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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 199 records · Page 11
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

A method for assessing economic, environmental, and reliability tradeoffs of interregional transmission connecting ERCOT (the Texas grid) to the eastern and western grids

Reliable development of the power grid is an evolving concern for humanity due to extreme weather that frequently threatens power sector infrastructure. The state of Texas is a uniquely structured testbed for grid planners to study when looking for solutions to development, innovation, and overcoming such challenges. Because of its size and islanded structure, Texas is small enough to model, but big enough to matter. Texas is a global leader in energy production, energy consumption, and maintains an unusually diverse fuel mix. In addition, the state has experienced winter freezes, heat waves, wind storms, droughts and floods that have threatened power sector infrastructure or caused recent blackouts and calls for demand side conservation. One of the most devastating of these events was the North American winter storm, dubbed “Winter Storm Uri” by the Weather Channel, that froze the region in February 2021 and led to an extended power outage event that put the majority of Texan residents in darkness for days. While preparing to avoid such outage events in the future, various tools have been proposed to improve grid reliability, including energy efficiency, demand response, and distributed energy resources. An additional option would be to develop interregional transmission that connects the Texas grid to other national grids. To assess the merits of this idea, we developed a novel, universally-applicable and internationally-relevant framework to study how the Texas grid would evolve alongside access to various interregional ties. This method allows us to stress the synthetic grid structure and analyze how it would respond to the shock of a simulated winter storm event. Our method leverages open-source modeling tools, such as PowerGenome, pyGRETA, and GenX to synthesize unique zonal grid data, construct a consolidated network of model regions, and simulate different developmental pathways of capacity expansion and operational dispatch. We demonstrate our method with an analysis connecting the Electric Reliability Council of Texas (ERCOT), the grid that serves most of Texas, the Western Electricity Coordinating Council (WECC), the grid that serves the western half of the contiguous U.S., and the Eastern Interconnect, the grid that serves the eastern half of the contiguous U.S. Our results indicate that the cost-optimal capacity of interregional transmission connecting the ERCOT grid to other grids lies between 9–13 GW assuming baseline conditions. Building this amount of connecting capacity in one or multiple directions lowers the costs and emissions of development and operation by up to $16 billion and 257 million metric tonnes (MMT) respectively. Additionally, our results show that the interregional connections between ERCOT and other national grids reduce the amount of total load shed required through mild winter storm events. However, our results also show that there is a threshold of very extreme winter storm conditions, spanning multiple service areas, above which the connections exacerbate resource adequacy problems. Therefore, the results indicate that the connections need to be carefully planned alongside the rest of the grid infrastructure to avoid over-reliance on specific resources or technology options.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Integrated path planning and control through proximal policy optimization for a marine current turbine

This paper presents an integrated path planning and tracking control framework for a marine current turbine (MCT), where the MCT is treated as an energy-harvesting autonomous underwater vehicle (AUV). Considering the ocean (space of action) is continuous, the proposed framework employs two modules to address path planning and path tracking enabled by the proximal policy optimization (PPO) algorithm, which is a policy gradient deep reinforcement learning (RL) method. Further, to enable fully autonomous operation in a stochastic oceanic environment, the proposed path planning seeks a primary objective of maximizing the harvested energy; then, the path tracking module is designed to minimize the tracking error and avoid collisions with static and dynamic obstacles. Using field-collected acoustic Doppler current profiler (ADCP) data, the performance of the proposed framework is evaluated. Comparative studies with baseline algorithms in three different scenarios of path planning, path tracking without an obstacle, and path tracking with collision avoidance verify the effectiveness of our proposed approach.

16 TIDAL AND WAVE POWER↗
DOE OSTI2020

The second-generation Shifted Boundary Method and its numerical analysis

Recently, the Shifted Boundary Method (SBM) was proposed within the class of unfitted (or immersed, or embedded) finite element methods. By reformulating the original boundary value problem over a surrogate (approximate) computational domain, the SBM avoids integration over cut cells and the associated problematic issues regarding numerical stability and matrix conditioning. Accuracy is maintained by modifying the original boundary conditions using Taylor expansions. Hence the name of the method, that shifts the location and values of the boundary conditions. In this article, we present enhanced variational SBM formulations for the Poisson and Stokes problems with improved flexibility and robustness. These simplified variational forms allow to relax some of the assumptions required by the mathematical proofs of stability and convergence of earlier implementations. First, we show that these new SBM implementations can be proved asymptotically stable and convergent even without the rather restrictive assumption that the inner product between the normals to the true and surrogate boundaries is positive. Second, we show that it is not necessary to introduce a stabilization term involving the tangential derivatives of the solution at Dirichlet boundaries, therefore avoiding the calibration of an additional stabilization parameter. Finally, we prove enhanced L 2 -estimates without the cumbersome assumption – of earlier proofs – that the surrogate domain is convex. Instead we rely on a conventional assumption that the boundary of the true domain is smooth, which can also be replaced by requiring convexity of the true domain. The aforementioned improvements open the way to a more general and efficient implementation of the Shifted Boundary Method, particularly in complex three-dimensional geometries. We complement these theoretical developments with numerical experiments in two and three dimensions.

42 ENGINEERING↗
DOE OSTI2021

Implicit highly-coupled single-ion Hall-MHD formulation for hybrid particle-in-cell codes

The rudiments of a particle-based single-fluid two-temperature magnetohydrodynamic (MHD) algorithm have been outlined in Thoma et al. (2013). The extension of this algorithm to include the effect of Hall physics is described in this paper. An implicit leapfrog version of the algorithm, which allows timesteps large compared to the resistive decay time and other relevant timescales, has recently been added to a hybrid particle-in-cell code. In standard MHD the Hall term in the generalized Ohm’s law can often be neglected when the Hall parameter is small. This term must, however, be retained in regimes where it is non-negligible. The retention of displacement current in Maxwell’s equations avoids the numerical difficulties associated with the whistler mode, which are encountered in standard explicit Hall-MHD codes, and allows the algorithm to be incorporated into hybrid particle-in-cell codes, for which particles may migrate from a kinetic to fluid to MHD description based upon local ambient plasma conditions. A highly-coupled implicit Hall-MHD formalism is presented, in which displacement current can either be retained or neglected. Even when displacement current is neglected, the highly-coupled implicit formalism avoids the restrictive timesteps for the whistler mode in explicit Hall-MHD codes. A comparison of numerical and analytic dispersion analysis demonstrates the feasibility of this approach and establishes relevant constraints to assure numerical stability. The implementation of the algorithm is described, and test simulation results in 1D and 2D in both linear and nonlinear regimes are presented.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Comparison of vapour pressure osmometry, freezing point osmometry and direct membrane osmometry for determining the osmotic pressure of concentrated solutions

Osmometry is the analytical method of measuring osmotic pressure ($π$) and related colligative properties. Accurately measuring $π$ is essential for applications that use osmosis, including drug delivery systems and water filtration methods such as forward osmosis. The three most common forms of directly or indirectly measuring $π$ are vapour pressure osmometry (VPO), freezing point osmometry (FPO), and direct membrane osmometry (DMO). In this report, the performance of VPO, FPO, and DMO are compared for various aqueous solutions, including small molecule and polymer solutes, and potentially more difficult samples such as concentrated, carbonated, or viscous solutions. Furthermore, potential problems with each of the three methods are examined. Good practices can avoid inaccuracies in DMO due to external concentration polarization and solute diffusion through the membrane. Similarly, it is important to be aware of and avoid weaknesses in VPO and FPO in order to obtain reliable results. Even with care, however, the three methods still give different values of $π$ for concentrated aqueous solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

The value of integrating a geothermal district heating system into a microgrid

As electrical grids increasingly rely on variable renewable energy, maintaining reliability and cost efficiency becomes more complex. To address these challenges, this study analyzed the integration of geothermal district heating as a grid-responsive thermal resource within a microgrid in Tuttle, Oklahoma. Building energy modeling using EnergyPlus estimated annual district heating demand at 2.9 GWh, with a peak load of 2.8 MW th . Techno-economic analyses were conducted to meet the heating demand under three geothermal scenarios, varying by production depth, flow rate, and thermal output, each supplemented by natural gas peaking boilers. In parallel, equivalent electrical load profiles were developed using typical coefficients of performance (COPs) for air-source heat pumps and electric boilers to establish an electrified baseline scenario. A complete end-use electrical load profile was also developed for the microgrid using Cambium dataset. The modeling results demonstrated reliable and economic operation of the geothermal systems over 30 years, with COPs ranging from 2.6 to 8.9 and the lowest levelized heating cost at $\$$54.6/MWh. Geothermal integration reduced electricity consumption by up to 94.7 % compared to the non-geothermal base case, yielding annual energy savings of up to $\$$803 k. Avoided grid costs ranged from $\$$65 k–$\$$147 k per year, with individual events avoiding up to $\$$4,863 per hour. Grid-responsive operation further reduced wholesale energy costs by 53–56 %. These findings demonstrate geothermal heating, traditionally treated as a non-grid-responsive thermal resource, can be reconfigured to support dynamic grid services, offering a scalable pathway to enhance reliability and reduce costs in renewable-rich microgrids and district heating networks.

15 GEOTHERMAL ENERGY↗
DOE OSTI2021

A review of thermal physics and management inside lithium-ion batteries for high energy density and fast charging

Traditionally it has been assumed that battery thermal management systems should be designed to maintain the battery temperature around room temperature. That is not always true as lithium-ion battery (LIB) R&D is pivoting towards the development of high energy density and fast charging batteries. Therefore, it is necessary to have a comprehensive review of thermal considerations for LIBs targeted for high energy density and fast charging, i.e., the optimal thermal condition, thermal physics (heat transport and generation) inside the battery, and thermal management strategies. As the energy density and charge rate increases, the optimal battery temperature can shift to be higher than room temperature. In the first part of the review various sources of heat generation inside LIBs and various approaches to minimizing battery heat generation are summarized. The importance of heat of mixing due to ion diffusion during fast charging is also highlighted. To improve the temperature uniformity and avoid excessive internal temperature rise, heat transfer inside the battery needs to be enhanced, and reducing the thermal contact resistance between the electrodes and separator can significantly increase the effective thermal conductivity of batteries. In the second part of the review various challenges and latest developments related to thermal transport and properties of LIBs are discussed. Finally, a summary of latest advancement on smart control of internal temperature of LIBs is discussed as depending on the ambient temperature and the optimal temperature; the battery heat needs to be retained or dissipated to elevate or avoid temperature rise.

25 ENERGY STORAGE↗
DOE OSTI2022

New data-driven approach to bridging power system protection gaps with deep learning

Protection is a critical function in power systems to avoid equipment damage, maintain personnel safety, and support system reliability. However, current protective relay technology cannot adequately protect equipment and personnel from effects of some events; these deficiencies are termed protection gaps. In this paper, a data-driven approach is proposed to complement traditional protection technology and distinguish fault conditions from transients caused by normal operations. A combined convolutional neural network and long short-term memory (CNN-LSTM) network is implemented to achieve data translation invariance and capture the temporal correlation of the time-series input data. As a result, the data-driven method can accurately detect system faults despite variation and noise in the input data. In addition, using the CNN-LSTM--based method avoids the complicated, manual feature extraction procedure required by many traditional data-driven methods. The effectiveness of the proposed approach is tested on two kinds of protection gaps: high-impedance faults and transformer inter-turn faults. Lastly, a transfer learning method is also proposed to address the common issue of data-driven methods for which real-world training data are scarce. Extensive study results demonstrate that the proposed approach can accurately bridge power system protection gaps.

42 ENGINEERING↗
DOE OSTI2023

Think before you throw! An analysis of behavioral interventions targeting PET bottle recycling in the United States

The United States generates 42 Mt of plastic waste each year and is one of the biggest contributors to ocean plastic waste. Consequently, plastic has become synonymous with the linear economy, and many scholars are studying and proposing circular economy solutions to mitigate plastic pollution. Recycling has received much attention from both social sciences and engineering as a circular economy strategy, but no study has yet quantified how behavioral interventions could asymmetrically affect different populations. Here, this study combines agent-based modeling, material flow analysis, system dynamics, and life cycle assessment to assess the effect of four behavioral interventions on the collection rates of polyethylene terephthalate bottle waste, displaced virgin plastic manufacturing, and avoided greenhouse gas (GHG) emissions. Results show that, while behavioral interventions would require about 300–900 GJ of additional energy at end-of-life due to improved collection rates, they would avoid about 500–700 thousand metric tons of GHG emissions. Results also illustrate the importance of habits in disposal behaviors and show that different forms of interventions can be better adapted to particular social contexts than others. While the circular economy and its application to plastic waste should certainly not be restricted to recycling, this study demonstrates that improved collection rates and recycling technologies can contribute to reducing the amount of plastic waste polluting our oceans.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2021

Efficient kinetic thermal inverse modeling for organic material decomposition

The prevalent use of organic materials in manufacturing is a fire safety concern, and motivates the need for predictive thermal decomposition models. A critical component of predictive modeling is numerical inference of kinetic parameters from bench scale data. Currently, an active area of computational pyrolysis research focuses on identifying efficient, robust methods for optimization. This paper demonstrates that kinetic parameter calibration problems can successfully be solved using classical gradient-based optimization. We explore calibration examples that exhibit characteristics of concern: high nonlinearity, high dimensionality, complicated schemes, overlapping reactions, noisy data, and poor initial guesses. The examples demonstrate that a simple, non-invasive change to the problem formulation can simultaneously avoid local minima, avoid computation of derivative matrices, achieve a computational efficiency speedup of 10x, and make optimization robust to perturbations of parameter components. Techniques from the mathematical optimization and inverse problem communities are employed. By re-examining gradient-based algorithms, we highlight opportunities to develop kinetic parameter calibration methods that should outperform current methods.

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

High pressure/high temperature multiphase simulations of dodecane injection to nitrogen: Application on ECN Spray-A

The present work investigates the complex phenomena associated with pressure/high temperature dodecane injection for the Engine Combustion Network (ECN) Spray-A case, employing more elaborate thermodynamic closures, to avoid well known deficiencies concerning density and speed of sound prediction using traditional cubic models. A tabulated thermodynamic approach is proposed here, based on log 10 (p)-T tables, providing very high accuracy across a large range of pressures, spanning from 0 to 2500 bar, with only a small number of interpolation points. The tabulation approach is directly extensible to any thermodynamic model, existing or to be developed in the future. Here NIST REFPROP properties are used, combined with PC-SAFT Vapor-Liquid-Equilibrium to identify the liquid in mixtures penetration, hence avoiding the use of an arbitrary threshold for mass fraction. Identified liquid and vapour penetration are compared against experimental data from the ECN database showing a good agreement, within approximately 3–8% for axial penetration of liquid, 2% for vapor axial penetration and within experimental uncertainty for radial distribution of mass fraction. Analysis of the vortex evolution indicates that driving mechanisms behind the jet break-up are vortex tilting/stretching, then baroclinic torque, leading to Rayleigh-Taylor instabilities, closely followed by vortex dilation and finally viscous effects.

42 ENGINEERING↗
DOE OSTI2022

Economic and Environmental Analysis to Evaluate the Potential Value of Co-Optima Diesel Bioblendstocks to Petroleum Refiners

The U.S. petroleum refining sector is undergoing a period of historic transformation, catalyzed by the decarbonization of the U.S. economy. Diesel-boiling-range bioblendstocks have gained traction, owing to their superior fuel properties and environmental performance as compared to traditional petroleum fuels. This work couples refinery linear programming models with life cycle assessment to quantify the potential economic and environmental benefits, and trade-offs, of blending diesel-boiling-range bioblendstocks at petroleum refineries. Linear programming models were developed in Aspen Process Industry Modeling Systems (PIMS) for three representative petroleum refinery configurations of differing complexity. Seven diesel-boiling-range bioblendstocks: 4-butoxyheptane, 5-ethyl-4-propylnonane, soy biodiesel, sludge hydrothermal liquefaction diesel, polyoxymethylene ethers, renewable diesel, and hexyl hexanoate, were investigated to identify key fuel properties that influence refineries' economics and to track the effect of adding bioblendstocks on refinery-wide cradle-to-gate greenhouse gases (GHG) emissions. These analyses considered blending levels from 10 to 30 vol% and fuel demand projections over the period 2040 to 2050. This analysis determines that bioblendstock sulfur content and cetane number are the primary fuel attributes with the potential to provide value to refiners. Life cycle assessment results indicate that the use of diesel-boiling-range bioblendstocks can reduce cradle-to-gate refinery GHG emissions by up to ~ 40 % relative to conventional refinery operations when considering carbon uptake in the supply chain of the bioblendstock. Refinery-wide marginal GHG abatement costs range from 120 to 3,600 USD2016/metric tons carbon dioxide equivalent avoided across the scenarios evaluated. Reducing the price of bioblendstocks is identified as a key to their adoption.

ADVANCED PROPULSION SYSTEMS,BIOMASS FUELS,ENERGY P↗
DOE OSTI2020

Multi-device study of temporal characteristics of magnetohydrodynamic modes initiating disruptions

Disruptions in tokamaks are often preceded by magnetohydrodynamic (MHD) instabilities that can rotate or become locked to the wall. Measurements from magnetic diagnostics in the presence of MHD mode precursors to disruptions can yield potentially valuable input to the plasma control system, with a view to disruption avoidance, prediction and mitigation. This report presents an exploratory analysis of the growth of MHD modes and corresponding time scales on the basis of magnetic measurements in multiple tokamaks. To this end, a database was compiled using disruptive discharges from COMPASS, ASDEX Upgrade, DIII-D and JET, manually classified according to disruption root cause, and characterized by a great diversity of operational conditions and mode dynamics. The typical time during which a mode can be detected using saddle coils and the duration of the locked mode phase in the database both extend over several orders of magnitude, but generally the time scales increase with plasma size. Several additional factors are discussed that can influence these durations, including the disruption root cause. A scaling law for the locked phase duration was estimated, yielding predictions toward ITER of the order of hundreds of milliseconds or even seconds. In addition, a scaling law for the mode amplitude at the disruption onset, proposed earlier by de Vries et al. (2016), is applied to the database, and its predictive capabilities are assessed. Despite significant uncertainty on the predictions from both scaling laws, encouraging trends are observed of the fraction of disruptions that may be detected with sufficient warning time to allow mitigation or even avoidance, based solely on observations of MHD mode dynamics. When combined with similar analysis of measurements from diagnostics that are sensitive to other disruption precursors, our analysis methods and results may contribute to the reliability, robustness and generalization of disruption warning schemes for ITER.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Co-simulation of transactive energy markets: A framework for market testing and evaluation

The proliferation of distributed energy resources (DER)—and the ability to intelligently control these assets—is re-defining the electrical distribution system. As the number of controllable devices rapidly expands, grid operators must determine how to incorporate these assets while delivering reliable, equitable, and affordable electricity. One possible approach is to establish distribution-level electricity markets and allow devices/aggregations of devices to participate in price establishment. While this approach purports some of the same benefits as the highly successful wholesale electricity markets (i.e., open competition, efficient price discovery, reduced communication overhead), this needs to be researched and quantified via an analysis platform that models distribution-level markets at the appropriate fidelity. Specifically, the simultaneous evaluation of market performance, DER performance, DER bidding approaches, and distribution feeder power quality requires modeling that spans multiple technical areas. Co-simulation has emerged as a powerful tool in addressing this type of problem, where outputs depend on a range of underlying areas of expertise and associated models. In this paper we describe a solution, as implemented in the HELICS co-simulation platform, where we include (1) high fidelity house models, (2) intelligent bidding agents, (3) a modular market integration/design, and (4) a distribution feeder model. We then present a case study where we test two different market designs: (1) a pseudo-wholesale double-blind auction, and (2) an asynchronous matching market. In this work, the markets are run under two DER penetration levels and economic results are compared to full retail net energy metering and avoided cost net metering scenarios that bookend current approaches to remuneration of DER participation. We show the potential for transactive markets to provide increased value for most customers relative to net metering (and all customers relative to avoided cost scenarios) while decreasing costs for the utility.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Superconductivity in WBe 2

WBe 2 , which occurs in space group 194, with hexagonal symmetry P6 3 /mmc, is prepared by arc-melting at temperatures above 2200 C, where Be vapor loss is significant. This study is motivated by recent work on MoB 2 and WB 2 , both superconductors (T c =32 and 17 K respectively) under high (∼70 GPa) pressure. In order to avoid the known Be-rich superconducting phases (WBe 13 and WBe 22 ) in the complex phase diagram, both known to be superconducting at 4.1 K, the sample was prepared with a slight (∼5 %) excess of W. The resultant sample, prepared using high purity (99.999 %) Be, is essentially single phase WBe 2 , with some spread in its superconducting properties due to the known homogeneity range. (WBe 2 forms in space group 194 between approximately W 1.02 Be 1.98 and W 0.88 Be 2.12 .) Characterization was carried out with x-ray diffraction, electrical resistivity, ρ, in zero and applied magnetic fields, and specific heat. The resistivity in zero and applied fields and specific heat data indicate that our sample of WBe 2 is a bulk superconductor at ambient pressure with a T c onset in ρ at 1.05 K, and T c (ρ→0) at ∼0.86 K. Furthermore, there is no signature of superconductivity in ρ at 4.1 K, indicating successful avoidance of WBe 13 and WBe 22 . The ρ data in field indicate an upper critical field of approximately 400 gauss.

Electrical transport↗
DOE OSTI2024

Recommendations for improving rigor and reproducibility in site specific characterization

Heterogeneous catalysis is driven by the interaction of reactant molecules and the catalyst surface. The locus of this interaction as well as the surrounding ensemble of atoms is referred to as the catalyst active site. Active site characterization attempts to distinguish active catalytic sites from inactive surface sites, to elucidate the structural and chemical nature of active sites, and to quantify active site concentration. Numerous techniques have been demonstrated to provide compositional and structural information about the active sites within a catalyst. However, each technique has its own limitations and experimental pitfalls that can lead to data misinterpretation or irreproducible results. Further, this work aims to provide an overview of the types of data that can be collected, to outline common experimental challenges and how to avoid them, and to assemble relevant references for the most used active site characterization techniques. More broadly, we aim to outline best practices for researchers to collect, interpret, and report active site characterization data in a way that provides the most benefit to the broader catalysis community. Increasing the rigor and reproducibility of active site characterization offers a strategy to better link properties with catalytic performance and to enable the community to develop consensus concerning these relationships.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

An integrated biorefinery approach to obtain xylo-oligosaccharides from corncob using lactic acid-rich fermentation broth

Although xylo-oligosaccharides production from lignocelluloses via lactic acid hydrolysis is advantageous in terms of high yields with less by-products, the use of high purity lactic acid inevitably increases the cost of xylo-oligosaccharides production. The utilization of lactic acid-rich fermentation broth for xylo-oligosaccharides production can avoid the separation and purification of lactic acid. However, the feasibility of lactic acid-rich fermentation broth for xylo-oligosaccharides production from lignocelluloses was unclear. In this work, the results indicated that the highest xylo-oligosaccharides yield of 72% was obtained from corncob by lactic acid-rich fermentation broth pretreatment and xylanase hydrolysis. Subsequently, monosaccharides-rich hydrolysate (90.9 g/L) was obtained from solid residues of corncob by cellulase hydrolysis. Lactic acid-rich fermentation broth was produced by Weizmannia coagulans fermentation of the monosaccharide-rich hydrolysate. Besides, the obtained xylo-oligosaccharides and lactic acid mixture might be used as feed additives, avoiding the purification and separation of lactic acid or xylo-oligosaccharides. Meanwhile, the production cost of feed grade xylo-oligosaccharides from this work was much lower than the current market price. Overall, this work proposed a new strategy for efficient and environmental-friendly production of xylo-oligosaccharides from corncob.

09 BIOMASS FUELS↗
DOE OSTI2021

B-PINNs: Bayesian Physics-informal Neural Networks for Forward and Inverse PDE Problems with Noisy Data

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward and inverse nonlinear problems described by partial differential equations (PDEs) and noisy data. In this Bayesian framework, the Bayesian neural network (BNN) combined with a PINN for PDEs serves as the prior while the Hamiltonian Monte Carlo (HMC) or the variational inference (VI) could serve as an estimator of the posterior. B-PINNs make use of both physical laws and scattered noisy measurements to provide predictions and quantify the aleatoric uncertainty arising from the noisy data in the Bayesian framework. Compared with PINNs, in addition to uncertainty quantification, B-PINNs obtain more accurate predictions in scenarios with large noise due to their capability of avoiding overfitting. We conduct a systematic comparison between the two different approaches for the B-PINNs posterior estimation (i.e., HMC or VI), along with dropout used for quantifying uncertainty in deep neural networks. Our experiments show that HMC is more suitable than VI with mean field Gaussian approximation for the B-PINNs posterior estimation, while dropout employed in PINNs can hardly provide accurate predictions with reasonable uncertainty. Finally, we replace the BNN in the prior with a truncated Karhunen-Loève (KL) expansion combined with HMC or a deep normalizing flow (DNF) model as posterior estimators. The KL is as accurate as BNN and much faster but this framework cannot be easily extended to high-dimensional problems unlike the BNN based framework.

Non linear PDEs, Noisy data, Bysian physics inform↗