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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

MLOps for Beam Controls

Machine learning operations (MLOps) is the standardization and streamlining of the ML development lifecycle to address the challenges associated with large-scale machine learning applications. The full MLOps pipeline consists of open-source tools: DataHub, MinIO and MLflow. It is being used for dataset management and model development to handle changing data dependencies, varying business needs, reproducibility, and diverse teams working with differing tools and skills. To demonstrate the completion of an MLOps pipeline for particle accelerator operations, we are deploying a simple script that computes settings for the Booster’s gradient magnet power supply. Once the demonstration is complete, we will develop and deploy ML-based optimization algorithms to improve Booster’s overall efficiency. This MLOps pipeline opens the gate to systematically develop and deploy ML applications for accelerator controls and diagnostics.

43 PARTICLE ACCELERATORS↗
DOE OSTI2023

Machine learning methods for particle stress development in suspension Poiseuille flows

Numerical simulations are used to study the dynamics of a developing suspension Poiseuille flow with monodispersed and bidispersed neutrally buoyant particles in a planar channel, and machine learning is applied to learn the evolving stresses of the developing suspension. The particle stresses and pressure develop on a slower time scale than the volume fraction, indicating that once the particles reach a steady volume fraction profile, they rearrange to minimize the contact pressure on each particle. Here we consider how the stress development leads to particle migration, time scales for stress development, and present a new physics-informed Galerkin neural network that allows for learning the particle stresses when direct measurements are not possible. The particle fluxes are compared with the Suspension Balance Model with good agreement. We show that when stress measurements are possible, the MOR-physics operator learning method can also capture the particle stresses.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2026

AI-Ready Control System for the Fermilab Accelerator Complex

Reliable, high-intensity operation of the Fermilab Accelerator Complex is critical to the success of the Long-Baseline Neutrino Facility and Deep Underground Neutrino Experiment. We describe the requirements and infrastructure necessary to support routine use of artificial intelligence and machine learning (AI/ML) in the accelerator control system. Three capabilities are identified: a machine learning operations (MLOps) framework standardizing the lifecycle of AI/ML automation from data management through deployment and monitoring; a data quality framework defining and enforcing standards required to build trustworthy AI/ML applications; and workflow integration with large language models to assist physicists, engineers, and operators with information retrieval, code development, and routine analysis. Use cases spanning beam diagnostics, beam control, and support system automation illustrate the technical requirements across the complex.

43 PARTICLE ACCELERATORS↗
DOE OSTI2025

Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications

In this work we introduce a novel two-level overlapping additive Schwarz preconditioner for accelerating the training of scientific machine learning applications. The design of the proposed preconditioner is motivated by the nonlinear two-level overlapping additive Schwarz preconditioner. The neural network parameters are decomposed into groups (subdomains) with overlapping regions. In addition, the network’s feed-forward structure is indirectly imposed through a novel subdomain-wise synchronization strategy and a coarse-level training step. Through a series of numerical experiments, which consider physicsinformed neural networks and operator learning approaches, we demonstrate that the proposed two-level preconditioner significantly speeds up the convergence of the standard (LBFGS) optimizer while also yielding more accurate machine learning models. Moreover, the devised preconditioner is designed to take advantage of model-parallel computations, which can further reduce the training time.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Optimizing the optimizer for physics-informed neural networks and Kolmogorov-Arnold networks

Physics-Informed Neural Networks (PINNs) have revolutionized the computation of PDE solutions by integrating partial differential equations (PDEs) into the neural network’s training process as soft constraints, becoming an important component of the scientific machine learning (SciML) ecosystem. More recently, physics-informed Kolmogorv-Arnold networks (PIKANs) have also shown to be effective and comparable in accuracy with PINNs. In their current implementation, both PINNs and PIKANs are mainly optimized using first-order methods like Adam, as well as quasi-Newton methods such as BFGS and its low-memory variant, L-BFGS. However, these optimizers often struggle with highly nonlinear and non-convex loss landscapes, leading to challenges such as slow convergence, local minima entrapment, and (non)degenerate saddle points. In this study, we investigate the performance of Self- Scaled BFGS (SSBFGS), Self-Scaled Broyden (SSBroyden) methods and other advanced quasi-Newton schemes, including BFGS and L-BFGS with different line search strategies. These methods dynamically rescale updates based on historical gradient information, thus enhancing training efficiency and accuracy. We systematically compare these optimizers – using both PINNs and PIKANs – on key challenging PDEs, including the Burgers, Allen-Cahn, Kuramoto-Sivashinsky, Ginzburg-Landau, and Stokes equations. Additionally, we evaluate the performance of SSBFGS and SSBroyden for Deep Operator Network (DeepONet) architectures, demonstrating their effectiveness for data-driven operator learning. Our findings provide state-of-the-art results with orders-of-magnitude accuracy improvements without the use of adaptive weights or any other enhancements typically employed in PINNs. More broadly, our work reveal insights into the effectiveness of quasi-Newton optimization strategies in significantly improving the convergence and accurate generalization of PINNs and PIKANs.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2017

Slipstream pilot-scale demonstration of a novel amine-based post-combustion technology for carbon dioxide capture from coal-fired power plant flue gas

Post-combustion CO 2 capture (PCC) technology offers flexibility to treat the flue gas from both existing and new coal-fired power plants and can be applied to treat all or a portion of the flue gas. Solvent-based technologies are today the leading option for PCC from commercial coal-fired power plants as they have been applied in large-scale in other applications. Linde and BASF have been working together to develop and further improve a PCC process incorporating BASF’s novel aqueous amine-based solvent technology. This technology offers significant benefits compared to other solvent-based processes as it aims to reduce the regeneration energy requirements using novel solvents that are very stable under the coal-fired power plant feed gas conditions. BASF has developed the desired solvent based on the evaluation of a large number of candidates. In addition, long-term small pilot-scale testing of the BASF solvent has been performed on a lignite-fired flue gas. In coordination with BASF, Linde has evaluated a number of options for capital cost reduction in large engineered systems for solvent-based PCC technology. This report provides a summary of the work performed and results from a project supported by the US DOE (DE-FE0007453) for the pilot-scale demonstration of a Linde-BASF PCC technology using coal-fired power plant flue gas at a 1-1.5 MWe scale in Wilsonville, AL at the National Carbon Capture Center (NCCC). Following a project kick-off meeting in November 2011 and the conclusion of pilot plant design and engineering in February 2013, mechanical completion of the pilot plant was achieved in July 2014, and final commissioning activities were completed to enable start-up of operations in January 2015. Parametric tests were performed from January to December 2015 to determine optimal test conditions and evaluate process performance over a variety of operation parameters. A long-duration 1500-hour continuous test campaign was performed from May to August 2016 at a selected process condition to evaluate process performance and solvent stability over a longer period similar to how the process would operate as a continuously running large-scale PCC plant. The pilot plant integrated a number of unique features of the Linde-BASF technology aimed at lowering overall energy consumption and capital costs. During the overall test period including startup, parametric testing and long-duration testing, the pilot plant was operated for a total of 6,764 hours out of which testing with flue gas was performed for 4,109 hours. The pilot plant testing demonstrated all of the performance targets including CO 2 capture rate exceeding 90%, CO 2 purity exceeding 99.9 mol% (dry), flue gas processing capacity up to 15,500 lbs/hr (equivalent to 1.5 MWe capacity slipstream), regeneration energy as low as 2.7 GJ/tonne CO 2 , and regenerator operating pressure up to 3.4 bara. Excellent solvent stability performance data was measured and verified by Linde and BASF during both test campaigns. In addition to process data, significant operational learnings were gained from pilot tests that will contribute greatly to the commercial success of PCC. Based on a thorough techno-economic assessment (TEA) of the Linde-BASF PCC process integrated with a 550 MWe supercritical coal-fired power plant, the net efficiency of the integrated power plant with CO 2 capture is increased from 28.4% with the DOE/NETL Case 12 reference to 30.9% with the Linde-BASF PCC plant previously presented utilizing the BASF OASE® blue solvent [Ref. 4], and is further increased to 31.4% using a Linde-BASF PCC plant with BASF OASE® blue solvent and an advanced stripper interstage heater (SIH) configuration. The Linde-BASF PCC plant incorporating the BASF OASE® blue solvent also results in significantly lower overall capital costs, thereby reducing the cost of electricity (COE) and cost of CO 2 captured from $147.25/MWh and $56.49/MT CO 2 , respectively, for the reference DOE/NETL Case 12 plant, to $128.49/MWh and $41.85/MT CO2 for process case LB1, respectively, and $126.65/MWh and $40.66/MT CO 2 for process case SIH, respectively. With additional innovative Linde-BASF PCC process configuration improvements, the COE and cost of CO 2 captured can be further reduced to $125.51/MWh and $39.90/MT CO 2 for a further optimized PCC process defined as LB1-CREB. Most notably, the Linde-BASF process options assessed have already demonstrated the potential to lower the cost of CO 2 captured below the DOE target of $40/MT CO 2 at the 550 MWe scale for second generation PCC technologies. Project organization, structure, goals, tasks, accomplishments, process criteria and milestones will be presented in this report along with highlights and key results from parametric and long-duration testing of the Linde-BASF PCC pilot. The parametric and long-duration testing campaigns were aimed at validating the performance of the PCC technology against targets determined from a preliminary techno-economic assessment. The stability of the solvent with extended operation in a realistic power plant setting was measured with performance verified. Additionally, general solvent classification information, process operating conditions, normalized solvent performance data, solvent stability test results, flue gas conditions data, CO 2 purity data in the gaseous product stream, steam requirements and process flow diagrams, and updated process economic data for a scaled-up 550 MWe supercritical power plant with CO 2 capture are presented and discussed in this report.

20 FOSSIL-FUELED POWER PLANTS↗
DOE OSTI2025

Computationally efficient models for aqueous organic redox flow batteries

The rising usage of intermittent energy has garnered the need for large scale energy storage systems. Redox flow batteries (RFB) based energy storage system shows promising potential. Numerical simulations and machine learning approaches have been widely used to study RFB performance. The development of autonomous material discovery framework and digital twin of energy storage system usually needs to query cell performance through fast response models. In this study, two computationally efficient models are introduced: a physics-based analytical flow battery model (EZBattery), and a machine learning operator model (Deep Operator Network, denoted by DeepONet). Both models can provide cell performance near instantly, and prediction accuracy was systematically examined on an application of evaluating the performances of a 780 cm 2 aqueous organic redox flow battery (AORFB), using potential anolyte candidates in dihydroxyphenazine (DHP)-based family of organic materials. A validated computationally expansive 3-dimensional multi-physics finite element model by COMSOL was used as the ground truth and provided the training data set for the DeepONet. 1280 samples were generated with 10 properties to mimic the different possible anolyte candidates, and the cell performances were evaluated under 10 different combined operating conditions. The accuracy comparisons for the two computationally efficient models show that both models can provide comparable accuracy in predicting cell charging/discharging voltage curves. DeepONet can provide slightly higher overall accuracy than EZBattery with faster calculation speed, but highly relies on the training dataset. EZBattery does not need a training dataset and can provide interpretable physics-based explanations of the results, while being more flexible to adjust to adapt any different cell designs, flow battery architectures, and electrolyte materials.

Analytical model↗
DOE OSTI2025

Neural chaos: A spectral stochastic neural operator

Building surrogate models for operators with uncertainty quantification capabilities is essential for many engineering applications where randomness–such as variability in material properties, boundary conditions, and initial conditions–is unavoidable. Polynomial Chaos Expansion (PCE) is widely recognized as a go-to method for constructing stochastic surrogates in both intrusive and non-intrusive ways, and it has recently been used in the context of operator learning. However, its application becomes challenging for complex or high-dimensional processes, as achieving accuracy requires higher-order polynomials, which can increase computational demand and/or the risk of overfitting. Furthermore, PCE requires specialized treatments to manage random variables that are not independent, and these treatments may be problem-dependent or may fail with increasing complexity. Here, in this work, we adopt the same formalism as the spectral expansion used in PCE; however, we replace the classical polynomial basis functions with neural network (NN) basis functions to leverage their expressivity. To achieve this, we propose an algorithm that identifies NN-parameterized basis functions in a purely data-driven manner, without any prior assumptions about the joint distribution of the random variables involved, whether independent or dependent, or about their marginal distributions. The proposed algorithm identifies each NN-parameterized basis function sequentially, ensuring they are orthogonal with respect to the data distribution. The basis functions are constructed directly on the joint stochastic variables without requiring a tensor product structure or assuming independence of the random variables. This approach may offer greater flexibility for complex stochastic models, while simplifying implementation compared to the tensor product structures typically used in PCE to handle random vectors. This is particularly advantageous given the current state of open-source packages, where building and training neural networks can be done with just a few lines of code and extensive community support. We demonstrate the effectiveness of the proposed scheme through several numerical examples of varying complexity and provide comparisons with classical PCE.

Polynomial chaos expansion↗
DOE OSTI2015

SU-E-I-80: Quantification of Respiratory and Cardiac Motion Effect in SPECT Acquisitions Using Anthropomorphic Models: A Monte Carlo Simulation Study

Purpose: The purpose of the present study was to quantify, evaluate the impact of cardiac and respiratory motion on clinical nuclear imaging protocols. Common SPECT and scintigraphic scans are studied using Monte Carlo (MC) simulations, comparing the resulted images with and without motion. Methods: Realistic simulations were executed using the GATE toolkit and the XCAT anthropomorphic phantom as a reference model for human anatomy. Three different radiopharmaceuticals based on 99mTc were studied, namely 99mTc-MDP, 99mTc—N—DBODC and 99mTc—DTPA-aerosol for bone, myocardium and lung scanning respectively. The resolution of the phantom was set to 3.5 mm{sup 3}. The impact of the motion on spatial resolution was quantified using a sphere with 3.5 mm diameter and 10 separate time frames, in the ECAM modeled SPECT scanner. Finally, respiratory motion impact on resolution and imaging of lung lesions was investigated. The MLEM algorithm was used for data reconstruction, while the literature derived biodistributions of the pharmaceuticals were used as activity maps in the simulations. Results: FWHM was extracted for a static and a moving sphere which was ∼23 cm away from the entrance of the SPECT head. The difference in the FWHM was 20% between the two simulations. Profiles in thorax were compared in the case of bone scintigraphy, showing displacement and blurring of the bones when respiratory motion was inserted in the simulation. Large discrepancies were noticed in the case of myocardium imaging when cardiac motion was incorporated during the SPECT acquisition. Finally the borders of the lungs are blurred when respiratory motion is included resulting to a dislocation of ∼2.5 cm. Conclusion: As we move to individualized imaging and therapy procedures, quantitative and qualitative imaging is of high importance in nuclear diagnosis. MC simulations combined with anthropomorphic digital phantoms can provide an accurate tool for applications like motion correction techniques’ optimization. This research has been co-funded by the European Union (European Social Fund) and Greek national resources under the framework of the ‘Archimedes III: Funding of Research Groups in TEI of Athens’ project of the ‘Education & Lifelong Learning’ Operational Programme.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2021

Real Time - Optimal Power Flow Based Distributed Energy Resources Management System (DERMS) (CRADA Number CRD-20-16909 Final Report)

The integration of behind-the-meter distributed energy resources (DERs) into distribution systems brings transformative changes to power systems. This requires operators and planners to find solutions to modernize electric grids and to effectively manage DERs for grid services. NREL developed novel DER management algorithms (referred to as Real-Time Optimal Power Flow, RT-OPF) through U.S. Department of Energy (DOE)-funded efforts, including Advanced Research Projects Agency–Energy (ARPA-E) Network Optimized Distributed Energy Systems (NODES) funding. This cutting-edge control technology aims to modernize distribution systems with large amounts of DER integration, which will help utilities solve issues brought by renewable integration and build resilient and renewable-based electric grids nationwide. Utilidata worked with NREL to investigate the commercialization opportunity of this RT-OPF-based distributed energy resource management system (DERMS). In this project, NREL performs the technology transfer of the RT-OPF to Utilidata to help them fully understand the RT-OPF solution, to identify potential engineering hurdles, and to assess the expected commercial value of various RT-OPF use cases and deployment. The technology transfer work includes two major tasks. First, NREL performs an in-depth knowledge transfer of the entire RT-OPF solution to Utilidata to help them gain an extensive and detailed understanding of the complete RT-OPF solution. In this task, NREL provides exhaustive information (e.g., documentation, code packages, laboratory and field trial data, performance results) while conducting in-depth training sessions to provide a thorough explanation of the entire solution. NREL hosts meetings to present different topics related to the RT-OPF solution, and question-and-answer sessions are included in each meeting to better explain the RT-OPF-related work. Second, the RT-OPF simulations are performed in a laboratory environment. The main objectives of this task are to walk through with Utilidata engineers how to set up a simulation of RT-OPF, identifying each RT-OPF code block/component in operation, learning how these components interact with each other, and eventually running RT-OPF simulations under various system conditions. This task helps Utilidata engineers understand performance limitations and constraints while also quantifying the commercial value of the RT-OPF for different use cases. Based on these two tasks, Utilidata engineers should be able to define and prioritize the next steps of RT-OPF implementation with an eye toward commercial success and scalability of the solution. The next steps are expected to be part of a new project following the conclusion of this project.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Reducing Operator Complexity of Galerkin Coarse-grid Operators with Machine Learning

Here, we propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in multigrid (MG) methods, addressing the well-known issue of increasing operator complexity. Guided by the MG theory on spectrally equivalent coarse-grid operators, we have developed novel machine learning algorithms that utilize neural networks combined with smooth test vectors from multigrid eigenvalue problems. The proposed method demonstrates promise in reducing the complexity of coarse-grid operators while maintaining overall MG convergence for solving parametric partial differential equation problems. Numerical experiments on anisotropic rotated Laplacian and linear elasticity problems are provided to showcase the performance and comparison with existing methods for computing non-Galerkin coarse-grid operators.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

GOOML (Geothermal Operational Optimization with Machine Learning) [SWR-23-01]

The Geothermal Operational Optimization with Machine Learning (GOOML) is a partnership between NREL and Upflow, NZ, awarded in response to the U.S. Department of Energy's Geothermal Technologies Office's Funding Opportunity Announcement (FOA) to expand the role of advanced analytics and automation in geothermal operations through machine learning. Partnering with industry (Contact Energy Limited ("Contact"), Ngati Tuwharetoa Geothermal Assets Limited ("NTGA"), Ormat Technologies Inc. ("Ormat") and Flow State Solutions Limited ("FSS"), GOOML was created to improve the operational efficiency of geothermal power plant steam fields through the analysis of historical operational data and the application of custom machine learning algorithms. NREL's contributions include machine learning, coding, and data management expertise as well as access to high-performance compute solutions. GOOML can increase geothermal operational efficiency through development of a digital system twin that can be utilized to provide optimal geothermal operating conditions for real-world geothermal fields. GOOML allows users to analyze field production histories in detail, develop models, and train machine learning algorithms to identify opportunities for increased geothermal efficiency, detect potential trouble, and allow predictive scenario modeling. Preliminary experiments have demonstrated a potential to increase total generation by as much as 12% through ML optimization of the utilization of existing steam field resources.

Buster, Grant↗
DOE OSTI2023

DeepGraphONet: A Deep Graph Operator Network to Learn and Zero-Shot Transfer the Dynamic Response of Networked Systems

This article develops a deep graph operator network (DeepGraphONet) framework that learns to approximate the dynamics of a complex system (e.g., the power grid or traffic) with an underlying subgraph structure. Here, we build our DeepGraphONet by fusing the ability of graph neural networks to exploit spatially correlated graph information and deep operator networks to approximate the solution operator of dynamical systems. The resulting DeepGraphONet can then predict the dynamics within a given short/medium-term time horizon by observing a finite history of the graph state information. Furthermore, we design our DeepGraphONet to be resolution independent. That is, we do not require the finite history to be collected at the exact/same resolution. In addition, to disseminate the results from a trained DeepGraphONet, we design a zero-shot learning strategy that enables using it on a different subgraph. Finally, empirical results on the transient stability prediction problem of power grids and traffic flow forecasting problem of a vehicular system illustrate the effectiveness of the proposed DeepGraphONet.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Machine Learning Derived Dynamic Operating Reserve Requirements in High-Renewable Power Systems

Accurately forecasting wind and solar power output poses challenges for deeply decarbonized electricity systems. Grid operators must commit resources to provide reserves to ensure reliable operations in the face of forecast errors, a process which can increase fuel consumption and emissions. We apply neural network-based machine learning to expand the usefulness of median point forecast data by creating probabilistic distributions of short-term uncertainty in demand, wind, and solar forecasts that adapt to prevailing grid conditions. Machine learning derived estimates of forecast errors compare favorably to estimates based on incumbent methods. Reserves derived from machine learning are usually smaller than values derived using incumbent methods, which enables fuel savings during most hours. Machine learning reserves are generally larger than incumbent reserves during times of higher forecast error, potentially improving system reliability. Performance is tested using multi-stage production simulation modeling of the California Independent System Operator (CAISO) system. Machine learning reserves provide production cost and greenhouse gas (GHG) emission reductions of approximately 0.3% relative to historical 2019 requirements. Savings in the 2030 timeframe are highly dependent on battery storage capacity. At lower levels of battery capacity, savings of 0.4% from machine learning reserves are shown. Significant quantities of battery storage are expected to be added to meet California's resource adequacy needs and GHG reduction targets. Addition of these batteries saturate reserve needs and results in minimal within-hour balancing costs in 2030.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Machine Learning Assisted Reservoir Operation Model for Long–Term Water Management Simulation

This study explores strategies for long-term reservoir simulations by combining generic rule-based reservoir management model (RMM) and machine learning (ML) models for two major multipurpose reservoirs — Allatoona Lake and Lake Sidney Lanier in the southeastern United States. First, a standalone RMM is developed to simulate daily release and storage during Water Year 1981–2015. Next, using Long-Short Term Memory (LSTM) as the ML technique, a standalone LSTM model is trained based on reservoir inflow and meteorological observations to simulate reservoir release and estimate reservoir storage through water balance calculation. Three hybrid modeling strategies are developed, one using RMM output as an additional LSTM input (H1), another using LSTM as the initial release estimate in RMM (H2), and the third combining the first two strategies (H3). The Nash–Sutcliffe efficiency (NSE) for release (NSE-r), storage (NSE-s), and their mean (NSE-avg) are used for model evaluation. Overall, H1 improves NSE-r to 0.65 and 0.54 for Allatoona and Lanier, respectively, compared to standalone RMM (0.44 and 0.21); however, its storage trajectory did not produce a physically feasible solution, similar to LSTM. H2 and especially H3 show that they can retain the best features from RMM and LSTM, with H3 NSE-avg being 0.695 and 0.55 for Allatoona and Lanier outperforming RMM (0.615 and 0.29). In conclusion, the findings suggest a robust simulation capacity for large-scale water management in future studies.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2022

Physics-informed regularization and structure preservation for learning stable reduced models from data with operator inference

Operator inference learns low-dimensional dynamical-system models with polynomial nonlinear terms from trajectories of high-dimensional physical systems (non-intrusive model reduction). Here, this work focuses on the large class of physical systems that can be well described by models with quadratic and cubic nonlinear terms and proposes a regularizer for operator inference that induces a stability bias onto learned models. The proposed regularizer is physics informed in the sense that it penalizes higher-order terms with large norms and so explicitly leverages the polynomial model form that is given by the underlying physics. This means that the proposed approach judiciously learns from data and physical insights combined, rather than from either data or physics alone. Additionally, a formulation of operator inference is proposed that enforces model constraints for preserving structure such as symmetry and definiteness in linear terms. Numerical results demonstrate that models learned with operator inference and the proposed regularizer and structure preservation are accurate and stable even in cases where using no regularization and Tikhonov regularization leads to models that are unstable.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Learning the solution operator of parametric partial differential equations with physics-informed DeepONets

Partial differential equations (PDEs) play a central role in the mathematical analysis and modeling of complex dynamic processes across all corners of science and engineering. Their solution often requires laborious analytical or computational tools, associated with a cost that is markedly amplified when different scenarios need to be investigated, for example, corresponding to different initial or boundary conditions, different inputs, etc. In this work, we introduce physics-informed DeepONets, a deep learning framework for learning the solution operator of arbitrary PDEs, even in the absence of any paired input-output training data. We illustrate the effectiveness of the proposed framework in rapidly predicting the solution of various types of parametric PDEs up to three orders of magnitude faster compared to conventional PDE solvers, setting a previously unexplored paradigm for modeling and simulation of nonlinear and nonequilibrium processes in science and engineering.

97 MATHEMATICS AND COMPUTING↗