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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 271 records · Page 15
All sourcesNASA NTRSDOE OSTI
DOE OSTI2021

DEVELOPMENT OF STABLE ANODE AND CATHODE MATERIALS FOR RECHARGEABLE BATTERIES

Batteries have been employed in a variety of applications, such as portable electronics, electric vehicles (EVs), and stationary energy storage to preserve energy from other renewable sources (like wind or solar energy). The ultimate goal is to develop high energy density, long life span, better safety, and low cost of the batteries. However, current commercialized batteries (like lead-acid, zinc-alkaline, lithium-ion batteries (LIBs)) could not fulfill all the demands of diversified applications. LIBs predominate the market because of their high energy density. To achieve a higher capacity of the cell, high-nickel layered (Ni > 90%) cathode materials are promising candidates since they compose high specific capacity and discharge voltage. In chapter 1, an introduction to cell energy density and the development of high-nickel layered cathode materials along with associated obstacles of poor cycling stability and thermal stability have been discussed. Associated works like doping or surface coating have also been mentioned in this section. In chapter 2, Al doping in high-nickel layered cathode materials to enhance the structural and thermal stability was introduced. Uniform incorporation of Al doping is achieved by mechanical fusion and calcination processes. The Al doping not only decreased the Li/Ni mixing ratio but also enhance the thermal resistance to oxygen evolution because of strong Al-O bonding, which leads to elevated electrochemical and thermal stability. In chapter 3, TiN is implemented as a Ti dopant for high-nickel layered cathode materials to improve the electrochemical performance in the LIBs. The Ti not only diffused within the bulk structure but also formed segregation on the surface, which improved the structural stability and led to better cycling performance. Although LIBs deliver high energy density, safety concerns of flammable organic electrolytes have not been resolved yet. Therefore, the aqueous rechargeable zinc-ion batteries (ZIB) have been praised for their safe, low-cost, eco-friendly stationary energy storage, which is considered as a complementary system to LIBs. In chapter 4, the mechanism, advantages, and challenges of ZIBs would be given and the strategies for solving the zinc metal anode issues have been discussed in this section. In chapter 5, a polymer coating method was reported to facilitate Zn deposition/ stripping by coordination with Zn2+ and prevented direct contact with aqueous electrolyte to block corrosion side-reactions. With this coating, a boost in a lifetime (up to 400 hours) and lower polarization under extremely high current conditions (10 mA cm-2) have been achieved in repeated Zn deposition/ stripping cycling.

25 ENERGY STORAGE↗
DOE OSTI2021

Surface and Bulk Oxygen Kinetics of BaCo 0.4 Fe 0.4 Zr 0.2-X Y X O 3-δ Triple Conducting Electrode Materials

Triple ionic-electronic conductors have received much attention as electrode materials. In this work, the bulk characteristics of oxygen diffusion and surface exchange were determined for the triple-conducting BaCo 0.4 Fe 0.4 Zr 0.2-X Y X O 3-δ suite of samples. Y substitution increased the overall size of the lattice due to dopant ionic radius and the concomitant formation of oxygen vacancies. Oxygen permeation measurements exhibited a three-fold decrease in oxygen permeation flux with increasing Y substitution. The DC total conductivity exhibited a similar decrease with increasing Y substitution. These relatively small changes are coupled with an order of magnitude increase in surface exchange rates from Zr-doped to Y-doped samples as observed by conductivity relaxation experiments. The results indicate that Y-doping inhibits bulk O 2- conduction while improving the oxygen reduction surface reaction, suggesting better electrode performance for proton-conducting systems with greater Y substitution.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Reactive transport modeling of organic carbon degradation in marine methane hydrate systems

Abstract Natural methane hydrate has often been observed in sand layers that contain no particulate organic carbon (POC), but are surrounded by organic-rich, fine-grained marine muds. In this paper, we develop a reactive transport model (RTM) of a microbially-mediated set of POC degradation reactions, including hydrolysis of POC driven by extracellular enzymes, fermentation of the resulting high-molecular weight dissolved organic carbon (HMW-DOC), and methanogenesis that consumes low-molecular weight dissolved organic carbon (LMW-DOC). These processes are mediated by two groups of microbes, fermenters and methanogens that are heterogeneously distributed in different lithologies, with the largest numbers of microbes in the large pores of coarse-grained layers. We find that the RTM can reproduce methane hydrate occurrences observed in two different geological environments, at Walker Ridge Site 313-H (Gulf of Mexico) and IODP Site U1325 (Cascadia Margin). We also find that microbes can degrade POC even if they are physically separated, as extracellular enzymes and DOC can diffuse away from where they are produced by microbes. Microbial activity is highest at relatively early times after burial at shallow depths and near lithological boundaries, where concentration gradients transport solutes to intervals that contain the most microbes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Comparing Tandem Cell Designs for Electrochemical CO 2 Reduction to Ethylene

Electrochemical carbon dioxide reduction (CO 2 R) is a promising approach for the decentralized production of fuels such as ethylene (C 2 H 4 ). However, the use of Cu, the most efficient metal CO 2 R catalyst for the generation of C 2 H 4 known to date, generally yields a product stream with poor selectivity. In an effort to increase selectivity, the reaction from CO 2 to C 2 H 4 can be broken down into two steps using tandem CO 2 R electrolyzers: formation of CO from CO 2 and subsequent reduction of CO to C 2 H 4 . Here, in this study, we present two novel tandem electrolyzer architectures that closely integrate two cathodes, one for CO generation and one for conversion to C 2 H 4 , while still enabling independent electrical control of the cathodic surfaces. Cathode segmentation in each of these designs also permits the controlled sequencing of mass flow of chemical intermediates in the order of Au to Cu cathode catalysts, in contrast to earlier work relying on uncontrolled, passive diffusion to facilitate the flow of chemical intermediates between catalysts. When comparing the performance of the newly developed electrolyzer cell designs with a dual electrolyzer system, we found that the dual electrolyzer system yields the highest C 2 H 4 faradaic efficiencies (FEs) of 31% and C 2 H 4 concentrations (∼8 mol %). However, a single Cu-containing electrolyzer outperformed all three tandem systems in terms of C 2 H 4 FE (34%). Our findings, enabled by independent control of the two tandem cathode surfaces, indicate that tandem CO 2 R systems need to be evaluated carefully by testing them at various relevant current densities.

C2H4↗
DOE OSTI2023

Utah FORGE 5-2557: Fluid and Temperature in Fracture Mechanics and Coupled THMC Processes - Workshop Presentation

This is a presentation on the Role of Fluid and Temperature in Fracture Mechanics and Coupled Thermo-Hydro-Mechanical-Chemical (THMC) Processes for Enhanced Geothermal Systems project by Purdue University, presented by Distinguished Professor of Physics & Astronomy, Laura J. Pyrak-Nolte. The project's objective was to develop and validate a macroscopic model that accounts for local deformation/frictional behavior, seismic/aseismic behavior, chemical reactions, and determine the adequacy of classic Coulomb failure vs. rate-and-state friction. This presentation was featured in the Utah FORGE R&D Annual Workshop on September 8, 2023. The workshop provided a valuable opportunity to explore the progress made in each of the 17 Research and Development projects funded under Solicitation 2020-1 which aim to enhance our understanding of the crucial factors influencing the development of Enhanced Geothermal Systems (EGS) reservoirs and resources.

15 GEOTHERMAL ENERGY↗
DOE OSTI2025

Atom Efficiency of Pd Sites for Methane Combustion: Single Atom Catalysts Versus Nanocatalysts

Methane combustion is an important reaction for energy production and methane removal from the atmosphere. This reaction highly relies on the use of noble metal Pd-based catalysts, which therefore drives the pursuit of catalysts with high atomic dispersion and activity. In this work, Pd/ceria catalysts dominated with Pd single atoms or nanosized Pd clusters (∼1 nm) are prepared and characterized by combining high-resolution high-angle annular dark-field scanning transmission electron microscopy (HAADF-STEM), in situ diffuse reflectance infrared Fourier-transform spectroscopy (DRIFTS), and Raman and X-ray absorption spectroscopy (XAS) techniques. By comparing the turnover frequencies (TOF; per every Pd atom) of Pd/ceria single atom catalysts and nanocatalysts, it is found that the atom efficiency of Pd is increased by 10 ∼30 times from single atom catalysts to nanocatalysts. For Pd single atom catalysts, although their activity can be tuned by changing the local structures, the intrinsic activity and number of active sites need to be further improved by engineering the surfaces of supports. For nanosized Pd species, despite the high TOF, the Pd atoms in the bulk structure are not directly participating in the catalytic reaction. Furthermore, this work highlights the importance of increasing the intrinsic activity of individual noble atoms, as well as the homogeneity of their local structures. For Pd/ceria systems reported in this work, our results indicate that from the application point of view, at the current stage, it is not practical to replace Pd nanocatalysts with single atom catalysts for methane combustion.

Pd↗
DOE OSTI2024

Interpenetrating 3D Electrodes for High-Rate Alkaline Water Splitting

Mass transfer is critical for the reaction kinetics and efficiency of alkaline water splitting (AWS). For AWS to operate at high current densities (hundreds of mA/cm 2 ), the device architecture must ensure a large catalytic surface area, rapid ion diffusion, and minimal solution and charge transfer resistances. Effective electrodes should also facilitate gas bubble detachment and release. 3D-printed electrodes have shown promise, but stacking them increases the ion diffusion length and solution resistance. Here we demonstrate a new device architecture with interpenetrating gyroid electrodes, providing a large ion-accessible surface area and gas diffusion channels. This design significantly reduces the interelectrode distance, lowering ion diffusion length and solution resistance. Simulations show faster ion diffusion and higher current density in the interpenetrating configuration compared with separate electrodes. This improved performance, especially at low temperatures and high current densities, highlights a promising strategy for enhancing AWS and other electrochemical systems limited by slow ion diffusion.

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

Real-Time Observation of the Diffusion Mechanism Progression from Liquid to Solid State of Transition Metal Complexes

Copper complexes have recently shown remarkable performance upon conversion from liquid-based to solid-state hole transport materials (HTMs) in mesoscopic solar cells; however, the diffusion mechanism is not clear. Here, we apply an in situ solidification analysis of the charge diffusion and find that the dominant mechanism of [Cu(dmbpy) 2 ] 2+/+ (dmbpy = 6,6'-dimethyl-2,2'-bipyridine) changes from ionic to electronic diffusion. Through use of the modified Dahms–Luff equation, a fast self-exchange rate constant of hole-hopping in the HTM of 8.3 × 10 8 (±5 × 10 7 ) M –1 s –1 is calculated, which indicates a small reorganization energy of 0.47 eV. These findings present a new methodology to analyze the transport mechanism of solids, reveal the mechanism of charge transport in molecular-based HTMs, and offer insight into ways to control the flow of charge in optoelectronic systems

14 SOLAR ENERGY↗
DOE OSTI2024

Electrolyte Assisted Hydrogen Storage Reactions (Final Technical Report)

The goal of this project is to address critical deficiencies of hydrogen storage systems design based on hydride materials, as originally identified by the DOE Hydrogen Storage Engineering Center of Excellence (HSECoE). Baseline hydrogen storage technology presently relies on compressed gas operating at ~700 bar pressure, which imposes huge demands on fuel delivery, fuel storage and system cost. For onboard storage applications, Type IV composite overwrapped pressure vessels and associated balance-of-plant components are necessary to ensure safe and effective fuel delivery. However, such compressed gas technology falls well-short of volumetric targets even at 700 bar, given the density of gaseous molecular hydrogen is only 40 g·H2/l at ambient temperatures. One alternative is to utilize hydride materials which accommodate hydrogen in atomic form. Certain hydrides can attain volumetric densities that exceed the density of liquid H2 (71 g·H2/l) while also offering advantageous thermodynamic properties. However, such material systems presently rely on solid-state diffusion for hydrogen release, which has a very high activation barrier for atom mobility and, thus, requires impractically-high temperatures for operation. The initial focus of our research effort is to employ and demonstrate an electrolyte system to mediate the diffusion of species at lower temperatures relevant to transportation applications, with the goal of establishing the critical factors necessary to obviate the need for high-temperature release of hydrogen. A parallel goal of this exploratory effort is to determine the effectiveness of modest electrochemical potentials in overcoming any endothermic requirements for hydrogen release in a similar electrolyte-promoted scenario.

08 HYDROGEN↗
DOE OSTI2023

Revealing in-plane movement of platinum in polymer electrolyte fuel cells after heavy-duty vehicle lifetime

Fuel cell heavy-duty vehicles (HDVs) require increased durability of oxygen-reduction-reaction electrocatalysts, making knowledge of realistic degradation mechanisms critical. Here identical-location micro-X-ray fluorescence spectroscopy was performed on membrane electrode assemblies. The results exposed heavy in-plane movement of electrocatalyst after HDV lifetime, suggesting that electrochemical Ostwald ripening may not be a local effect. Development of local loading hotspots and preferential movement of electrocatalyst away from cathode catalyst layer cracks was observed. The heterogeneous degradation exhibited by a modified cathode gas diffusion layer membrane electrode assembly after HDV lifetime was successfully quantified by the identical-location approach. Further synchrotron micro-X-ray diffraction and micro-X-ray fluorescence experiments were performed to obtain the currently unknown correlation between electrocatalyst nanoparticle size increase and loading change. A direct correlation was discovered which developed only after HDV lifetime. Finally, the work provides a route to engineer immediate system-level mitigation strategies and to develop structured cathode catalyst layers with durable electrocatalysts.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Ionic Liquid-Enhanced Interfaces to Boost Reactive C O2 Capture

The addition of ionic liquids (ILs) to a mixture containing a molecular solvent and other ionic species can induce the heterogeneous redistribution of cations and anions at the gas–liquid interface. This nonuniform redistribution of cations and anions driven by the differences in the solvophilicity of ions can improve the thermophysical and interfacial properties of such mixtures, creating a local chemical environment that is conducive to some reactions. In this work, ILs are added to a mixture of potassium hydroxide (KOH) and ethylene glycol (EG), used as a reactive absorbent and electrolyte in the migration-assisted moisture-gradient (MAMG) process for CO 2 capture. Molecular dynamics (MD) simulations are employed to probe into the effects of complex ion–ion and ion–solvent interactions and to examine the chemical composition at the gas–liquid interface. A total of 12 systems are investigated using molecular simulations to identify trends in the performance of IL additives based on the choice of cation, anion, and IL concentration. The cation effects are studied using IL additives based on 1-ethyl-3-methylimidazolium ([EMIM] + ) and 1-butyl-3-methylimidazolium ([BMIM] + ), while the impact of anions is examined using additives based on dicyanamide [DCA] − , triflate [TfO] − , bistriflimide [NTf 2 ] − , and hexafluorophosphate [PF 6 ] − anions, respectively. The influence of the IL concentration is also evaluated at molar concentrations between 1% and 4%. The simulation results indicate that the use of IL additives can affect the physical CO 2 solubility, surface tension, and the localization of CO 2 around the [OH] − ions at the gas–liquid interface. It is also evident that the choice of cations, anions, and IL concentration determines the extent to which the IL additives impact the local physicochemical properties. Physical dissolution, diffusive transport, and interaction with [OH] − are critical intermediate steps toward reactive CO 2 capture using a liquid absorbent. Hence, the improvement in one or more of these properties, aided by IL additives, is expected to improve the overall CO 2 capture performance. Experiments reaffirmed the impact of IL additives on CO 2 capture performance and the sensitivity to the choice of the cation, anion, and concentration of the IL additive.

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

Bi‐Continuous W‐Rich Refractory High Entropy Alloy‐Cu Composite: Toward Material Innovation of Nuclear Reactor Coolant System

Abstract Refractory high‐entropy alloys (RHEAs) are considered promising candidate materials for next‐generation nuclear reactors due to their superior mechanical strength, irradiation resistance, and thermal stability at high temperatures. However, the significant positive heat of mixing between refractory alloying elements and Cu, commonly used in cooling systems, poses challenges in forming composite structures. This study addresses the issue using a liquid metal dealloying (LMD) process. A precursor alloy (WTaVTi) with a directional dendrite‐interdendrite structure is fabricated and reacted with molten Cu at 1200 °C for 96 h. This approach produced a RHEA‐Cu composite with a stable interface between RHEA (W 31.5 Ta 30.9 V 21.4 Ti 14.3 ) and Cu, featuring a spontaneously formed W‐rich interlayer that enhances interfacial bonding. The composite showed excellent irradiation resistance, with 30% less swelling under α‐ion irradiation than pure W. It also exhibited low thermal conductivity at room temperature, but reached ≈120 W m −1 ·K −1 at ≈650 °C, surpassing pure W. This temperature‐dependent rise in κ, with a positive gradient of +0.075 W m −1 ·K − 2 , is attributed to decreasing diffuse mismatch at elevated temperatures. The large‐scale reaction and stable microstructure achieved through LMD process highlight its industrial potential. This work offers a strategy for developing high‐performance materials by combining RHEA's radiation resistance with Cu's thermal conductivity for extreme environments.

Chemistry↗
DOE OSTI2022

Predictive Large-Eddy Simulation of Supercritical-Pressure Reactive Flows in the Cold Ignition Regime

This report describes a one-year study performed under DOE sponsorship, continuing the investigation of high-pressure turbulent reactive flows. The interest is in the effect of the chemical species distribution in high-pressure turbulent flows in the presence of strong temperature gradients as would occur during reactions in realistic flows. The prime example of such flows are boundary layers in which the wall is at a lower temperature than that of the fluid, as would be the case in Diesel engines. Previous DOE BES work in the program further highlighted the importance of the boundary layer as a configuration for fundamental studies: soot formation in boundary layers is still a problem poorly understood and depends on the availability of particular chemical species at that location, and when boundary layer Large Eddy Simulations results were compared with measurements, the agreement was unfavorable, showing that this important ‘unit’ problem is not well understood. To understand this unit problem, modeling and Direct Numerical Simulations of this unit problem were conducted for the simplest possible multispecies system, that is a binary-species system. The results discovered a new phenomenon, that is, Soret effect induced uphill diffusion. The far-reaching implication is that through an imposed wall/fluid temperature difference it is possible to control the distribution of the species in the boundary layer. Because the results have been documented in one paper published in the refereed literature, and also in conference papers, this final report is in the form of an Executive Summary succinctly describing the results and putting them in perspective with respect to existing information. The refereed and conference papers published are individually listed as Appendices and attached to this report. One manuscript is still in progress and is thus not listed.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2024

Deuterium Permeation Through a Self-Supported Palladium-Silver Membrane in Helium Gas Mixtures

Palladium membranes and membrane reactors can separate and purify tritium from impurities in the plasma exhaust processing system for the fusion energy fuel cycle. Membranes can also act as a continuous separation method to remove tritium from helium streams in the breeder blanket tritium extraction system, such as from the purge gas of solid breeders. To investigate the potential of these membranes for these applications, we performed a deuterium permeation campaign with a self-supported palladium-silver (Pd-25Ag wt%) tube of 0.15 m length, 76 µ m wall thickness, and 3.0 mm inner diameter. A gas mixture of 3.95% D 2 and a balance of He was delivered to the inside of the tube and D permeated radially outwards through the membrane into a vacuum chamber. Permeation experiments were conducted at 300 ° C, 350 ° C, 400° C, and 450°C, from 100 to 1000 sccm total flow rate, and with total pressures of 90, 150, 190, and 250 kPa. Further, deuterium permeation was consistently lower than predicted from diffusion-limited permeation models, thus we developed a transport model that included gas-phase mass transfer and surface reactions to model experimental results. The dissociation constant was optimized to fit the developed model to experimental data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2025

Best of both worlds: Enforcing detailed balance in machine learning models of transition rates

The slow microstructural evolution of materials often plays a key role in determining material properties. When the unit steps of the evolution process are slow, direct simulation approaches such as molecular dynamics become prohibitive and Kinetic Monte-Carlo (kMC) algorithms, where the state-to-state evolution of the system is represented in terms of a continuous-time Markov chain, are instead frequently relied upon to efficiently predict long-time evolution. The accuracy of kMC simulations however relies on the complete and accurate knowledge of reaction pathways and corresponding kinetics. This requirement becomes extremely stringent in complex systems such as concentrated alloys where the astronomical number of local atomic configurations makes the a priori tabulation of all possible transitions impractical. Machine learning models of transition kinetics have been used to mitigate this problem by enabling the efficient on-the-fly prediction of kinetic parameters. While conventional KMC methods based on transition state theory naturally yield reversible dynamics that exactly obey the detailed balance criterion, providing strong guarantees on the properties of the stationary distribution, many recently-proposed ML-based approaches to barrier predictions provide no such guarantees. In this study, we derive conditions under which physics-informed ML architectures exactly enforce the detailed balance condition by construction, even when relying on non-extensive descriptions of states in terms of local environments around mobile defects. In conclusion, using the diffusion of a vacancy in a concentrated alloy as an example, we show that such ML architectures also exhibit superior performance in terms of prediction accuracy, demonstrating that the imposition of physical constraints can facilitate the accurate learning of barriers at no increase in computational cost.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Nuclear Theory from First Principles to Forefront Experiments (Final Report for DE-SC0018638)

The Lee research group is a part of the Nuclear Lattice Effective Field Theory Collaboration, which has developed and performed ab initio lattice simulations of nuclear structure, scattering, reactions, and many-body systems. The other senior members of the collaboration include Ulf-G. Meißner at Bonn/Julich, Evgeny Epelbaum and Hermann Krebs at Bochum, Timo Lahde and Thomas Luu at Julich, and Gautam Rupak at Mississippi State. Our letter “Ab initio alpha-alpha scattering” was featured in a Nature News and Views article. Another letter “Nuclear binding near a quantum phase transition” was highlighted in a Viewpoint article in the online APS journal Physics as well as a news article in the IOP publication Physics World (September 21, 2016). Our letter “Eigenvector continuation with subspace learning” was also highlighted a Synopsis article in Physics. There are many promising ab initio approaches being used to calculate the properties of few-and many-nucleon systems. This includes the no-core shell model, symmetry-adapted no-core shell model quantum Monte Carlo, auxiliary-field diffusion Monte Carlo, self-consistent Green’s functions, many-body perturbation theory, in-medium similarity renormalization group, and coupled cluster methods. Lattice effective field theory is another ab initio approach which combines the framework of effective field theory with lattice Monte Carlo methods to allow favorable scaling from few- to many-body systems. Perhaps the most important aspect of lattice effective field theory is that its strengths and weaknesses are orthogonal to that of other ab initio methods. For example, lattice effective field theory has little difficulty in probing cluster structures and collectivity, while such features are much more difficult using other methods. Furthermore it can be used to compute superfluid condensate fractions as well as the phase diagram of strongly matter and the density and temperature dependence of clustering. Lattice effective field theory was first used in simulations of infinite nuclear matter and infinite neutron matter with pions and without pions. In addition to the efforts by our collaboration, there have been recent efforts by other groups as well.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

Development of a scalable, robust electrocatalytic technology for conversion of CO 2 to formic acid via microstructured materials

This project was funded by the Bioenergy Engineering for Product Synthesis (BEEPS) program under the Funding Opportunity Announcement (FOA) DE-FOA-0001916 Topic Area 5 “Rewiring Carbon Utilization”. This FOA sought projects that would electrocatalytically reduce CO 2 to a carbon intermediate and then upconvert to a multi-carbon product or fuel via non-photosynthetic biological system engineering. The project sought to combine the expertise of OCO Chem, whose chief scientist had previously developed an efficient electrocatalytic reactor for conversion of CO 2 to formate with potential to scale, Montana State University investigators who had recently patented a method for laterally grading membranes with the potential of improving reactant distribution and more uniform efficiency across membrane-based reactors, and University of South Florida which had recently discovered a novel C-C bond forming reaction not known to naturally occur in biological systems and which uses C1 substrates and circumvents the central microbial metabolism.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2022

HomPINNs: Homotopy physics-informed neural networks for learning multiple solutions of nonlinear elliptic differential equations

Physics-informed neural networks (PINNs) based machine learning is an emerging framework for solving nonlinear differential equations. However, due to the implicit regularity of neural network structure, PINNs can only find the flattest solution in most cases by minimizing the loss functions. In this paper, we combine PINNs with the homotopy continuation method, a classical numerical method to compute isolated roots of polynomial systems, and propose a new deep learning framework, named homotopy physics-informed neural networks (HomPINNs), for solving multiple solutions of nonlinear elliptic differential equations. The implementation of an HomPINN is a homotopy process that is composed of the training of a fully connected neural network, named the starting neural network, and training processes of several PINNs with different tracking parameters. The starting neural network is to approximate a starting function constructed by the trivial solutions, while other PINNs are to minimize the loss functions defined by boundary condition and homotopy functions, varying with different tracking parameters. These training processes are regraded as different steps of a homotopy process, and a PINN is initialized by the well-trained neural network of the previous step, while the first starting neural network is initialized using the default initialization method. Finally, several numerical examples are presented to show the efficiency of our proposed HomPINNs, including reaction-diffusion equations with a heart-shaped domain.

97 MATHEMATICS AND COMPUTING↗