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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 505 records · Page 28
All sourcesNASA NTRSDOE OSTI
DOE OSTI2017

Greening the Grid: Pathways to Integrate 175 Gigawatts of Renewable Energy into India's Electric Grid, Vol. I -- National Study

The use of renewable energy (RE) sources, primarily wind and solar generation, is poised to grow significantly within the Indian power system. The Government of India has established a target of 175 gigawatts (GW) of installed RE capacity by 2022, including 60 GW of wind and 100 GW of solar, up from 29 GW wind and 9 GW solar at the beginning of 2017. Thanks to advanced weather and power system modeling made for this project, the study team is able to explore operational impacts of meeting India's RE targets and identify actions that may be favorable for integration. Our primary tool is a detailed production cost model, which simulates optimal scheduling and dispatch of available generation in a future year (2022) by minimizing total production costs subject to physical, operational, and market constraints. Our team comprises a core group from the Power System Operation Corporation, Ltd. (POSOCO), which is the national grid operator (with representation from the National, Southern, and Western Regional Load Dispatch Centers) under Ministry of Power, National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory (LBNL), and a broader modeling team that includes Central Electricity Authority (CEA), POWERGRID (the central transmission utility, CTU), and State Load Dispatch Centers in Maharashtra, Gujarat, Tamil Nadu, Karnataka, Rajasthan, and Andhra Pradesh. Our model includes high-resolution wind and solar data (forecasts and actuals), unique properties for each generator, CEA/CTU's anticipated buildout of the power system, and enforced state-to-state transmission flows. Assuming the fulfillment of current efforts to provide better access to the physical flexibility of the power system, we find that power system balancing with 100 GW of solar and 60 GW of wind is achievable at 15-minute operational timescales with minimal RE curtailment. This RE capacity meets 22% of total projected 2022 electricity consumption in India with annual RE curtailment of 1.4%, in line with experiences in other countries with significant RE penetrations (Bird et al. 2016). Changes to operational practice can further reduce the cost of operating the power system and reduce RE curtailment. Coordinating scheduling and dispatch over a broader area is the largest driver to reduce costs, saving INR 6300 crore (USD $920 million) annually when optimized regionally. Lowering minimum operating levels of coal plants (from 70% to 40%) is the biggest driver to reduce RE curtailment - from 3.5% down to 0.76%. In fact, this operating property is more influential than faster thermal generation ramp rates in lowering the projected levels of curtailment. While this study does not answer every question relevant to planning for India's 2022 RE targets, it is an important step toward analyzing operational challenges and cost saving opportunities using state-of-the-art power system planning tools. Further analysis can build upon this basis to explore optimal renewable resource and intrastate transmission siting, system stability during contingencies, and the influence of total power system investment costs on customer tariffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Greening the Grid: Pathways to Integrate 175 Gigawatts of Renewable Energy into India’s Electric Grid, Vol. 1. National Study

The use of renewable energy (RE) sources, primarily wind and solar generation, is poised to grow significantly within the Indian power system. The Government of India has established a target of 175 gigawatts (GW) of installed RE capacity by 2022, including 60 GW of wind and 100 GW of solar, up from 29 GW wind and 9 GW solar at the beginning of 2017. Using advanced weather and power system modeling made for this project, the study team is able to explore operational impacts of meeting India’s RE targets and identify actions that may be favorable for integration. Our primary tool is a detailed production cost model, which simulates optimal scheduling and dispatch of available generation in a future year (2022) by minimizing total production costs subject to physical, operational, and market constraints. Our team comprises a core group from the Power System Operation Corporation, Ltd. (POSOCO), which is the national grid operator (with representation from the National, Southern, and Western Regional Load Dispatch Centers) under Ministry of Power, National Renewable Energy Laboratory (NREL), and Lawrence Berkeley National Laboratory (Berkeley Lab), and a broader modeling team that includes Central Electricity Authority (CEA), POWERGRID (the central transmission utility, CTU), and State Load Dispatch Centers in Maharashtra, Gujarat, Tamil Nadu, Karnataka, Rajasthan, and Andhra Pradesh. Our model includes high-resolution wind and solar data (forecasts and actuals), unique properties for each generator, CEA/CTU’s anticipated buildout of the power system, and enforced state-to-state transmission flows. Assuming the fulfillment of current efforts to provide better access to the physical flexibility of the power system, we find that power system balancing with 100 GW of solar and 60 GW of wind is achievable at 15-minute operational timescales with minimal RE curtailment. This RE capacity meets 22% of total projected 2022 electricity consumption in India with annual RE curtailment of 1.4%, in line with experiences in other countries with significant RE penetrations (Bird et al. 2016). Changes to operational practice can further reduce the cost of operating the power system and reduce RE curtailment. Coordinating scheduling and dispatch over a broader area is the largest driver to reduce costs, saving INR 6300 crore (USD 980 million) annually when optimized regionally. Lowering minimum operating levels of coal plants (from 70% to 40%) is the biggest driver to reduce RE curtailment—from 3.5% down to 0.76%. In fact, this operating property is more influential than faster thermal generation ramp rates in lowering the projected levels of curtailment. While this study does not answer every question relevant to planning for India’s 2022 RE targets, it is an important step toward analyzing operational challenges and cost saving opportunities using state-of-the-art power system planning tools. Further analysis can build upon this basis to explore optimal renewable resource and intrastate transmission siting, system stability during contingencies, and the influence of total power system investment costs on customer tariffs.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2020

Conservation Voltage Reduction (CVR) via Two-Timescale Control in Unbalanced Power Distribution Systems

Voltage control devices are employed in power distribution systems to reduce the power consumption by operating the system closer to the lower acceptable voltage limits; this technique is called conservation voltage reduction (CVR). The different modes of operation for system’s legacy devices (with binary control) and new devices (e.g. smart inverters with continuous control) coupled with variable photovoltaic (PV) generation results in voltage fluctuations which makes it challenging to achieve CVR objective. This paper presents a two-timescale control of feeder’s voltage control devices to achieve CVR that includes (1)a centralized controller operating in a slower time-scale to coordinate voltage control devices across the feeder and (2) local controllers operating in a faster timescale to mitigate voltage fluctuations due to PV variability. The centralized controller utilizes a three-phase optimal power flow model to obtain the decision variables for both legacy devices and smart inverters. The local controllers operate smart inverters to minimize voltage fluctuations and restore nodal voltages to their reference values by adjusting the reactive power support. The proposed approach is validated using the IEEE-123 bus (medium-size) and R3-12.47-2 (large-size) feeders. It is demonstrated that the proposed approach is effective in achieving the CVR objective for unbalanced distribution systems.

optimal control, distributed generation, fluctuati↗
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↗
DOE OSTI2021

Hidden transformations in entropy-stabilized oxides

We report entropy-stabilized oxides (ESO) display a reversible entropy-driven phase transformation that can be leveraged to produce a continuum of metastable phase states, allowing for property optimization and novel functionalities. X-ray absorption spectroscopy reveals that entropic stabilization extends to the electronic structure (valence state and cation coordination) in sintered (Co,Cu,Mg,Ni,Zn)O, manifesting as a tunable lattice distortion in the entropy-stabilized phase. Co, Cu, and Zn ions reversibly transform from six-fold to four-fold coordinated structures and from low to high valence states due to the competition between electronic structures that are equilibrium and enthalpy-driven or metastable and entropy-driven. The segregation of a Cu-rich tenorite phase and a Co-rich spinel phase influences the electronic structure evolution. ESOs can adjust their electronic structures through heat treatment, providing a powerful tool for developing functional properties. These results indicate that the definition of entropy stabilization should include entropy-stabilized electronic structures, providing motivation to reassess previously studied HEO materials.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

X-ray Scattering and Coarse-Grained Simulations for Clustering and Interactions of Monoclonal Antibodies at High Concentrations

Attractive protein-protein interactions (PPI) in concentrated monoclonal antibody (mAb) solutions may lead to reversible oligomers (clusters) that impact colloidal stability and viscosity. Herein, the PPI are tuned for two mAbs via the addition of arginine (Arg), NaCl, or ZnSO 4 as characterized by the structure factor ( S eff (q)) with small angle x-ray scattering (SAXS). The SAXS data are fit with molecular dynamics simulations by placing a physically relevant short-ranged attractive interaction on selected beads in coarse-grained 12 bead models of the mAb shape. The optimized 12-bead models are then used to differentiate key microstructural properties, including center of mass radial distribution functions ( g COM (r)), coordination numbers and cluster size distributions (CSD). The addition of co-solutes results in more attractive Seff(q) relative to the no co-solute control for all systems tested, with the most attractive systems showing an upturn at low q . Only the All1 model with an attractive site in each Fab and Fc region (possessing Fab-Fab, Fab-Fc and Fc-Fc interactions) can reproduce this upturn, and the corresponding CSDs show the presence of larger clusters compared to the control. In general, for models with similar net attractions, i.e., second osmotic virial coefficients, the size of the clusters increases as the attraction is concentrated on a smaller number of evenly distributed beads. Here, the cluster size distributions from simulations are used to improve the understanding and prediction of experimental viscosities. The ability to discriminate between models with bead interactions at particular Fab and Fc bead sites from SAXS simulations, and to provide real space properties (CSD and g COM (r)), will be of interest in engineering protein sequence and formulating protein solutions for weak PPI to minimize aggregation and viscosities.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2018

Assessing Substitution Effects on Surface Chemistry by in Situ Ambient Pressure X-ray Photoelectron Spectroscopy on Perovskite Thin Films, BaCe x Zr 0.9– x Y 0.1 O 2.95 ( x = 0; 0.2; 0.9)

Performance of proton-solid oxide fuel cells (H+-SOFC) is governed by ion transport through solid/gas interfaces. Major breakthroughs are then intrinsically linked to a detailed understanding of how parameters tailoring bulk proton conductivity affect surface chemistry in situ, at an early stage. In this work, we studied proton and oxygen transport at the interface between H+-SOFC electrolyte BaCexZr0.9–xY0.1O2.95 (x = 0; 0.2; 0.9) thin films and the gas (100 mTorr of H2O and O2) by using synchrotron-based ambient pressure X-ray photoelectron spectroscopy at operating temperature (>400 °C). We developed highly textured BaCexZr0.9–xY0.1O2.95 epitaxial thin films, which exhibit high level of in-plane proton conductivity, that is, up to 0.08 S cm–1 at 500 °C for x = 0.9. Upon applying 100 mTorr water partial pressure above 300 °C, major changes are observed only in the O 1s and Y 3d core level spectra, with a clear Zr/Ce ratio dependency. OH– formation is favored by Ce content while initiated near Y. Hydration is also associated with surface secondary phase growth comprising oxygen-under-coordinated yttrium and/or yttrium hydroxide. With BaCe0.2Zr0.7Y0.1O2.95, high levels of ionic conductivities and chemical stability are obtained as a result of the optimized surface reaction kinetics, with low activation energy barrier for proton transport while restraining formation of OH–/SO42– adsorb species.

bio-inspired, energy storage (including batteries ↗
DOE OSTI2020

New interaction potentials for borate glasses with mixed network formers

Here, we adapt and apply a recently developed optimization scheme used to obtain effective potentials for aluminosilicate glasses to include the network former boron into the interaction parameter set. As input data for the optimization, we used the radial distribution functions of the liquid at high temperature generated by ab initio molecular dynamics simulations, and density, coordination, and elastic modulus of glass at room temperature from experiments. The new interaction potentials are shown to reliably reproduce the structure, coordination, and mechanical properties over a wide range of compositions for binary alkali borates. Furthermore, the transferability of these new interaction parameters allows mixing to reliably reproduce the properties of various boroaluminate and borosilicate glasses.

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

Reinforcement Learning for Volt- Var Control: A Novel Two-stage Progressive Training Strategy

This paper develops a reinforcement learning (RL) approach to solve a cooperative, multi-agent Volt-Var Control (VVC) problem for high solar penetration distribution systems. The ingenuity of our RL method lies in a novel two-stage progressive training strategy that can effectively improve training speed and convergence of the machine learning algorithm. In Stage 1 (individual training), while holding all the other agents inactive, we separately train each agent to obtain its own optimal VVC actions in the action space: fconsume, generate, do-nothingg. In Stage 2 (cooperative training), all agents are trained again coordinatively to share VVC responsibility. Rewards and costs in our RL scheme include (i) a system-level reward (for taking an action), (ii) an agent-level reward (for doing-nothing), and (iii) an agent-level action cost function. This new framework allows rewards to be dynamically allocated to each agent based on their contribution while accounting for the trade-off between control effectiveness and action cost. The proposed methodology is tested and validated in a modified IEEE 123-bus system using realistic PV and load profiles. Simulation results confirm that the proposed approach is robust and computationally efficient; and it achieves desirable volt-var control performance under a wide range of operation conditions.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2022

Quantum Distributed Unit Commitment: An Application in Microgrids

The dawn of quantum computing brings on a revolution in the way combinatorially complex power system problems such as Unit Commitment are solved. The Unit Commitment problem complexity is expected to increase in the future because of the trend toward the increase of penetration of intermittent renewables. Even though quantum computing has proven effective for solving a host of problems, its applications for power systems’ problems have been rather limited. Here, in this paper, a quantum unit commitment is innovatively formulated and the quantum version of the decomposition and coordination alternate direction method of multipliers (ADMM) is established. The above is achieved by devising quantum algorithms and by exploiting the superposition and entanglement of quantum bits (qubits) for solving subproblems, which are then coordinated through ADMM to obtain feasible solutions. The main contributions of this paper include: 1) the innovative development of a quantum model for Unit Commitment; 2) development of decomposition and coordination-supported framework which paves the way for the utilization of limited quantum resources to potentially solve the large-scale discrete optimization problems; 3) devising the novel quantum distributed unit commitment (QDUC) to solve the problem in a larger scale than currently available quantum computers are capable of solving. The QDUC results are compared with those from its classical counterpart, which validate the efficacy of quantum computing.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Assessment of CReST-VCT Deployment in Real-Time Environments: Communication System Examination

Incorporation of decentralized generation or distributed energy resources (DERs) such as solar and wind, is transforming the electricity grid. These resources have the potential to provide greater overall value when they are grid connected and coordinated between transmission and distribution systems. The Coordinated Real-Time Sub-Transmission Volt-VAr Control Tool (CReST-VCT) has been proposed to provide co-optimization between transmission and distribution systems maximizing DER utilization while maintaining overall grid stability. In this paper, we examine the communication systems that are necessary to support the integration of the CReST-VCT optimization mechanism in a real-time operational environment. The required communication interfaces will be identified based on the operation model of CReST-VCT. The characteristics of the communication systems at these interfaces will be described to establish the context within which CReST-VCT will operate. The related protocols and cybersecurity domain will be reviewed. Potential issues and concerns will then be identified to guide subsequent integration efforts.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2017

Resilience Design Patterns: A Structured Approach to Resilience at Extreme Scale

Reliability is a serious concern for future extreme-scale high-performance computing (HPC) systems. Projections based on the current generation of HPC systems and technology roadmaps suggest the prevalence of very high fault rates in future systems. While the HPC community has developed various resilience solutions, application-level techniques as well as system-based solutions, the solution space remains fragmented. There are no formal methods and metrics to integrate the various HPC resilience techniques into composite solutions, nor are there methods to holistically evaluate the adequacy and efficacy of such solutions in terms of their protection coverage, and their performance \& power efficiency characteristics. Additionally, few of the current approaches are portable to newer architectures and software environments that will be deployed on future systems. In this paper, we develop a structured approach to the design, evaluation and optimization of HPC resilience using the concept of design patterns. A design pattern is a general repeatable solution to a commonly occurring problem. We identify the problems caused by various types of faults, errors and failures in HPC systems and the techniques used to deal with these events. Each well-known solution that addresses a specific HPC resilience challenge is described in the form of a pattern. We develop a complete catalog of such resilience design patterns, which may be used by system architects, system software and tools developers, application programmers, as well as users and operators as essential building blocks when designing and deploying resilience solutions. We also develop a design framework that enhances a designer's understanding the opportunities for integrating multiple patterns across layers of the system stack and the important constraints during implementation of the individual patterns. It is also useful for defining mechanisms and interfaces to coordinate flexible fault management across hardware and software components. The resilience patterns and the design framework also enable exploration and evaluation of design alternatives and support optimization of the cost-benefit trade-offs among performance, protection coverage, and power consumption of resilience solutions. Here, the overall goal of this work is to establish a systematic methodology for the design and evaluation of resilience technologies in extreme-scale HPC systems that keep scientific applications running to a correct solution in a timely and cost-efficient manner despite frequent faults, errors, and failures of various types.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Enabling DER Participation in Frequency Regulation Markets

Distributed energy resources (DERs) are playing an increasing role in ancillary services for the bulk grid, particularly in frequency regulation. In this article, we propose a framework for collections of DERs, combined to form microgrids and controlled by aggregators, to participate in frequency regulation markets. Our approach covers both the identification of bids for the market clearing stage and the mechanisms for the real-time allocation of the regulation signal. The proposed framework is hierarchical, consisting of a top layer and a bottom layer. The top layer consists of the aggregators communicating in a distributed fashion to optimally disaggregate the regulation signal requested by the system operator. The bottom layer consists of the DERs inside each microgrid whose power levels are adjusted so that the tie line power matches the output of the corresponding aggregator in the top layer. The coordination at the top layer requires the knowledge of cost functions, ramp rates, and capacity bounds of the aggregators. We develop meaningful abstractions for these quantities respecting the power flow constraints and taking into account the load uncertainties and propose a provably correct distributed algorithm for optimal disaggregation of regulation signals among the microgrids.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2019

Fundamental Insights into the Reactivity and Utilization of Open Metal Sites in Cu(I)-MFU-4 l

Metal organic frameworks (MOFs) having open metal sites have the potential to approach the activity of homogeneous organometallic complexes, thus combining the advantages of homogeneous and heterogeneous catalysis. We pre-sent a fundamental study of the effectiveness of incorporating open metal sites into MOFs. We have modeled the binding of a series of adsorbates in a Cu(I) substituted MOF, Cu(I)-MFU-4l using density functional theory, and compared the activity of the Cu(I) sites in Cu(I)-MFU-4l with two different Cu(I) scorpionate complexes. The computational results confirm the single-site nature of the Cu(I) active site. This is further supported by complementary experiments to measure the chemisorption uptake inside our synthesized samples in order to estimate the amount of active Cu sites present. We observed a level of chemisorption that is roughly half the theoretical maximum, which implies that only half of the Cu atoms incorporated into MFU-4l via metal-ion exchange are able to act as binding sites. We speculate that the inactive Cu atoms are coordinately saturated Cu(II) sites. Furthermore, our work suggests that the performance of Cu(I)-MFU-4l could be significantly increased by optimizing the metal exchange and activation processes.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2019

Dual-nitrogen-source engineered Fe–N x moieties as a booster for oxygen electroreduction

Metal–air batteries, particularly Zn–air batteries, have triggered considerable enthusiasm of communities due to their high theoretical power density. Developing highly active, cost-effective and alternative non-precious metal catalysts for the oxygen reduction reaction (ORR) is pivotal for popularizing zinc–air batteries. The rational design and synthesis of this type of catalyst are therefore critical, but it is still challenging to control the well-defined active sites as expected. In this paper, we report a dual-nitrogen-source mediated route for synergistically controlling the formation of active Fe–N x moieties that are embedded in the carbon matrix. The facile control of coordination structures of precursors by this dual-nitrogen-source approach is revealed to play a key role in this report. Impressively, the optimized dual-nitrogen-source derived catalyst (i.e. Fe–N–C-800) exhibits prominently enhanced ORR activity with a half-wave potential of 0.883 V in alkaline electrolyte, higher by 32 mV and 72 mV than those derived from individual nitrogen sources, which is also further evaluated in primary Zn–air batteries. The enhanced ORR activity of Fe–N–C-800 is attributed to the rich Fe–N x active sites derived from the dual-nitrogen-source approach.

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

Probing exciton diffusion dynamics in photosynthetic supercomplexes via exciton–exciton annihilation

Photosynthesis converts solar energy into chemical energy through coordinated energy transfer between light-harvesting complexes and reaction centers (RCs). Understanding exciton motion, particularly the exciton diffusion length, is essential for optimizing energy efficiency in photosystems. In this work, we combine intensity-cycling transient absorption spectroscopy with kinetic Monte Carlo (kMC) simulation to investigate exciton motion in the C2S2 photosystem II supercomplex of spinach. Using exciton–exciton annihilation, revealed in the fifth-order response, we experimentally estimate an exciton diffusion length of 10.9 nm based on a 3D normal diffusion model, suggesting the ability of excitons to traverse the supercomplex. However, kMC simulations reveal that exciton motion is sub-diffusive because of spatial constraints and the strong RC traps. An anomalous diffusion model analysis of the experimental data yields a diffusion length of 9.7 nm, while the simulated diffusion length is 7.4 nm. The variable exciton residence time across subunits, partly influenced by their connectivity to the trap, indicates inhomogeneous annihilation probability and suggests how plants balance efficient light harvesting with photoprotection. We also explore the influence of specific assumptions in the annihilation simulation, which are challenging to access in more complex environments, such as the thylakoid membrane. Our study provides a framework for studying exciton dynamics using exciton–exciton annihilation, which can be extended to understand the light-harvesting efficiencies of larger, more complex photosynthetic assemblies.

Zhang, Kunyan (ORCID:000000026830409X)↗
DOE OSTI2022

Fed-DeepONet: Stochastic Gradient-Based Federated Training of Deep Operator Networks

The Deep Operator Network (DeepONet) framework is a different class of neural network architecture that one trains to learn nonlinear operators, i.e., mappings between infinite-dimensional spaces. Traditionally, DeepONets are trained using a centralized strategy that requires transferring the training data to a centralized location. Such a strategy, however, limits our ability to secure data privacy or use high-performance distributed/parallel computing platforms. To alleviate such limitations, in this paper, we study the federated training of DeepONets for the first time. That is, we develop a framework, which we refer to as Fed-DeepONet, that allows multiple clients to train DeepONets collaboratively under the coordination of a centralized server. To achieve Fed-DeepONets, we propose an efficient stochastic gradient-based algorithm that enables the distributed optimization of the DeepONet parameters by averaging first-order estimates of the DeepONet loss gradient. Then, to accelerate the training convergence of Fed-DeepONets, we propose a moment-enhanced (i.e., adaptive) stochastic gradient-based strategy. Finally, we verify the performance of Fed-DeepONet by learning, for different configurations of the number of clients and fractions of available clients, (i) the solution operator of a gravity pendulum and (ii) the dynamic response of a parametric library of pendulums.

Moya, Christian↗