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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 433 records · Page 24
All sourcesNASA NTRSDOE OSTI
NASA NTRS1986

Calculations of cosmogenic nuclide production rates in the Earth's atmosphere and their inventories

The production rates of cosmogenic isotopes in the Earth's atmosphere and their resulting terrestrial abundances have been calculated, taking into account both geomagnetic and solar-modulatory effects. The local interstellar flux was assumed to be that of Garcia-Munoz, et al. Solar modulation was accounted for using the heliocentric potential model and expressed in terms of the Deep River neutron monitor count rates. The geomagnetic field was presented by vertical cutoffs calculated by Shea and Smart and the non-vertical cutoffs calculated using ANGRI. The local interstellar particle flux was first modulated using the heliocentric potential field. The modulated cosmic-ray fluxes reaching the earth's orbit then interacted with the geomagnetic field as though it were a high-pass filter. The interaction of the cosmic radiation with the Earth's atmosphere was calculated utilizing the Bolztmann transport equation. Spallation cross sections for isotope production were calculated using the formalism of Silberberg and Tsao and other cross sections were taken from standard sources. Inventories were calculated by accounting from the variation in solar modulation and geomagnetic field strength with time. Results for many isotope, including C-14, Be-7 and Be-10 are in generally good agreement with existing data. The C-14 inventory, for instance, amounts to 1.75/sq cm(e)/s, in excellent agreement with direct estimates.

Obrien, K.↗
NASA NTRS1991

Design of multihundred-watt dynamic isotope power system for robotic space missions

The design of a multihundred-watt dynamic isotope power system (DIPS) based on the US Department of Energy (DOE) general-purpose heat source (GPHS) and small (multihundred-watt) free-piston Stirling engine (FPSE) is described as a potential lower cost alternative to radioisotope thermoelectric generators (RTGs). The design is targeted at the power needs of future unmanned deep space and planetary surface exploration missions. Since the competitive potential of FPSE as an isotope convertor was first identified, work has focused on the feasibility of directly integrating GPHS with the Stirling heater head. Thermal modeling of various radiatively coupled heat source/heater head geometries has been performed using data furnished by the developers of FPSE and GPHS. The analysis indicates that, for the 1050 K heater head configurations considered, GPHS fuel clad temperatures remain safe operating limits under all conditions including shutdown of one engine on a twin engine unit. Based on these results, preliminary characterizations of multihundred-watt units have been established. They indicate that, per electrical watt, the GPHS/small Stirling DIPS will be roughly equivalent to MOD RTG in size and mass but will require about a third the amount of isotope fuel.

Bents, D. J.↗
DOE OSTI2022

Indications of a Decrease in the Depth of Deep Convective Cores with Increasing Aerosol Concentration during the CACTI Campaign

Abstract An aerosol indirect effect on deep convective cores (DCCs), by which increasing aerosol concentration increases cloud-top height via enhanced latent heating and updraft velocity, has been proposed in many studies. However, the magnitude of this effect remains uncertain due to aerosol measurement limitations, modulation of the effect by meteorological conditions, and difficulties untangling meteorological and aerosol effects on DCCs. The Cloud, Aerosol, and Complex Terrain Interactions (CACTI) campaign in 2018–19 produced concentrated aerosol and cloud observations in a location with frequent DCCs, providing an opportunity to examine the proposed aerosol indirect effect on DCC depth in a rigorous and robust manner. For periods throughout the campaign with well-mixed boundary layers, we analyze relationships that exist between aerosol variables (condensation nuclei concentration > 10 nm, 0.4% cloud condensation nuclei concentration, 55–1000-nm aerosol concentration, and aerosol optical depth) and meteorological variables [level of neutral buoyancy (LNB), convective available potential energy, midlevel relative humidity, and deep-layer vertical wind shear] with the maximum radar-echo-top height and cloud-top temperature (CTT) of DCCs. Meteorological variables such as LNB and deep-layer shear are strongly correlated with DCC depth. LNB is also highly correlated with three of the aerosol variables. After accounting for meteorological correlations, increasing values of the aerosol variables [with the exception of one formulation of aerosol optical depth (AOD)] are generally correlated at a statistically significant level with a warmer CTT of DCCs. Therefore, for the study region and period considered, increasing aerosol concentration is mostly associated with a decrease in DCC depth.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Aerodynamic Analysis of Wind Loading on Parabolic Trough Collectors Using High-Fidelity CFD Modeling

Wind loading on parabolic solar collector support structures is the key driver for material costs. As identified by NREL's CSP Best Practices project [1], ability to predict wind-loading in deep-arrays and the impact of edge effects has potential to decrease levelized cost of electricity (LCoE) by 15%. In this study, we present a high-fidelity computational model that can model the flow around deep arrays of parabolic troughs under varying turbulent inflow conditions. Ability to accurately reproduce atmospheric boundary layer (ABL) profiles is first demonstrated through Large Eddy Simulation (LES) simulations and compared against wind tunnel measurements. Thereafter, unsteady turbulent flow past single row and six row configurations is computed using hybrid RANS/LES simulations. Investigations of wind loading, through parametric tilt angle variations of single row and on waked collectors in six-row configuration, are used to highlight design considerations for parabolic troughs only possible through high-fidelity unsteady calculations.

aerodynamics↗
DOE OSTI2023

Accurate prediction of carbon dioxide capture by deep eutectic solvents using quantum chemistry and a neural network

Carbon dioxide (CO 2 ) emissions from fossil fuel combustion are a significant source of greenhouse gas, contributing in a major way to global warming and climate change. Carbon dioxide capture and sequestration is gaining much attention as a potential method for controlling these greenhouse gas emissions. Among the environmentally friendly solvents, deep eutectic solvents (DESs) have demonstrated the potential capability for carbon capture. To establish a theoretical framework for DES activity, thermodynamics modeling and solubility predictions are significant factors to anticipate and understand the system behavior. Here, in this study, we combine the COSMO-RS model with machine learning techniques to predict the solubility of CO 2 in various deep eutectic solvents. A comprehensive data set was established comprising 1973 CO 2 solubility data points in 132 different DESs at a variety of temperatures, pressures, and DES molar ratios. This data set was then utilized for the further verification and development of the COSMO-RS model. The CO 2 solubility (ln(x CO 2 )) in DESs calculated with the COSMO-RS model differs significantly from the experiment with an average absolute relative deviation (AARD) of 23.4%. A multilinear regression model was developed using the COSMO-RS predicted solubility and a temperature-pressure dependent parameter, which improved the AARD to 12%. Finally, a machine learning model using COSMO-RS-derived features was developed based on an artificial neural network algorithm. The results are in excellent agreement with the experimental CO 2 solubilities, with an AARD of only 2.72%. The ML model will be a potentially useful tool for the design and selection of DESs for CO 2 capture and utilization.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1992

A theory for narrow-banded radio bursts at Uranus - MHD surface waves as an energy driver

A possible scenario for the generation of the narrow-banded radio bursts detected at Uranus by the Voyager 2 planetary radio astronomy experiment is described. In order to account for the emission burstiness which occurs on time scales of hundreds of milliseconds, it is proposed that ULF magnetic surface turbulence generated at the frontside magnetopause propagates down the open/closed field line boundary and mode-converts to kinetic Alfven waves (KAW) deep within the polar cusp. The oscillating KAW potentials then drive a transient electron stream that creates the bursty radio emission. To substantiate these ideas, Voyager 2 magnetometer measurements of enhanced ULF magnetic activity at the frontside magnetopause are shown. It is demonstrated analytically that such magnetic turbulence should mode-convert deep in the cusp at a radial distance of 3 RU.

Farrell, W. M.↗
NASA NTRS1982

Single-mode fiber systems for deep space communication network

The present investigation is concerned with the development of single-mode optical fiber distribution systems. It is pointed out that single-mode fibers represent potentially a superior medium for the distribution of frequency and timing reference signals and wideband (400 MHz) IF signals. In this connection, single-mode fibers have the potential to improve the capability and precision of NASA's Deep Space Network (DSN). Attention is given to problems related to precise time synchronization throughout the DSN, questions regarding the selection of a transmission medium, and the function of the distribution systems, taking into account specific improvements possible by an employment of single-mode fibers.

Lutes, G.↗
NASA NTRS2003

Low-Power SOI CMOS Transceiver

The work aims at developing a low-power Silicon on Insulator Complementary Metal Oxide Semiconductor (SOI CMOS) Transceiver for deep-space communications. RF Receiver must accomplish the following tasks: (a) Select the desired radio channel and reject other radio signals, (b) Amplify the desired radio signal and translate them back to baseband, and (c) Detect and decode the information with Low BER. In order to minimize cost and achieve high level of integration, receiver architecture should use least number of external filters and passive components. It should also consume least amount of power to minimize battery cost, size, and weight. One of the most stringent requirements for deep-space communication is the low-power operation. Our study identified that two candidate architectures listed in the following meet these requirements: (1) Low-IF receiver, (2) Sub-sampling receiver. The low-IF receiver uses minimum number of external components. Compared to Zero-IF (Direct conversion) architecture, it has less severe offset and flicker noise problems. The Sub-sampling receiver amplifies the RF signal and samples it using track-and-hold Subsampling mixer. These architectures provide low-power solution for the short- range communications missions on Mars. Accomplishments to date include: (1) System-level design and simulation of a Double-Differential PSK receiver, (2) Implementation of Honeywell SOI CMOS process design kit (PDK) in Cadence design tools, (3) Design of test circuits to investigate relationships between layout techniques, geometry, and low-frequency noise in SOI CMOS, (4) Model development and verification of on-chip spiral inductors in SOI CMOS process, (5) Design/implementation of low-power low-noise amplifier (LNA) and mixer for low-IF receiver, and (6) Design/implementation of high-gain LNA for sub-sampling receiver. Our initial results show that substantial improvement in power consumption is achieved using SOI CMOS as compared to standard CMOS process. Potential advantages of SOI CMOS for deep-space communication electronics include: (1) Radiation hardness, (2) Low-power operation, and (3) System-on-Chip (SOC) solutions.

Fujikawa, Gene↗
NASA NTRS1985

A numerical study of global axisymmetric states and their stability to quasi-geostrophic disturbances

A steady, axisymmetric model of the general circulation is developed as a basis for climate stability studies. The model includes the effects of heating, rotation, and internal friction, but neglects topography. It is assumed that the axisymmetric flow may be modeled by making the Boussinesq and deep convection approximations. The hydrostatic assumption is not made, thus permitting the advective terms to be included in the vertical equation of motion. The initial set of five primitive equations is reduced to three equations in terms of the zonal velocity, meridional streamfunction, and the potential temperature perturbation. The application of the Boussinesq, deep convection, and quasi-geostrophic assumptions limits the ranges of the heating and rotation rates. For values not too far from typical atmospheric values, the model produces a stability boundary separating Hadley from Rossby flow. The boundary is characterized by a particular value of vertical wind shear, which suggests that baroclinic instability is the primary mechanism for the loss of stability. The initial growth rates are largest for longitudinal waves 4-7, also in agreement with studies of baroclinic instability.

Henderson, H. W.↗
DOE OSTI2025

Structure, dynamics, and electrochemistry of choline chloride/ethylene glycol eutectic solvents at an electrode surface explored by molecular dynamics simulations

Choline chloride and ethylene glycol mixtures with 1:2, 1:4, and 1:6 molar ratios on the surfaces of graphite and gold electrodes were studied using classical molecular dynamics simulations. Both neutral and charged electrodes were considered. The liquid composition, solvation structure, molecular orientation, and dynamics at the electrode surface are significantly different from those of the bulk liquid. These properties strongly depend on the electrode material and charge density, whereas they are less sensitive to the overall solvent composition. The effect of the electrode on the composition, structure, and orientation of the liquid fades beyond ∼10 Å from the surface of the electrode. This distance corresponds to about two layers of the structured solvent, despite the fact that the layered structure extends to at least five layers or about 25 Å. However, the electrode influences solvent dynamics over a longer distance. The electrochemical properties of the eutectic solvent at both electrode surfaces were also studied. The simulations captured the experimental differential capacitance shapes for both electrode systems, although the magnitudes and exact shapes differ. The simulations further revealed that the solvent in the first solvation layer can both overscreen and underscreen the electrode charges depending on the electrode material and electrode potential.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
NASA NTRS1994

Influence of ocean surface conditions on atmospheric vertical thermodynamic structure and deep convection

The authors analyze the influence of Sea Surface Temperature (SST) and surface wind divergence on atmospheric thermodynamic structure and the resulting effects on the occurrence of deep convection using National Meteorological Center radiosonde data and International Satellite Cloud Climatology Program data for July 1983-July 1985. The onset of deep convection requires not only the existence of positive convective available potential energy (CAPE), but also an unstable planetary boundary layer (PBL). A stable PBL is observed to suppress deep convection even when CAPE is positive. Variations of SST have a major effect on CAPE, but surface wind divergence can also affect deep convection by changing the lapse rate in the lower troposphere and humidity in the PBL. Specifically, when SST is greater than or equal to 28 C, CAPE is always positive, and surface wind divergence does not qualitatively change the buoyancy profile above the PBL. Strong surface wind divergence, however, stabilizes the PBL so as to suppress the initiation of deep convection. In warm SST regions, CAPE is greater than 0 regardless of assumptions about condensate loading, although the pseudoadiabatic limit is more consistent with the observed deep convection than the reversible moist-adiabatic limit under these circumstances. When SST is less than 27 C, CAPE is usually negative and inhibits convection, but strong surface wind convergence can destabilize the inversion layer and moisten the PBL enough to make the atmosphere neutrally stable in the mean. As a result, deep convection is generally enhanced either when SST is greater than or equal to 28 C in the absence of strong surface wind divergence or when strong surface wind convergence occurs even if SST is less than 27 C. The anomalous suppression of deep convection in the warm area of the equatorial west Pacific lying between the intertropical convergence zone (ITCZ) and south Pacific convergence zone (SPCZ) is probably caused by dryness in the PBL and an inversion in that area. The seasonal cycles of deep convection and surface wind divergence are in phase with the maximum solar radiation and lead SST for one to three months in the central Pacific. The change of PBL relative humidity plays a critical role in the changeover to convective instability in this case. The seasonal change of deep convection and associated clouds seems not to have important effects on the seasonal change of local SST in the central Pacific.

Fu, Rong↗
NASA NTRSDate not supplied

An Orbital Photogeologic Map of the Jezero Crater Rim: Diverse Targets for Mars 2020 Future Exploration.

The Perseverance rover on the Mars 2020 mission is currently collecting samples in Jezero crater for potential future return to Earth by the Mars Sample Return (MSR) mission. Jezero is a 45 km diameter mid- to late-Noachian-aged crater selected for its diverse geology and potential for preserving evidence of ancient life. The rover is approaching the crater rim, an area of interest for its potential to preserve diverse lithologies representative of a large period of geologic history. It has significant astrobiological potential, as it may preserve evidence of uplifted deep crust and ancient hydrothermal environments. Impact megabreccia in the crater rim may be exhumed pre-Noachian crust from the Isidis impact, which would likely be the oldest materials ever investigated by a rover on Mars. Additionally, the rim hosts outcrops of the regionally extensive and potentially volcanic olivine/carbonate unit and mafic capping unit, which could have implications for the evolution of Mars volcanism. Regional maps have delineated the lithologies present in and around Jezero as a whole. The largest scale that the crater rim geology has been mapped is 1:5000.

M C Deahn↗
NASA NTRS2017

The Opportunity in Commercial Approaches for Future NASA Deep Space Exploration Elements

In 2011, NASA released a report assessing the market for commercial crew and cargo services to low Earth orbit (LEO). The report stated that NASA had spent a few hundred million dollars in the Commercial Orbital Transportation Services (COTS) program on the portion related to the development of the Falcon 9 launch vehicle. Yet a NASA cost model predicted the cost would have been significantly more with a non-commercial cost-plus contracting approach. By 2016 a NASA request for information stated it must "maximize the efficiency and sustainability of the Exploration Systems development programs", as "critical to free resources for reinvestment...such as other required deep space exploration capabilities." This work joins the previous two events, showing the potential for commercial, public private partnerships, modeled on programs like COTS, to reduce the cost to NASA significantly for "...other required deep space exploration capabilities." These other capabilities include landers, stages and more. We mature the concept of "costed baseball cards", adding cost estimates to NASA's space systems "baseball cards." We show some potential costs, including analysis, the basis of estimates, data sources and caveats to address a critical question - based on initial assessment, are significant agency resources justified for more detailed analysis and due diligence to understand and invest in public private partnerships for human deep space exploration systems? The cost analysis spans commercial to cost-plus contracting approaches, for smaller elements vs. larger, with some variation for lunar or Mars. By extension, we delve briefly into the potentially much broader significance of the individual cost estimates if taken together as a NASA investment portfolio where public private partnership are stitched together for deep space exploration. How might multiple improvements in individual systems add up to NASA human deep space exploration achievements, realistically, affordably, sustainably, in a relevant timeframe?

cost modeling estimation↗
DOE OSTI2021

Teaching a neural network to attach and detach electrons from molecules

Abstract Interatomic potentials derived with Machine Learning algorithms such as Deep-Neural Networks (DNNs), achieve the accuracy of high-fidelity quantum mechanical (QM) methods in areas traditionally dominated by empirical force fields and allow performing massive simulations. Most DNN potentials were parametrized for neutral molecules or closed-shell ions due to architectural limitations. In this work, we propose an improved machine learning framework for simulating open-shell anions and cations. We introduce the AIMNet-NSE (Neural Spin Equilibration) architecture, which can predict molecular energies for an arbitrary combination of molecular charge and spin multiplicity with errors of about 2–3 kcal/mol and spin-charges with error errors ~0.01e for small and medium-sized organic molecules, compared to the reference QM simulations. The AIMNet-NSE model allows to fully bypass QM calculations and derive the ionization potential, electron affinity, and conceptual Density Functional Theory quantities like electronegativity, hardness, and condensed Fukui functions. We show that these descriptors, along with learned atomic representations, could be used to model chemical reactivity through an example of regioselectivity in electrophilic aromatic substitution reactions.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Global patterns of diversity and metabolism of microbial communities in deep-sea hydrothermal vent deposits

When deep-sea hydrothermal fluids mix with cold oxygenated fluids, minerals precipitate out of solution and form hydrothermal deposits. These actively venting deep-sea hydrothermal deposits support a rich diversity of thermophilic microorganisms which are involved in a range of carbon, sulfur, nitrogen, and hydrogen metabolisms. Global patterns of thermophilic microbial diversity in deep-sea hydrothermal ecosystems have illustrated the strong connectivity between geological processes and microbial colonization, but little is known about the genomic diversity and physiological potential of these novel taxa. Here we explore this genomic diversity in 42 metagenomes from four deep-sea hydrothermal vent fields and a deep-sea volcano collected from 2004 to 2018 and document their potential implications in biogeochemical cycles. Our dataset represents 3635 metagenome-assembled genomes encompassing 511 novel and recently identified genera from deep-sea hydrothermal settings. Some of the novel bacterial (107) and archaeal genera (30) that were recently reported from the deep-sea Brothers volcano were also detected at the deep-sea hydrothermal vent fields, while 99 bacterial and 54 archaeal genera were endemic to the deep-sea Brothers volcano deposits. We report some of the first examples of medium- (≥ 50% complete, ≤ 10% contaminated) to high-quality (> 90% complete, < 5% contaminated) MAGs from phyla and families never previously identified, or poorly sampled, from deep-sea hydrothermal environments. We greatly expand the novel diversity of Thermoproteia, Patescibacteria (Candidate Phyla Radiation, CPR), and Chloroflexota found at deep-sea hydrothermal vents and identify a small sampling of two potentially novel phyla, designated JALSQH01 and JALWCF01. Metabolic pathway analysis of metagenomes provides insights into the prevalent carbon, nitrogen, sulfur, and hydrogen metabolic processes across all sites and illustrates sulfur and nitrogen metabolic “handoffs” in community interactions. We confirm that Campylobacteria and Gammaproteobacteria occupy similar ecological guilds but their prevalence in a particular site is driven by shifts in the geochemical environment. Our study of globally distributed hydrothermal vent deposits provides a significant expansion of microbial genomic diversity associated with hydrothermal vent deposits and highlights the metabolic adaptation of taxonomic guilds. Collectively, our results illustrate the importance of comparative biodiversity studies in establishing patterns of shared phylogenetic diversity and physiological ecology, while providing many targets for enrichment and cultivation of novel and endemic taxa.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2026

Data for The Stem Cell-Type Transcriptome of Bioenergy Sorghum Reveals the Spatial Regulation of Secondary Cell Wall Networks

Bioenergy sorghum is a low-input, drought-resilient, deep-rooting annual crop that has high biomass yield potential enabling the sustainable production of biofuels, biopower, and bioproducts. Bioenergy sorghum’s 4-5 m stems account for ~80% of the harvested biomass. Stems accumulate high levels of sucrose that could be used to synthesize bioethanol and useful biopolymers if information about stem cell-type gene expression and regulation was available to enable engineering. To obtain this information, Laser Capture Microdissection (LCM) was used to isolate and collect transcriptome profiles from five major cell types that are present in stems of the sweet sorghum Wray. Transcriptome analysis identified genes with cell-type specific and cell-preferred expression patterns that reflect the distinct metabolic, transport, and regulatory functions of each cell type. Analysis of cell-type specific gene regulatory networks (GRNs) revealed that unique TF families contribute to distinct regulatory landscapes, where regulation is organized through various modes and identifiable network motifs. Cell-specific transcriptome data was combined with a stem developmental transcriptome dataset to identify the GRN that differentially activates the secondary cell wall (SCW) formation in stem xylem sclerenchyma and epidermal cells. The cell-type transcriptomic dataset provides a valuable source of information about the function of sorghum stem cell types and GRNs that will enable the engineering of bioenergy sorghum stems.

Software↗
DOE OSTI2020

Chapter Nine - Automated Optimal Control in Energy Systems: The Reinforcement Learning Approach

With the development of smart grid technologies an increasing number of new devices and participants have joined modern energy systems and are inevitably making them more complicated and interdependent than ever. Optimally controlling such a complex energy system and maintaining its operation in a high-efficient, secure, and resilient manner are challenging tasks to the system operators. Fortunately, the revolution in deep learning and artificial intelligence (AI), both from hardware and algorithms perspectives, has provided new ideas and solutions to many previously intractable problems. As a result, this advance in computer science also sparked great research interests in utilizing AI in solving engineering problems related to the modern energy systems. Among many AI techniques, deep reinforcement learning (DRL) has demonstrated great potential for solving sequential optimization problems, which are very common in the engineering domains. Its ability to handle nonlinearity and stochasticity in controlled systems has out-competed many traditional optimal control algorithms. Therefore in this chapter, we focus on the state-of-the-art of DRL concepts and related algorithms, compare their pros and cons with traditional optimal control approaches and discuss the typical workflow for leveraging RL in solving complex problems in modern energy systems.

artificial intelligence↗
DOE OSTI2024

Separable physics-informed DeepONet: Breaking the curse of dimensionality in physics-informed machine learning

The deep operator network (DeepONet) has shown remarkable potential in solving partial differential equations (PDEs) by mapping between infinite-dimensional function spaces using labeled datasets. However, in scenarios lacking labeled data, the physics-informed DeepONet (PI-DeepONet) approach, which utilizes the residual loss of the governing PDE to optimize the network parameters, faces significant computational challenges, particularly due to the curse of dimensionality. This limitation has hindered its application to high-dimensional problems, making even standard 3D spatial with 1D temporal problems computationally prohibitive. Additionally, the computational requirement increases exponentially with the discretization density of the domain. Here, to address these challenges and enhance scalability for high-dimensional PDEs, we introduce the Separable physics-informed DeepONet (Sep-PI-DeepONet). This framework employs a factorization technique, utilizing sub-networks for individual one-dimensional coordinates, thereby reducing the number of forward passes and the size of the Jacobian matrix required for gradient computations. By incorporating forward-mode automatic differentiation (AD), we further optimize computational efficiency, achieving linear scaling of computational cost with discretization density and dimensionality, making our approach highly suitable for high-dimensional PDEs. We demonstrate the effectiveness of Sep-PI-DeepONet through three benchmark PDE models: the viscous Burgers’ equation, Biot’s consolidation theory, and a parameterized heat equation. Our framework maintains accuracy comparable to the conventional PI-DeepONet while reducing training time by two orders of magnitude. Notably, for the heat equation solved as a 4D problem, the conventional PI-DeepONet was computationally infeasible (estimated 289.35 h), while the Sep-PI-DeepONet completed training in just 2.5 h. These results underscore the potential of Sep-PI-DeepONet in efficiently solving complex, high-dimensional PDEs, marking a significant advancement in physics-informed machine learning.

Neural operator↗