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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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At least 667 records · Page 37
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Learning heterogeneous reaction kinetics from X-ray videos pixel by pixel

Reaction rates at spatially heterogeneous, unstable interfaces are notoriously difficult to quantify, yet are essential in engineering many chemical systems, such as batteries and electrocatalysts. Experimental characterizations of such materials by operando microscopy produce rich image datasets, but data-driven methods to learn physics from these images are still lacking because of the complex coupling of reaction kinetics, surface chemistry and phase separation. Here we show that heterogeneous reaction kinetics can be learned from in situ scanning transmission X-ray microscopy (STXM) images of carbon-coated lithium iron phosphate (LFP) nanoparticles. Combining a large dataset of STXM images with a thermodynamically consistent electrochemical phase-field model, partial differential equation (PDE)-constrained optimization and uncertainty quantification, we extract the free-energy landscape and reaction kinetics and verify their consistency with theoretical models. We also simultaneously learn the spatial heterogeneity of the reaction rate, which closely matches the carbon-coating thickness profiles obtained through Auger electron microscopy (AEM). Across 180,000 image pixels, the mean discrepancy with the learned model is remarkably small (<7%) and comparable with experimental noise. Our results open the possibility of learning nonequilibrium material properties beyond the reach of traditional experimental methods and offer a new non-destructive technique for characterizing and optimizing heterogeneous reactive surfaces.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

The role of geography in the complex diffusion of innovations

The urban–rural divide is increasing in modern societies calling for geographical extensions of social influence modelling. Improved understanding of innovation diffusion across locations and through social connections can provide us with new insights into the spread of information, technological progress and economic development. In this work, we analyze the spatial adoption dynamics of iWiW, an Online Social Network (OSN) in Hungary and uncover empirical features about the spatial adoption in social networks. During its entire life cycle from 2002 to 2012, iWiW reached up to 300 million friendship ties of 3 million users. We find that the number of adopters as a function of town population follows a scaling law that reveals a strongly concentrated early adoption in large towns and a less concentrated late adoption. We also discover a strengthening distance decay of spread over the life-cycle indicating high fraction of distant diffusion in early stages but the dominance of local diffusion in late stages. The spreading process is modelled within the Bass diffusion framework that enables us to compare the differential equation version with an agent-based version of the model run on the empirical network. Although both model versions can capture the macro trend of adoption, they have limited capacity to describe the observed trends of urban scaling and distance decay. We find, however that incorporating adoption thresholds, defined by the fraction of social connections that adopt a technology before the individual adopts, improves the network model fit to the urban scaling of early adopters. Controlling for the threshold distribution enables us to eliminate the bias induced by local network structure on predicting local adoption peaks. Finally, we show that geographical features such as distance from the innovation origin and town size influence prediction of adoption peak at local scales in all model specifications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Machine learning and serving of discrete field theories

A method for machine learning and serving of discrete field theories in physics is developed. The learning algorithm trains a discrete field theory from a set of observational data on a spacetime lattice, and the serving algorithm uses the learned discrete field theory to predict new observations of the field for new boundary and initial conditions. The approach of learning discrete field theories overcomes the difficulties associated with learning continuous theories by artificial intelligence. The serving algorithm of discrete field theories belongs to the family of structure-preserving geometric algorithms, which have been proven to be superior to the conventional algorithms based on discretization of differential equations. The effectiveness of the method and algorithms developed is demonstrated using the examples of nonlinear oscillations and the Kepler problem. In particular, the learning algorithm learns a discrete field theory from a set of data of planetary orbits similar to what Kepler inherited from Tycho Brahe in 1601, and the serving algorithm correctly predicts other planetary orbits, including parabolic and hyperbolic escaping orbits, of the solar system without learning or knowing Newton’s laws of motion and universal gravitation. The proposed algorithms are expected to be applicable when the effects of special relativity and general relativity are important.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Magnetic field mapping of inaccessible regions using physics-informed neural networks

A difficult problem concerns the determination of magnetic field components within an experimentally inaccessible region when direct field measurements are not feasible. In this paper, we propose a new method of accessing magnetic field components using non-disruptive magnetic field measurements on a surface enclosing the experimental region. Magnetic field components in the experimental region are predicted by solving a set of partial differential equations (Ampere’s law and Gauss’ law for magnetism) numerically with the aid of physics-informed neural networks (PINNs). Prediction errors due to noisy magnetic field measurements and small number of magnetic field measurements are regularized by the physics information term in the loss function. We benchmark our model by comparing it with an older method. The new method we present will be of broad interest to experiments requiring precise determination of magnetic field components, such as searches for the neutron electric dipole moment.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Enhancing high-fidelity nonlinear solver with reduced order model

Abstract We propose the use of reduced order modeling (ROM) to reduce the computational cost and improve the convergence rate of nonlinear solvers of full order models (FOM) for solving partial differential equations. In this study, a novel ROM-assisted approach is developed to improve the computational efficiency of FOM nonlinear solvers by using ROM’s prediction as an initial guess. We hypothesize that the nonlinear solver will take fewer steps to the converged solutions with an initial guess that is closer to the real solutions. To evaluate our approach, four physical problems with varying degrees of nonlinearity in flow and mechanics have been tested: Richards’ equation of water flow in heterogeneous porous media, a contact problem in a hyperelastic material, two-phase flow in layered porous media, and fracture propagation in a homogeneous material. Overall, our approach maintains the FOM’s accuracy while speeding up nonlinear solver by 18–73% (through suitable ROM-assisted FOMs). More importantly, the proximity of ROM’s prediction to the solution space leads to the improved convergence of FOMs that would have otherwise diverged with default initial guesses. We demonstrate that the ROM’s accuracy can impact the computational efficiency with more accurate ROM solutions, resulting in a better cost reduction. We also illustrate that this approach could be used in many FOM discretizations (e.g., finite volume, finite element, or a combination of those). Since our ROMs are data-driven and non-intrusive, the proposed procedure can easily lend itself to any nonlinear physics-based problem.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

On fast simulation of dynamical system with neural vector enhanced numerical solver

The large-scale simulation of dynamical systems is critical in numerous scientific and engineering disciplines. However, traditional numerical solvers are limited by the choice of step sizes when estimating integration, resulting in a trade-off between accuracy and computational efficiency. To address this challenge, we introduce a deep learning-based corrector called Neural Vector (NeurVec), which can compensate for integration errors and enable larger time step sizes in simulations. Our extensive experiments on a variety of complex dynamical system benchmarks demonstrate that NeurVec exhibits remarkable generalization capability on a continuous phase space, even when trained using limited and discrete data. NeurVec significantly accelerates traditional solvers, achieving speeds tens to hundreds of times faster while maintaining high levels of accuracy and stability. Moreover, NeurVec’s simple-yet-effective design, combined with its ease of implementation, has the potential to establish a new paradigm for fast-solving differential equations based on deep learning.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Physics informed deep neural network embedded in a chemical transport model for the Amazon rainforest

Secondary organic aerosols (SOA) are fine particles in the atmosphere, which interact with clouds, radiation and affect the Earth’s energy budget. SOA formation involves chemistry in gas phase, aqueous aerosols, and clouds. Simulating these chemical processes involve solving a stiff set of differential equations, which are computationally expensive steps for three-dimensional chemical transport models. Deep neural networks (DNNs) are universal function approximators that could be used to represent the complex nonlinear changes in aerosol physical and chemical processes; however, key challenges such as generalizability to extended time periods, preservation of mass balance, simulating sparse model outputs, and maintaining physical constraints have limited their use in atmospheric chemistry. Here, we develop an approach of using a physics-informed DNN that overcomes previous such challenges and demonstrates its applicability for the chemical formation processes of isoprene epoxydiol SOA (IEPOX-SOA) over the Amazon rainforest. The DNN is trained with data generated by simulating IEPOX-SOA over the entire atmospheric column, using the Weather Research and Forecasting Model coupled with Chemistry (WRF-Chem). The trained DNN is then embedded within WRF-Chem to replace the computationally expensive default solver of IEPOX-SOA formation. The trained DNN predictions generalizes well with the default model simulation of the IEPOX-SOA mass concentrations and its size distribution (20 size bins) over several days of simulations in both dry and wet seasons. The embedded DNN reduces the computational expense of WRF-Chem by a factor of 2. Our approach shows promise in terms of application to other computationally expensive chemistry solvers in climate models.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2021

Physics-informed machine learning

Despite great progress in simulating multiphysics problems using the numerical discretization of partial differential equations (PDEs), one still cannot seamlessly incorporate noisy data into existing algorithms, mesh generation remains complex, and high-dimensional problems governed by parameterized PDEs cannot be tackled. Moreover, solving inverse problems with hidden physics is often prohibitively expensive and requires different formulations and elaborate computer codes. Machine learning has emerged as a promising alternative, but training deep neural networks requires big data, not always available for scientific problems. Instead, such networks can be trained from additional information obtained by enforcing the physical laws (for example, at random points in the continuous space-time domain). Such physics-informed learning integrates (noisy) data and mathematical models, and implements them through neural networks or other kernel-based regression networks. Moreover, it may be possible to design specialized network architectures that automatically satisfy some of the physical invariants for better accuracy, faster training and improved generalization. Furthermore, we review some of the prevailing trends in embedding physics into machine learning, present some of the current capabilities and limitations and discuss diverse applications of physics-informed learning both for forward and inverse problems, including discovering hidden physics and tackling high-dimensional problems.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Learning nonlinear operators via DeepONet based on the universal approximation theorem of operators

It is widely known that neural networks (NNs) are universal approximators of continuous functions. However, a less known but powerful result is that a NN with a single hidden layer can accurately approximate any nonlinear continuous operator. This universal approximation theorem of operators is suggestive of the structure and potential of deep neural networks (DNNs) in learning continuous operators or complex systems from streams of scattered data. Here, in this work, we thus extend this theorem to DNNs. We design a new network with small generalization error, the deep operator network (DeepONet), which consists of a DNN for encoding the discrete input function space (branch net) and another DNN for encoding the domain of the output functions (trunk net). We demonstrate that DeepONet can learn various explicit operators, such as integrals and fractional Laplacians, as well as implicit operators that represent deterministic and stochastic differential equations. We study different formulations of the input function space and its effect on the generalization error for 16 different diverse applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Development of the Senseiver for efficient field reconstruction from sparse observations

Abstract The reconstruction of complex time-evolving fields from sensor observations is a grand challenge. Frequently, sensors have extremely sparse coverage and low-resource computing capacity for measuring highly nonlinear phenomena. While numerical simulations can model some of these phenomena using partial differential equations, the reconstruction problem is ill-posed. Data-driven-strategies provide crucial disambiguation, but these suffer in cases with small amounts of data, and struggle to handle large domains. Here we present the Senseiver, an attention-based framework that excels in reconstructing complex spatial fields from few observations with low overhead. The Senseiver reconstructs n -dimensional fields by encoding arbitrarily sized sparse sets of inputs into a latent space using cross-attention, producing uniform-sized outputs regardless of the number of observations. This allows efficient inference by decoding only a sparse set of output observations, while a dense set of observations is needed to train. This framework enables training of data with complex boundary conditions and extremely large fine-scale simulations. We build on the Perceiver IO by enabling training models with fewer parameters, which facilitates field deployment, and a training framework that allows a flexible number of sensors as input, which is critical for real-world applications. We show that the Senseiver advances the state-of-the-art of field reconstruction in many applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Solving sparse finite element problems on neuromorphic hardware

The finite element method (FEM) is one of the most important and ubiquitous numerical methods for solving partial differential equations (PDEs) on computers for scientific and engineering discovery. Applying the FEM to larger and more detailed scientific models has driven advances in high-performance computing for decades. Here we demonstrate that scalable spiking neuromorphic hardware can directly implement the FEM by constructing a spiking neural network that solves the large, sparse, linear systems of equations at the core of the FEM. We show that for the Poisson equation, a fundamental PDE in science and engineering, our neural circuit achieves meaningful levels of numerical accuracy and close to ideal scaling on modern, inherently parallel and energy-efficient neuromorphic hardware, specifically Intel’s Loihi 2 neuromorphic platform. We illustrate extensions to irregular mesh geometries in both two and three dimensions as well as other PDEs such as linear elasticity. Our spiking neural network is constructed from a recurrent network model of the brain’s motor cortex and, in contrast to black-box deep artificial neural network-based methods for PDEs, directly translates the well-understood and trusted mathematics of the FEM to a natively spiking neuromorphic algorithm.

Applied mathematics↗
DOE OSTI2021

A framework for data-driven solution and parameter estimation of PDEs using conditional generative adversarial networks

We employ and adapt the image-to-image translation concept based on conditional generative adversarial networks (cGAN) for learning a forward and an inverse solution operator of partial differential equations (PDEs). We focus on steady-state solutions of coupled hydromechanical processes in heterogeneous porous media and present the parameterization of the spatially heterogeneous coefficients, which is exceedingly difficult using standard reduced-order modeling techniques. We show that our framework provides a speed-up of at least 2,000 times compared to a finite-element solver and achieves a relative root-mean-square error (r.m.s.e.) of less than 2% for forward modeling. For inverse modeling, the framework estimates the heterogeneous coefficients, given an input of pressure and/or displacement fields, with a relative r.m.s.e. of less than 7%, even for cases where the input data are incomplete and contaminated by noise. The framework also provides a speed-up of 120,000 times compared to a Gaussian prior-based inverse modeling approach while also delivering more accurate results.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

Energy-efficient scientific computing using chemical reservoirs

The rapid growth of computing demands driven by scientific computing, data analytics, and artificial intelligence (AI) advancements has exposed the limitations of traditional digital processing systems. These systems are nearing physical energy barriers, making significant gains in energy efficiency increasingly unattainable. As we advance toward post-exascale computing, disruptive approaches are critical to overcoming these limitations. Among emerging analog solutions, biochemical computing offers a transformative path for achieving orders-of-magnitude improvements in energy efficiency. By leveraging the natural optimization capabilities of chemical reaction networks (CRNs), biochemical systems have the potential to meet high-performance computing needs through natural scalability. However, numerous challenges remain, including theoretical limitations in mapping computational problems to CRNs and practical barriers in implementing biochemical computing devices. In this paper, we present a framework for chemical computation using biochemical systems and introduce key components of our approach for energy-efficient scientific computing. We showcase the feasibility of this framework by solving a system of ordinary differential equations by emulating a chemical reservoir device, demonstrating its potential for addressing modern computing challenges. This work lays a foundational step toward harnessing the computational power of chemistry to design energy-efficient, scalable, high-performance next-generation computing systems.

Johnson, Connah G. M. [Pacific Northwest National ↗
DOE OSTI2026

A mathematical framework for thermodynamic computing with applications to chemical reaction networks

The widespread adoption of energy-intensive computing applications has led to a growing need for energy-efficient computing approaches. Thermodynamic computing offers a promising approach for low-energy computation by leveraging the intrinsic computational capabilities of physical, chemical, or biological systems. However, the mathematical foundations of thermodynamic computing require further development to fully realize the potential energy efficiencies, as well as to assess factors like noise and operational speed. In this paper, we establish a mathematical framework for utilizing thermodynamic processes to perform fundamental operations, including addition, subtraction, multiplication, and division. We highlight the use of chemical reactions as potential computational units and explore synthetic chemical and biochemical systems as practical implementations. Additionally, we demonstrate how these principles can be applied to solving complex mathematical problems, such as ordinary differential equations (ODEs) and suggest the necessary components to implement the thermodynamic computing framework using chemical reactions based in a microfluidic device. This work enhances our understanding of thermodynamic processes for natural computing as a basis for scalable, energy-efficient computation in paradigm disruptive next-generation systems.

Cannon, William R. [Pacific Northwest National Lab↗
DOE OSTI2021

Boundary layer description of directional polymer crystallisation

Nearly fifty years ago Lovinger and Gryte suggested that the directional crystallization of a polymer was analogous to the quiescent isothermal crystallization experiment but at a supercooling where the crystal growth velocity was equal to the velocity of the moving front. Our experiments showed that this equivalence holds in a detailed manner at low directional velocities. To understand the underlying physics of these situations, we modeled the motion of a crystallization front in a liquid where the left side boundary is suddenly lowered below the melting point (Stefan's problem) but with the modification that the crystallization kinetics follow a version of the Avrami model. Our numerical results surprisingly showed that the results of the polymer analog track with the Stefan results which were derived for a simple liquid that crystallizes completely at its melting point; in particular, the position of the crystal growth-front evolved with time exactly as in the Stefan problem. The numerical solution also showed that the temperature in the immediate vicinity of the growth-front decreased with increasing front velocity, which is in line with Lovinger and Gryte's ansatz. To provide a clear theoretical understanding of these numerical results we derive a boundary layer solution to the governing coupled differential equations of the polymer problem. The analytical results are in agreement with our observations from experiments and numerical computations but show that this equivalence between the small molecule and polymer analog only holds in the limit where the crystallization enthalpy is much larger than the rate at which heat is conducted away in the polymer. In particular, in the context of the temperature profile, the enthalpy generated by the crystallisation process which is spread out over a narrow spatial region can be approximated as a point source whose location and temperature correspond to the Lovinger–Gryte ansatz.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Learning effective SDEs from Brownian dynamic simulations of colloidal particles

We construct a reduced, data-driven, parameter dependent effective stochastic differential equation (eSDE) for electric-field mediated colloidal crystallization using data obtained from Brownian dynamics simulations. We use diffusion maps (a manifold learning algorithm) to identify a set of useful latent observables. In this latent space we identify an eSDE using a deep learning architecture inspired by numerical stochastic integrators and compare it with the traditional Kramers–Moyal expansion estimation. We show that the obtained variables and the learned dynamics accurately encode the physics of the Brownian dynamic simulations. We further illustrate that our reduced model captures the dynamics of corresponding experimental data. Further, our dimension reduction/reduced model identification approach can be easily ported to a broad class of particle systems dynamics experiments/models.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Absolute stimulated Raman side scatter in direct-drive laser-produced plasmas

Production of suprathermal electrons by stimulated Raman scattering (SRS) is a principal concern for contemporary direct-drive inertial confinement fusion experiments at the National Ignition Facility and similar systems since such electrons penetrate and preheat the target core, preventing efficient implosion. The higher temperatures and longer scale lengths in these experiments favor SRS over two-plasmon decay, which predominated in earlier experiments. In particular, current experiments are expected to exceed the threshold for absolute Raman side scatter, which would then dominate the interaction since it grows temporally until saturated by nonlinear mechanisms such as hot-electron production. Until recently, analyses of SRS side scatter have treated the case of a single laser beam incident on a plasma, but the direct-drive approach to laser fusion employs a multitude of beams to drive the implosion. Here in this paper, we present an analysis that can be applied to an arbitrary number of beams with varied angles of incidence and polarizations. In the case of a single beam, it allows a physically motivated derivation and verification of an analytic threshold formula. In the general case of multiple beams and arbitrary orientation and polarizations, the threshold is found by numerical integration of a set of first-order linear partial differential equations.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Global geodesic acoustic mode in an ideal magnetohydrodynamic tokamak plasma

A concise and transparent second order ordinary differential equation (ODE) describing the radial structure of the global geodesic acoustic mode (GAM) is analytically presented in a low-β tokamak plasma. The large-aspect-ratio and circular cross section are assumed to linearize the ideal magnetohydrodynamic equations. We show clearly how finite β-dependent terms affect the global GAM frequency and radial mode structure. Here, a typical Wentzel–Kramers–Brillouin form of solution is found for some reversed shear equilibria. For some other equilibria with lower β, even also in a reversed shear tokamak, the GAM continuum is upraised by the high order β-dependent terms so that its maximum is beyond ω G , where ω G is the classical local frequency of GAM. As a result, no self-consistent solution to the ODE can be found.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗