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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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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Process intensification education contributes to sustainable development goals. Part 1

In 2015 all the United Nations (UN) member states adopted 17 sustainable development goals (UN-SDG) as part of the 2030 Agenda, which is a 15-year plan to meet ambitious targets to eradicate poverty, protect the environment, and improve the quality of life around the world. Although the global community has progressed, the pace of implementation must accelerate to reach the UN-SDG time-line. For this to happen, professionals, institutions, companies, governments and the general public must become cognizant of the challenges that our world faces and the potential technological solutions at hand, including those provided by chemical engineering. Process intensification (PI) is a recent engineering approach with demonstrated potential to significantly improve process efficiency and safety while reducing cost. It offers opportunities for attaining the UN-SDG goals in a cost-effective and timely manner. However, the pedagogical tools to educate undergraduate, graduate students, and professionals active in the field of PI lack clarity and focus. This paper sets out the state-of-the-art, main discussion points and guidelines for enhanced PI teaching, deliberated by experts in PI with either an academic or industrial background, as well as representatives from government and specialists in pedagogy gathered at the Lorentz Center (Leiden, The Netherlands) in June 2019 with the aim of uniting the efforts on education in PI and produce guidelines. In this Part 1, we discuss the societal and industrial needs for an educational strategy in the framework of PI. The terminology and background information on PI, as it relates to educational implementation in industry and academia, are provided as a preamble to Part 2, which presents practical examples that will help educating on Process Intensification.

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

Intrinsic size dependent plasticity in BCC micro-pillars under uniaxial tension and pure torsion

The mechanical behavior of submicron body-centered cubic (BCC) micro-pillars is investigated by three-dimensional dislocation dynamics (DD) simulations to better understand the governing mechanisms for size dependent plasticity under uniaxial tension and pure torsion. A formula is developed to compute the incremental plastic twist due to dislocation motion in DD simulations. The DD simulations show that different dislocation microstructures are created depending on the loading conditions, which leads to different size dependent mechanical behavior. While in tension plasticity is mainly governed by the kinetics of dislocation motion controlled partly by the surface dislocation sources, plastic flow in torsion is controlled by dislocation pile-ups associated with strain gradients. The simulation results also reveal a Bauschinger effect and plastic recovery under cyclic twist, which have been observed in recent experiments.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Carbon and energy cost impacts of electrification of space heating with heat pumps in the US

In order to meet climate goals, it will be necessary to significantly reduce the greenhouse gases emitted by homes. A key factor in the US is to reduce the on-site combustion of fossil fuels for heating end-uses and to replace this with use of electric heat pump technologies connected to a low-carbon grid. The replacement of natural gas furnaces with electric heat pumps is a key home decarbonization strategy. However, the potential for space heating electrification to reduce greenhouse gas emissions depends on the carbon dioxide equivalent (CO 2 e) content of the electricity used by the heat pump. This varies considerably depending on the source of electricity, with large state to state variability. Furthermore, household energy costs are likely to be impacted by the electrification of space heating, because retail energy prices for both natural gas and electricity in each state vary by factors of seven and four, respectively. Contractors, energy programs, government and building code officials, as well as consumers need clear indications of the likely CO 2 e and energy cost impacts of proposed electrification projects, because these will affect decarbonization choices and rationales around scaled heating electrification. Government and utility programs also need to be aware of the likely outcomes of any supported/incentivized measures. Here, in this paper, we investigate these effects by looking at new metrics to analyze the change in CO 2 e emitted and the cost to meet home heating loads when switching from a natural gas furnace to a heat pump for the contiguous 48 states of the mainland US.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2026

BMINN: Learning chemical potentials and parameters from voltage data for multi-phase battery modeling

Free-energy landscapes and chemical potentials govern the dynamics of phase transitions, transport, and stability in functional materials, yet they remain experimentally inaccessible under realistic operating conditions. Here we introduce a Bayesian model-integrated neural network (BMINN) that embeds physics-based formulations of non-autonomous partial differential-algebraic equations into probabilistic learning. This approach reconstructs hidden thermodynamics directly from macroscopic current-voltage data, providing quantitative access to metastable states, staging transitions, and energy barriers without synchrotron probes. Demonstrated on lithium-graphite electrodes, BMINN recovers full Gibbs free-energy landscapes with fidelity validated against operando X-ray diffraction. The framework generalizes across dynamical regimes, enabling accurate voltage prediction, internal state estimation, and inference of governing parameters. Beyond batteries, BMINN exemplifies a broadly applicable strategy for learning missing physics in multiphase, non-equilibrium systems, offering a new pathway to uncover hidden thermodynamic functions across condensed matter and materials physics.

25 ENERGY STORAGE↗
DOE OSTI2023

Suspending democratic (dis)belief: Nonliberal energy polities of solar power in Morocco and Tanzania

This paper proposes the concept of technodemocratic imaginaries (TDIMs) to supplement the widely-used framework of sociotechnical imaginaries (STIMs) for analyzing nonliberal political contexts in energy social science research. Taking the power of coproductionist analysis of STIMs seriously, TDIMs highlight the inherent instabilities within overarching STIMs by arguing that not only are particular groups marginalized and excluded but that they continue to practice and mobilize their own imaginaries of collective governance and justice vis-à-vis energy systems. In contrast, the existing idea of contested STIMs, in which a shared mode of knowledge politics undergirds different imaginaries, casts aside subaltern modes of political engagement and knowledge-making. TDIMs expand conceptions of democracy to include shared practices of credibility in nonliberal political orders. The intent is not to promote democratic relativism but rather to ask scholars and international energy-access practitioners to suspend their democratic disbelief when studying energy matters in so-called nonliberal contexts. We develop the concept of TDIMs by comparing two African nation-states–Morocco and Tanzania–to show how the states and subaltern groups do (or do not) develop TDIMs related to solar power. While international governance organizations often portray Morocco as authoritarian and Tanzania corrupt, each state differently experienced colonization and decolonization and practices different relationships with domestic subaltern groups. Whereas low-income citizens and indigenous groups seek integration into the Moroccan state’s STIM, the Maasai in Tanzania chart their own TDIM separate from the state and international development groups.

14 SOLAR ENERGY↗
DOE OSTI2025

Solar cities: A case study analysis of city-level enablers of expanded solar energy access

Rooftop solar photovoltaic (PV) adoption can benefit households by reducing electricity bills and enhancing energy resiliency. Low and moderate-income (LMI) households have been less likely to adopt PV and experience these benefits in the United States than higher-income households. Adopter income trends are often explored through quantitative analysis with limited explanatory power. Our quantitative analysis only explains around one-third of city-level variation in LMI adoption trends through socioeconomic factors such as median home values and income inequality and PV market factors such as cumulative adoption and incentives. We implement semi-structured interviews in three case studies of cities with relatively high rates of LMI PV adoption to better understand the factors that explain PV adopter income trends. The case studies partly reiterate findings from quantitative analysis, such as the role of PV incentives. The case studies reveal a broader set of LMI adoption drivers that are missed in quantitative analyses. The case studies show how city contexts can affect LMI adoption, such as the role of supportive city governments. The case studies also reveal the importance of partnerships, such as partnerships between city governments and state LMI PV program implementers. Finally, interviewees emphasized the importance of building trust among prospective LMI PV adopters. Interviewees suggested that partnerships, outreach, and consumer protection measures were crucial to building trust in PV installers among LMI households.

Adoption↗
DOE OSTI2023

Observation of two different cool flame regimes of diethyl ether in a counterflow burner

This short communication reports, for the first time, the existence of two different self-sustaining cool flame regimes of diethyl ether (DEE) in a diffusion counterflow burner: a weaker autoignition-assisted cool flame near the fuel burner and a normal diffusion cool flame near the stagnation plane. Here, the results show that the normal diffusion cool flame extinction limit increases monotonically with the fuel mole fraction, while the autoignition-assisted cool flame approaches a plateau and can exist at a fuel mole fraction below the normal diffusion cool flame. It is shown that both flame regimes are governed by the same low-temperature chain-branching reaction pathway of DEE. By using in situ laser diagnostics, entrainment of unburned fuel stream to oxygen stream at the outer edge of the fuel burner is identified as the governing physical mechanism causing a partially premixed self-sustained hollow cool flame structure. The results reveal that when a fuel with high low-temperature reactivity, two different cool flame regimes can be observed in a counterflow flame experiment. Future studies with high-reactivity fuels in a counterflow burner must ensure to distinguish between the two self-sustaining cool flame regimes. Moreover, the existence of these different cool flame regimes needs to be examined so that they would not trigger an uncontrolled combustion phasing in advanced engines fed with high low-temperature reactivity fuels.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Fatigue-crack propagation behavior in a high-carbon chromium SUJ2 bearing steel: Role of microstructure

High-carbon chromium martensite steels are commonly selected for bearing components in the power generation, automotive and aerospace industries where fatigue failure is a major concern. Accordingly, it is of importance to elucidate the structure-property relationships governing the fatigue properties of such bearing steels. Here, the role of microstructure in influencing the fatigue-crack propagation behavior of a high-carbon chromium SUJ2 bearing steel is examined with emphasis on three martensitic structures: (i) a fine-grained (~10 μm) structure with intragranular (but no intergranular) carbides, (ii) a coarser-grained (~25 μm) structure with discontinuous grain-boundary carbides primarily near triple junctions, and (iii) a coarse-grained (~31 μm) structure with continuous grain-boundary carbides. Although growth rates were fairly similar above ~10 -8 m/cycle, significant differences in behavior were observed at lower, near-threshold growth rates; specifically at a load ratio of 0.1, the ΔKth fatigue threshold was increased from 3.8 MPa m ½ in the fine-grained structure to 5.9 to 6.3 MPa m ½ in the two coarser-grained structures. The dominant factor governing such near-threshold behavior was found to be crack-tip shielding from roughness-induced crack closure, which was most pronounced in the coarser-grained structures; additionally, shielding from crack deflection and branching was apparent in these structures as the crack propagated through the network of intersecting martensite lamellae within the coarse grains. Compared to high-strength stainless steels and low-strength carbon steels, the fine-grained SUJ2 steel displays an exceptional combination of high strength and fatigue-crack growth resistance and is considered to be a superior structural alloy for bearing applications.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Physics-Informed Gaussian Process Regression for States Estimation and Forecasting in Power Grids

Real-time state estimation and forecasting are critical for the efficient operation of power grids. In this paper, a physics-informed Gaussian process regression (PhI-GPR) method is presented and used for forecasting and estimating the phase angle, angular speed, and wind mechanical power of a three-generator power grid system using sparse measurements. In standard data-driven Gaussian process regression (GPR), parameterized models for the prior statistics are fit by maximizing the marginal likelihood of observed data. In the PhI-GPR method, we propose to compute the prior statistics offline by solving stochastic differential equations (SDEs) governing the power grid dynamics. The short-term forecast of a power grid system dominated by wind generation is complicated by the stochastic nature of the wind and the resulting uncertainty in wind mechanical power. Here, we assume that the power grid dynamics are governed by swing equations, with the wind mechanical power fluctuating randomly in time. We solve these equations for the mean and covariances of the power grid states using the Monte Carlo simulation method. We demonstrate that the proposed PhI-GPR method can accurately forecast and estimate observed and unobserved states. For the considered problem, PhI-GPR has computational advantages over the ensemble Kalman filter (EnKF) method: In PhI-GPR, ensembles are computed offline and independently of the data acquisition process, whereas for EnFK, ensembles are computed online with data acquisition, rendering real-time forecast more challenging. We also demonstrate that the PhI-GPR forecast is more accurate than the EnKF forecast when the random mechanical wind power is non-Markovian. In contrast, the two methods produce similar forecasts for the Markovian mechanical wind power. For observed states, we show that PhI-GPR provides a forecast comparable to the standard data-driven GPR; both forecasts are significantly more accurate than the autoregressive integrated moving average (ARIMA) forecast. We also show that the ARIMA forecast is more sensitive to observation frequency and measurement errors than the PhI-GPR forecast.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Measurements of the thermal conductivity of reference liquids using a modified transient hot-wire needle probe

Many power generation processes feature some type of working fluid that plays a critical role in the transfer of heat throughout the system. To optimize thermal efficiencies, an accurate characterization of the temperature-dependent thermal conductivity of the fluid is needed. Herein, this study develops a time-domain Modified Transient Hot-wire Needle Probe to overcome phenomena that have impaired traditional measurement techniques when the fluid is both corrosive and at an elevated temperature. First, the physical design of the instrument is presented to demonstrate features that limit interference from corrosion, electrical conduction, and convective and radiative heat transfer. Next, a governing equation for 1D (radial) heat conduction is fully developed using the thermal quadrupoles technique. A finite-element study is performed for validation. A sensitivity analysis is done to assess the time-dependent influence of critical parameters in the governing equation for several samples. Finally, thermal conductivity measurements are presented for seven different liquid substances by fitting the thermal model to experimental data across a range of temperatures. Reference correlations are included for comparison. The sample thermal conductivity and ambient temperature of the experimental conditions range from 0.125–16.5$\frac{W}{m·K}$ and 10–400°C, respectively. The total uncertainty, comprised of both the experimental design and fitting process, of all measurements is quantified.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2026

A trait syndrome ties cell morphology to glycolysis across the yeast subphylum

Co-variation of traits provides fundamental insights into constraints governing their evolution. An inverse correlation between glucose uptake rates (GURs) and cell surface area-to-volume (SA:V) ratios across 11 yeast species was recently reported. Here, we expand the analysis to 282 species to assess the generalizability of this correlation across Saccharomycotina yeasts and the contribution of shared evolutionary history to the co-variation of these traits. Using phylogenetic regression models, we found extracellular acidification rates (ECARs, used as a proxy for GURs) were weakly, but significantly, correlated with SA:V across Saccharomycotina. ECARs were also correlated with genome sizes and growth rates. Our findings support the reported correlation between GURs and SA:V ratios, but suggest other associated traits, including genome sizes. Specifically, yeasts that consume glucose faster tend to have lower SA:V, faster growth rates, and larger genomes, suggesting a trait syndrome governing several metabolic, genomic, and morphological traits across the yeast subphylum.

biological sciences↗
DOE OSTI2022

Viscoelastic necking dynamics between attractive microgels

Hypothesis: Microgels can deform and interpenetrate and display colloid/polymer duality. The effective interaction of microgels in the collapsed state is governed by the interplay of polymer–solvent interfacial tension and bulk elasticity. A connecting neck is shown to mediate microgel interaction, but its temporal evolution has not been addressed. Here we hypothesize that the necking dynamics of attractive microgels exhibits liquid-like or solid-like behavior over different time and length scales. Experiments: We simulate the merging and pinching of attractive microgels with different crosslinking densities in explicit solvent using dissipative particle dynamics. The temporal coalescence dynamics of microgels is investigated and compared with simple liquid and polymeric droplets. We model the neck growth on long time scales using Maxwell model of polymer relaxation and compare the theoretical prediction with simulation data. The mechanical strength of the neck is characterized systematically via simulated pinch-off of microgels by steered molecular dynamics. Findings: We evidence a crossover in the coalescence dynamics reflecting the viscoelastic signature of microgels. In contrast to the common knowledge that viscoelastic materials respond elastically on short time scales, the early expansion of the microgel neck exhibits a linear behavior, similar to the viscous coalescence of liquid droplets. However, the late regime with arrested dynamics resembles sintering of solid particles. Through an analytical model relating microgel dynamics to neck growth, we show that the long-term behavior is governed by stress relaxation of the polymers in the neck region and predict an exponential decay in the rate of growth, which agrees favorably with the simulation. Different from coalescence, the thread thinning in microgel breakup primarily highlights its polymeric characteristics.

42 ENGINEERING↗
DOE OSTI2022

Analysis of water–energy nexus and trends in support of the sustainable development goals: A study using longitudinal water–energy use data

Water and energy are two critical natural resources necessary for human activities and socioeconomic development. Water and energy systems are highly interdependent, and water efficiency and energy efficiency are two related indicators for the United Nations' Sustainable Development Goals. It is critical to improve energy–water use efficiency to sustain socioeconomic development while reducing adverse effects on natural resources, society and the environment. By using longitudinal energy–water use data for China over the past 21 years, this paper develops a temporo-spatial study to address key issues and introduce analytical approaches needed to understand the water–energy nexus and support integrated resource planning and management to achieve the Sustainable Development Goals. Decomposition analysis indicates that the production effect was the dominating factor contributing the increase in the country's energy–water use, while energy–water efficiency is the major factor slowing the growth of the country's energy–water use. Changes and trends analyses show that the country's energy intensity, water intensity, and water/energy ratio significantly decreased from 1999 to 2019, but the rate of decline has slowed. The disparities of the country's provincial energy intensities, water intensities, and water/energy ratios significantly decreased with economic growth. Results suggest that improving energy–water efficiency is critical for the country to curb increasing energy and water use and achieve resource and environmental protection targets with rapid economic development. Furthermore, the disparities between regional energy-water efficiencies can be reduced along with economic growth, while an overheated economy can widen the disparities and result in unsustainable and inefficient utilization of resources. Government coordination, targets and policy as part of the efficiency governance system are critical for continuous energy–water efficiency improvement and directly influence the implementation and effectiveness of energy–water efficiency policy.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2019

A computational model for nanosecond pulse laser-plasma interactions

A multi-physics numerical model for laser-induced optical breakdown and laser-plasma interaction in a non-equilibrium gas is presented, accounting for: production of priming electrons via multi-photon ionization, energy absorption, cascade ionization, induced hydrodynamic response, and shock formation and propagation. The gas is governed by the Navier-Stokes equations, with non-equilibrium effects taken into account by means of a two-temperature model. The space-time dependence of the laser beam is modeled with a flux-tube formulation for the Radiative Transfer Equation. The flow governing equations are discretized in space using a second-order finite volume method. The semi-discrete equations are marched in time using an implicit-explicit (IMEX) dual time-stepping strategy, where diffusion and chemistry are solved implicitly, whereas convection is explicit. Application to a 20 ns long 50 mJ pulse laser-induced breakdown in quiescent O 2 shows the advantages of this temporal discretization during and just after the laser pulse, while a less-expensive symmetric Strang splitting (with implicit chemistry) is sufficient for the post-breakdown gas dynamics after ≃ 0.1 μs. The integrated model is shown to reproduce key features of corresponding experiments.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

NSFnets (Navier-Stokes flow nets): Physics-informed neural networks for the incompressible Navier-Stokes equations

In the last 50 years there has been a tremendous progress in solving numerically the Navier-Stokes equations using finite differences, finite elements, spectral, and even meshless methods. Yet, in many real cases, we still cannot incorporate seamlessly (multi-fidelity) data into existing algorithms, and for industrial-complexity applications the mesh generation is time consuming and still an art. Moreover, solving ill-posed problems (e.g., lacking boundary conditions) or inverse problems is often prohibitively expensive and requires different formulations and new computer codes. Here, we employ physics-informed neural networks (PINNs), encoding the governing equations directly into the deep neural network via automatic differentiation, to overcome some of the aforementioned limitations for simulating incompressible laminar and turbulent flows. We develop the Navier-Stokes flow nets (NSFnets) by considering two different mathematical formulations of the Navier-Stokes equations: the velocity-pressure (VP) formulation and the vorticity-velocity (VV) formulation. Since this is a new approach, we first select some standard benchmark problems to assess the accuracy, convergence rate, computational cost and flexibility of NSFnets; analytical solutions and direct numerical simulation (DNS) databases provide proper initial and boundary conditions for the NSFnet simulations. The spatial and temporal coordinates are the inputs of the NSFnets, while the instantaneous velocity and pressure fields are the outputs for the VP-NSFnet, and the instantaneous velocity and vorticity fields are the outputs for the VV-NSFnet. This is unsupervised learning and, hence, no labeled data are required beyond boundary and initial conditions and the fluid properties. The residuals of the VP or VV governing equations, together with the initial and boundary conditions, are embedded into the loss function of the NSFnets. No data is provided for the pressure to the VP-NSFnet, which is a hidden state and is obtained via the incompressibility constraint without extra computational cost. Unlike the traditional numerical methods, NSFnets inherit the properties of neural networks (NNs), hence the total error is composed of the approximation, the optimization, and the generalization errors. Here, we empirically attempt to quantify these errors by varying the sampling (“residual”) points, the iterative solvers, and the size of the NN architecture. For the laminar flow solutions, we show that both the VP and the VV formulations are comparable in accuracy but their best performance corresponds to different NN architectures. The initial convergence rate is fast but the error eventually saturates to a plateau due to the dominance of the optimization error. For the turbulent channel flow, we show that NSFnets can sustain turbulence at , but due to expensive training we only consider part of the channel domain and enforce velocity boundary conditions on the subdomain boundaries provided by the DNS data base. We also perform a systematic study on the weights used in the loss function for balancing the data and physics components, and investigate a new way of computing the weights dynamically to accelerate training and enhance accuracy. In the last part, we demonstrate how NSFnets should be used in practice, namely for ill-posed problems with incomplete or noisy boundary conditions as well as for inverse problems. We obtain reasonably accurate solutions for such cases as well without the need to change the NSFnets and at the same computational cost as in the forward well-posed problems. As a result, we also present a simple example of transfer learning that will aid in accelerating the training of NSFnets for different parameter settings.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

A gradient-based deep neural network model for simulating multiphase flow in porous media

We report simulation of multiphase flow in porous media is crucial for the effective management of subsurface energy and environment-related activities. The numerical simulators used for modeling such processes rely on spatial and temporal discretization of the governing mass and energy balance partial-differential equations (PDEs) into algebraic systems via finite-difference/volume/element methods. These simulators usually require dedicated software development and maintenance, and suffer low efficiency from a runtime and memory standpoint for problems with multi-scale heterogeneity, coupled-physics processes or fluids with complex phase behavior. Therefore, developing cost-effective, data-driven models can become a practical choice, and in this work, we choose deep learning approaches as they can handle high dimensional data and accurately predict state variables with strong nonlinearity. In this paper, we describe a gradient-based deep neural network (GDNN) constrained by the physics related to multiphase flow in porous media. We tackle the nonlinearity of flow in porous media induced by rock heterogeneity, fluid properties, and fluid-rock interactions by decomposing the nonlinear PDEs into a dictionary of elementary differential operators. We use a combination of operators to handle rock spatial heterogeneity and fluid flow by advection. Since the augmented differential operators are inherently related to the physics of fluid flow, we treat them as first principles prior knowledge to regularize the GDNN training. We use the example of pressure management at geologic CO 2 storage sites, where CO 2 is injected in saline aquifers and brine is produced, and apply GDNN to construct a predictive model that is trained with physics-based simulation data and emulates the physics process. We demonstrate that GDNN can effectively predict the nonlinear patterns of subsurface responses, including the temporal and spatial evolution of the pressure and saturation plumes. We also successfully extend the GDNN to convolutional neural network (CNN), namely gradient-based CNN (GCNN), and validate its capability to improve the prediction accuracy. GDNN has great potential to tackle challenging problems that are governed by highly nonlinear physics and enable the development of data-driven models with higher fidelity.

42 ENGINEERING↗
DOE OSTI2023

Jacobian-free Newton–Krylov method for the simulation of non-thermal plasma discharges with high-order time integration and physics-based preconditioning

A preconditioning framework for the numerical simulation of non-thermal streamer discharges is developed using the Jacobian-free Newton-Krylov (JFNK) method. A reduced plasma fluid model is considered, consisting of electrons, one positive ion, one negative ion, and the electrostatic potential. Here, the plasma kinetics model includes ionization, electron-ion recombination, electron attachment, electron detachment, and ion-ion recombination. The governing equations are made dimensionless, discretized in space with finite differences, and integrated in time with a fully implicit method based on high-order backward differentiation formulas. The preconditioning framework is based on a linearized form of the governing equations and physics-based operator splitting. The efficiency of the preconditioning strategy is assessed through two test cases: streamer propagation between parallel plates and an axisymmetric pin-to-pin discharge. The fully implicit approach overcomes traditional restrictions in the time step size due to processes such as electron drift, electron diffusion, and dielectric relaxation. Excellent performance is observed through relevant statistics of the JFNK solver, although the number of linear iterations increases for the pin-to-pin discharge when nonlinear numerical boundary conditions are imposed at the electrodes. Performance studies show scalability with O(100-1000) processors for O(10M) unknowns with ample room for optimization.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Residual-based error correction for neural operator accelerated infinite-dimensional Bayesian inverse problems

We explore using neural operators, or neural network representations of nonlinear maps between function spaces, to accelerate infinite-dimensional Bayesian inverse problems (BIPs) with models governed by nonlinear parametric partial differential equations (PDEs). Neural operators have gained significant attention in recent years for their ability to approximate the parameter-to-solution maps defined by PDEs using as training data solutions of PDEs at a limited number of parameter samples. The computational cost of BIPs can be drastically reduced if the large number of PDE solves required for posterior characterization are replaced with evaluations of trained neural operators. However, reducing error in the resulting BIP solutions via reducing the approximation error of the neural operators in training can be challenging and unreliable. We provide an a priori error bound result that implies certain BIPs can be ill-conditioned to the approximation error of neural operators, thus leading to inaccessible accuracy requirements in training. To reliably deploy neural operators in BIPs, we consider a strategy for enhancing the performance of neural operators: correcting the prediction of a trained neural operator by solving a linear variational problem based on the PDE residual. We show that a trained neural operator with error correction can achieve a quadratic reduction of its approximation error, all while retaining substantial computational speedups of posterior sampling when models are governed by highly nonlinear PDEs. The strategy is applied to two numerical examples of BIPs based on a nonlinear reaction–diffusion problem and deformation of hyperelastic materials. We demonstrate that posterior representations of the two BIPs produced using trained neural operators are greatly and consistently enhanced by error correction.

97 MATHEMATICS AND COMPUTING↗