explicit exchange functionals, provides an efficient method for accurate optical spectra. Both real-time propagation as well as frequency-resolved Casida-equation-type approaches for spectra are presented, and the method is applied to large molecular dyes.
OsO 4 and RuO 4 are molecular oxides with unique tetrameric structures and rare +8 oxidation states. Accurately modeling their properties remains challenging for density functional theory (DFT) due to weak intertetramer interactions, which standard functionals fail to capture. Here, in this work, we show that the van der Waals (vdW)-corrected density functional (vdW-DF-optB86b) provides structural parameters that are much closer to experimental values than the standard generalized gradient approximation, with volume predictions that fall within the experimentally observed range. Phonon band structure analysis shows that the inclusion of vdW interactions stabilizes soft phonon modes, highlighting the importance of dispersion corrections for accurate predictions of lattice dynamics. Experimental measurements of the phonon density of states for OsO 4 , obtained via inelastic neutron scattering, demonstrate good agreement with our vdW-DF-optB86b calculations. These results validate OsO 4 and RuO 4 as valuable benchmarks for structural and vibrational calculations via vdW-corrected DFT methods and offer insights for studying the broader class of sparse molecular materials.