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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Peer-to-peer communication control for resilient operations of networked cyberphysical systems

This report includes two main accomplishments of the peer-to-peer communication control for resilient operation of networked microgrids project in FY24, which include a scheme for cyberattack-aware coordination of networked microgrids for supporting voltages of bulk power systems and a scheme for price signal-based operations of EV-rich networked microgrids with mixed ownership. First, the cyberattack-aware scheme enables networked microgrids to distributedly determine the amount of reactive power injection to support the voltage of bulk power system (BPS) in a fair manner. In this scheme, a risk-informed algorithm is presented to generate the peer-to- peer (P2P) communication graph with minimal risk of attack on communication links. To deal with cyberattacks on MG controllers, the resilient consensus algorithm (CA) is utilized for MG controllers to robustly estimate the total reactive power headroom, from which the MGs can accurately provide the needed amount of reactive power injection for supporting the voltage of BPS. The CA implementation and performance within the P2P communication framework are demonstrated on the IEEE 39-bus system with 6 microgrids contained in the distribution feeder under different cyberattack scenarios. Second, the price-based scheme enables the usage of the real-time price signal for the operations of electric vehicle (EV)-rich networked-microgrids with mixed ownership, in which not all the microgrids can communicate with the distribution system operator (DSO). In this scheme, a max consensus is introduced to enable the real-time price signal to be propagated from the DSO to all the microgrids, from which each microgrid controller will manage the DERs to balance the load demand and the power injection from the EV charging stations within its microgrid. Numerical results over one day with 288 slots of 5-minute intervals on the modified 123-node test feeder including 3 microgrids with high penetration of EV are presented to evaluate how the price signal affects the operations of networked microgrids under different charging strategies of the EV charging stations. The result indicates that our proposed EVCS (dis)charging strategy, which leverages the flexibility of EVs to support the grid through discharging during peak demand, proves to be a cost-effective solution that reduces operational costs while improving the social welfare of EV charging.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Molten Salt Loop Operational Experience and Test Campaigns in FY24

The Facility to Alleviate Salt Technology Risks (FASTR) at the US Department of Energy (DOE) Oak Ridge National Laboratory (ORNL) was developed to demonstrate technology for high-temperature chloride salt systems (Figure 1). FASTR is primarily constructed using alloy C-276 and is designed to operate at temperatures of up to 725°C. The facility is loaded with 250 kg of NaCl-KCl-MgCl 2 salt. This salt provides a relevant test environment for de-risking technology while avoiding the costs and hazards associated with beryllium-based or uranium-bearing salts. The facility’s major components include a centrifugal pump for salt circulation, an air-based heat exchanger to reject heat, a suite of instrumentation, and trace heating to prevent salt freezing. The salt was purified in 2020 and 2022, and the pumped loop first operated in December 2022. FASTR is a unique US capability for high-temperature molten halide salt testing. FASTR’s scale, co located purification system, and relatively large power (465 kW) differentiates it from other testing systems. Furthermore, access to the DOE-supported facility and efficient communication of results— which are generally disseminated publicly—distinguish FASTR as being broadly significant throughout the molten salt reactor community. FASTR is similar to ORNL’s Liquid Salt Test Loop (LSTL), although FASTR contains chloride-based salt instead of the fluoride-based salt (LiF-NaF-KF) found in LSTL. Furthermore, FASTR is approximately 2× larger than LSTL in terms of pipe size and length, power, salt volume, flow rate, and number of thermocouples. The LSTL first operated in 2016. At the end of FY23, there was a suspected gas leak in the LSTL that halted operation. At the start of FY24, a leak in the LSTL pump’s tank gas space was confirmed. Because the gas-space leak prevented operation of LSTL, FY24 efforts were focused on operation of FASTR. This report summarizes the progress made during FY24 in support of the DOE Office of Nuclear Energy (DOE-NE) work package, AT-24OR070202 Salt Loop and Capability for Testing Sensors and Off Gas Components.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗
DOE OSTI2025

Operation of Argonne's Liquid Salt-Liquid Metal Separation Testbed for U/TRU Product Processing

Argonne National Laboratory has constructed a liquid salt-liquid metal separation testbed for use in the development and advancement of cathode processing of U/TRU co‑deposits generated by pyroprocessing of used nuclear fuel. The U/TRU product recovered from the electrorefiner contains adhered and entrained salt that must be removed prior to consolidation of the U/TRU alloy for use in advanced reactor fuel fabrication. The bottom pour operation utilizes the low melting points of U/TRU co‑deposits and higher densities of molten metals compared to molten salts to separate and consolidate the U/TRU product. Argonne’s testbed is designed to support the development and optimization of bottom-pouring configurations for batch and semi-continuous operations, integration of process monitoring and control technologies, and determination of operational requirements for implementing in an industrial setting. Scoping tests were performed to demonstrate operational aspects of the testbed, including operation using single-pour spout and dual-pour spout configurations, effectiveness of salt containment and extent of salt vaporization, and the use of sensor probes to detect the location of the interface between the metal and salt phases during pouring. Recommendations for process optimization testing for further development of bottom pour processing to separate U/TRU alloys from adhered salt were made based on the results of scoping tests. Completing the recommended activities will increase the technical readiness level (TRL) of the liquid salt-liquid metal separation operation and consolidation of U/TRU alloys to support industrialization of pyroprocessing.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2025

Characterization of Inlet Guide Vane Performance for Discharge Compressor Operation near the Dome of an sCO 2 Pumped Heat Energy Storage

Southwest Research Institute® (SwRI®) developed and tested a Variable Inlet Guide Vane (IGV herein) assembly on an integrally-geared sCO 2 compressor (IGC) to demonstrate compressor operation at both the compressor design point and near the dome and to define the operating limits of the compressor by monitoring for two-phase flow, flow turbulence from the IGVs, and compressor choke and surge as the CO 2 inlet temperature is varied. Performance testing was conducted on an existing integrally-geared, two-stage main compressor designed for near-critical-point operation with CO 2 . This testing campaign validated the IGV design and operation, as well as improved the understanding and confidence in operating compressors and predicting performance characteristics near the critical point where fluid properties change rapidly with temperature. In addition to improving the robust operating limits of an sCO 2 compressor, the development of an IGV for the IGC system improved off-design compressor efficiency by 12%.

25 ENERGY STORAGE↗
DOE OSTI2024

U.S. Department of Energy-National Lab Equity Summit: Grid Planning and Operations (Workshop Report)

This report summarizes the U.S. DOE and national laboratories equity summit that was held on February 5, 2024, and focused on grid planning and operations. The objectives of the summit were to connect DOE and lab researchers working on grid-related equity issues, share information on current and planned grid-related equity projects and initiatives, and inspire and educate participants by hearing from our panelists about solutions and challenges to integrating equity in grid planning and operations. The summit included two panels of industry leaders. The first was a state and community perspectives panel that included representatives from a state public utility commission (Oregon Public Utility Commission), a state energy office (Washington Department of Commerce), a state utility consumer advocate (Connecticut Consumer Counsel), and industry consultants (Elevated Engagement and ArkSpring Consulting). Panelists shared successes they have seen, critical challenges related to equity and grid planning and operations, and other considerations. The second panel addressed utility perspectives and included representatives from two utilities (Commonwealth Edison and Tacoma Power), the National Rural Electric Cooperative (NRECA), and a former utility employee and legal consultant. Panelists discussed the role of the utility concerning equity, the most significant technical and data modeling needs and opportunities, and the role the labs could help advance equity in grid planning and operations. There was also a session on partner organization presentations. Argonne National Laboratory made a short presentation on the Grid Modernization Laboratory Consortium (GMLC) project they are leading on equity-informed power system planning. NARUC, NASEO, and the Clean Energy States Alliance, as partners of the GMLC project also shared updates on relevant activities and resources. During the summit, there were two rounds of lightning presentations by national labs and DOE highlighting research that addresses equity and grid planning and operations (Tables 5 and 6 and slides in the Appendix). The goal of the lightning rounds was to share information between participants to encourage collaboration and leverage ongoing research at labs and DOE. The summit included two interactive exercises where summit participants shared their perspectives on relevant equity projects and initiatives (Table 2), key challenges regarding equity and grid planning and operations (Table 3), and promising innovations or progress (Table 4). At the end of the session, participants were asked to share essential insights from the event (Table 7) and an action they plan to take as a result of the event. Participants agreed that the event was useful in helping them share and learn from each other. The project team plans to use the information from the summit as a starting point to help inform future research and technical assistance. In 2026, another Equity Summit will be held (virtually or in person) as part of the same project to help raise awareness and disseminate research and resources completed during the project's duration.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2025

Block-Structured Operator Inference for Coupled Multiphysics Model Reduction

This work presents a block-structured formulation of Operator Inference as a way to learn structured reduced-order models for multiphysics systems. The approach specifies the governing equation structure for each physics component and the structure of the coupling terms. Once the multiphysics structure is specified, the reduced-order model is learned from snapshot data following the nonintrusive Operator Inference methodology. In addition to preserving physical system structure, which in turn permits preservation of system properties such as stability and second-order structure, the block-structured approach has the advantages of reducing the overall dimensionality of the learning problem and admitting tailored regularization for each physics component. The numerical advantages of the block-structured formulation over a monolithic Operator Inference formulation are demonstrated for aeroelastic analysis, which couples aerodynamic and structural models. For the benchmark test case of the AGARD 445.6 wing, block-structured Operator Inference provides an average 20% online prediction speedup over monolithic Operator Inference across subsonic and supersonic flow conditions in both the stable and fluttering parameter regimes while preserving the accuracy achieved with monolithic Operator Inference.

42 ENGINEERING↗
DOE OSTI2022

Improving Microalgal Biomass Productivity Using Weather-Forecast-Informed Operations

The operation of microalgal cultivation systems, such as culture dilution associated with harvests, affects biomass productivity. However, the constantly changing incident light and ambient temperature in the outdoor environment make it difficult to determine the operational parameters that result in optimal biomass growth. To address this problem, we present a pond operation optimization tool that predicts biomass growth based on future weather conditions to identify the optimal dilution rate that maximizes biomass productivity. The concept was tested by comparing the biomass productivities of three dilution scenarios: standard batch cultivation (no dilution), fixed-rate dilution (harvest 60% of the culture every three days), and weather-forecast-informed dilution. In the weather-forecast-informed case, the culture was diluted daily, and the dilution ratio was optimized by the operation optimization tool according to the future 24 h weather condition. The results show that the weather-forecast-informed dilution improved the biomass productivity by 47% over the standard batch cultivation and 20% over the fixed-rate dilution case. These results demonstrate that the pond operation optimization tool could help pond operators to make decisions that maximize biomass growth in the field under ever-changing weather conditions.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Characterizing the performance of a POPS miniaturized optical particle counter when operated on a quadcopter drone

We first validate the performance of the Portable Optical Particle Spectrometer (POPS), a small light-weight and high sensitivity optical particle counter, against a reference scanning mobility particle sizer (SMPS) for a month-long deployment in an environment dominated by biomass burning aerosols. Subsequently, we examine any biases introduced by operating the POPS on a quadcopter drone, a DJI Matrice 200 V2. We report the root mean square difference (RMSD) and mean absolute difference (MAD) in particle number concentrations (PNCs) when mounted on the UAV and operating on the ground and when hovering at 10 m. When wind speeds are low (less than 2.6 m s –1 ), we find only modest differences in the RMSDs and MADs of 5 % and 3 % when operating at 10 m altitude. When wind speeds are between 2.6 and 7.7 m s –1 the RMSDs and MADs increase to 26.2 % and 19.1 %, respectively, when operating at 10m altitude. No statistical difference in PNCs was detected when operating on the UAV in either ascent or descent. We also find size distributions of aerosols in the accumulation mode (defined by diameter, d, where 0.1 ≤ d ≤ 1 µm) are relatively consistent between measurements at the surface and measurements at 10 m altitude, while differences in the coarse mode (here defined by d > 1 µm) are universally larger. Our results suggest that the impact of the UAV rotors on the POPS PNCs are small at low wind speeds, but when operating under a higher wind speed of up to 7.6 m s –1 , larger discrepancies occur. In addition, it appears that the POPS measures sub-micron aerosol particles more accurately than super-micron aerosol particles when airborne on the UAV. These measurements lay the foundations for determining the magnitude of potential errors that might be introduced into measured aerosol particle size distributions and concentrations owing to the turbulence created by the rotors on the UAV.

47 OTHER INSTRUMENTATION↗
DOE OSTI2021

Coordination and control – limits in standard representations of multi-reservoir operations in hydrological modeling

Abstract. Major multi-reservoir cascades represent a primary mechanism for dealing with hydrologic variability and extremes within institutionally complex river basins worldwide. These coordinated management processes fundamentally reshape water balance dynamics. Yet, multi-reservoir coordination processes have been largely ignored in the increasingly sophisticated representations of reservoir operations within large-scale hydrological models. The aim of this paper is twofold, namely (i) to provide evidence that the common modeling practice of parameterizing each reservoir in a cascade independently from the others is a significant approximation and (ii) to demonstrate potential unintended consequences of this independence approximation when simulating the dynamics of hydrological extremes in complex reservoir cascades. We explore these questions using the Water Balance Model, which features detailed representations of the human infrastructure coupled to the natural processes that shape water balance dynamics. It is applied to the Upper Snake River basin in the western US and its heavily regulated multi-reservoir cascade. We employ a time-varying sensitivity analysis that utilizes the method of Morris factor screening to explicitly track how the dominant release rule parameters evolve both along the cascade and in time according to seasonal high- and low-flow events. This enables us to address aim (i) by demonstrating how the progressive and cumulative dominance of upstream releases significantly dampens the ability of downstream reservoir rules' parameters to influence flow conditions. We address aim (ii) by comparing simulation results with observed reservoir operations during critical low-flow and high-flow events in the basin. Our time-varying parameter sensitivity analysis with the method of Morris clarifies how independent single-reservoir parameterizations and their tacit assumption of independence leads to reservoir release behaviors that generate artificial water shortages and flooding, whereas the observed coordinated cascade operations avoided these outcomes for the same events. To further explore the role of (non-)coordination in the large deviations from the observed operations, we use an offline multi-reservoir water balance model in which adding basic coordination mechanisms drawn from the observed emergency operations is sufficient to correct the deficiencies of the independently parameterized reservoir rules from the hydrological model. These results demonstrate the importance of understanding the state–space context in which reservoir releases occur and where operational coordination plays a crucial role in avoiding or mitigating water-related extremes. Understanding how major infrastructure is coordinated and controlled in major river basins is essential for properly assessing future flood and drought hazards in a changing world.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2024

Experimental Operation of a Prototype 750C Advanced Chloride Molten Salt Bellows Valve

To achieve DOE 2030 SunShot targets that reduce the cost of liquid-based solar by an additional 40% to 70% beyond 2018 costs, a more reliable, highly manufacturable flow valve, capable of achieving operational temperatures of >700°C is required [1]. This paper investigates the development of an innovative high-temperature chloride molten salt valve, with operation up to 750°C. This valve is intended to be employed within Gen 3 CSP liquid-based thermal energy storage (TES) systems as well as Gen 4 modular salt reactor (MSR) technologies. This work details the general design and flow testing of a bellows-seal flow control valve (FCV). This design includes an integrated closed-loop thermal control system to ensure robust design for freeze-thaw cycles. The self-contained thermal management STM system, is unique in the salt valve industry since it is an integrated solution to provide a consistent, repeatable alternative to typical heat tracing. Additionally, the design includes the employment of a novel heat pipe valve stem to facilitate enhanced passive thermal management into the valve assembly. This valve stem heat pipe is designed to facilitate natural circulation within the bonnet to ensure robust operation, during both nominal and transient thermal operation. The valve body and trim will be designed using SS316H, consistent with Flowserve Corporation’s existing product base and is code qualified but will utilize clad material for materials corrosion, manufacturing cost reduction and compatibility to ensure design flexibility. A test campaign was performed in this investigation utilizing a novel 750°C ternary chloride (20%NaCl/40%MgCl2/40%KCl by mol. wt. %) molten salt flow loop. A discussion about the design and installation of the valves within this test bed is provided for this investigation. Valve test results from this study assessed Cv curves as well as multiple actuator cycles, under varying thermodynamic and operational mode conditions, which would be characteristic within a commercial molten salt facility. The results indicate nominal operation for the baseline design, though improved performance and reliability is expected with the full designed FCV.

Armijo, Kenneth (ORCID:0000000346832147)↗
DOE OSTI2022

Operator Insights and Usability Evaluation of Machine Learning Assistance for Power Grid Contingency Analysis

Introducing machine learning (ML) assistance into any established process comes with adoption barriers, including entrenched procedures, technological and human readiness levels, human-machine trust, and work culture resistance to change. These barriers are even greater in critical operations such as operating a national or regional power grid, in which both regulatory frameworks and the importance of maintaining reliability levels causes additional resistance to the adoption of new computational support. Developers of future systems and job aides must consider not only technical aspects, but also whether new systems are usable by power system operators. This work presents the methodology and results of a study to evaluate the usability and readiness of a prototype recommender system for power grid contingency analysis. We explore operator cognitive load and evaluate operator performance when solving a collection of scenarios both with and without recommender assistance. We also examine operator trust in the system. We report insights gained on the readiness of the system using a collection of evaluation techniques.

Human-Machine Teaming, Power Systems, usability ev↗
DOE OSTI2023

ICRH operations and experiments during the JET-ILW tritium and DTE2 campaigns

2021 has culminated with the completion of the JET-ILW DTE2 experimental campaign. This contribution summarizes Ion Cyclotron Resonance Heating (ICRH) operations from system and physics point of view. Improvements to the (ICRH) system, to operation procedures and to real time RF power control were implemented to address specific constraints from tritium and deuterium-tritium operations and increase the system reliability and power availability during D-T pulses. ICRH was operated without the ITER-Like Antenna (ILA) because water leaked from an in-vessel capacitor into the vessel on day-2 of the D-T campaign. Three weeks were required to identify and isolate the leak and resume plasma operations. Dedicated RF-Plasma Wall Interaction (PWI) experiments were conducted; tritium plasmas exhibit a higher level of Be sputtering on the outer wall and impurity content when compared to deuterium or hydrogen plasmas. The JET-DTE2 campaigns provided the opportunity to characterize ICRH schemes foreseen for the ITER operation, in the ITER like wall environment in ELMy H-mode scenarios aiming at maximizing fusion performance. The second harmonic tritium resonance heating and to a lesser extent minority 3He heating (ITER D-T ICRH reference schemes) lead to improved ion temperature and fusion performance when compared to hydrogen minority ICRH. However, these discharges suffered from a lack of stationarity and gradual impurity accumulation potentially because of a deficit of ICRH power when using JET antennas at lower frequencies. Fundamental deuterium ICRH was used in tritium-rich plasmas and with deuterium Neutral Beam Heating; this ICRH scheme proved to be very efficient boosting ion temperature and fusion performance in these plasmas.

Klepper, C. Christopher↗
DOE OSTI2023

Machine Learning in Power System Operations: Training Data

Reliability and stability of the electric grid today has depended upon operations of the grid which include the protective relay. Today, the electricity sector faces new challenges with the shift of generation resource characteristics away from the traditional “big iron” generation to inverter-based resources (IBR) which shift the physics and assumption used in grid operation and protection. These changing conditions represent new challenges for protective relays (identification of faults) and increased challenges for protection engineers (correct settings and configuration, reduction of mis-operations), both issues recognized in research and industry. Finding new approaches to reduce mis-operations in relaying and new approaches to fault identification is critical to grid operations. Using today’s modern technology of embedded systems, edge computing, machine learning (ML), and communications we can help address challenges and augment and improve on existing power system operations methodologies.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

State Machine Operation of Complex Systems

Operation of complex systems which depend on one or more other systems with many process variables often operate in more than one state. For each state there may be a variety of parameters of interest, and for each of these, one may require different alarm limits, different archiving needs, and have different critical parameters. Relying on operators to reliably change 10s-1000s of parameters for each system for each state is unreasonable.Not changing these parameters results in alarms being ignored or disabled, critical changes missed, and/or possible data archiving problems.To reliably manage the operation of complex systems, such as cryomodules (CMs), Fermilab is implementing state machines for each CM and an over-arching state machine for the PIP-II superconducting linac (SCL). The state machine transitions and operating parameters are stored/restored to/from a configuration database. Proper implementation of the state machines will not only ensure safe and reliable operation of the CMs, but will help ensure reliable data quality. A description of PIP-II SCL, details of the state machines, and lessons learned from limited use of the state machines in recent CM testing will be discussed.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

State Machine Operation of Complex Systems

Operation of complex systems which depend on one, or more, sub-systems with many process variables often operate in more than one state. For each state there may be a variety of parameters of interest, and for each of these, one may require different alarm limits, different archiving needs, and have different critical parameters. Relying on operators to reliably change 102-105 parameters for each system for each state is unreasonable. Not changing these parameters results in alarms being ignored or disabled, critical changes missed, and/or data archiving inefficiencies. To reliably manage the operation of complex systems, such as cryomodules (CMs), Fermilab is implementing state machines for each CM and an over-arching state machine for the PIP-II superconducting LINAC (SCL). The state machine transitions and operating parameters are stored/restored to/from a configuration database. Proper implementation of the state machines will not only ensure safe and reliable operation of the CMs, but will help ensure reliable data quality. A description of PIP-II SCL, details of the state machines, and plans for imminent use the state machines for CM testing will be discussed.

43 PARTICLE ACCELERATORS↗
DOE OSTI2024

OPER: Optimality-Guided Embedding Table Parallelization for Large-scale Recommendation Model

With the sharp increasing volume of user data, Deep Learning Recommendation Model (DLRM) becomes an indispensable infrastructure in large technology companies. However, large-scale DLRM on the multi-GPU platform is still inefficient due to unbalanced workload partitioning and intensive inter-GPU communication. To this end, we propose OPER, an OPtimality guided Embedding table placement for large-scale Recommendation model training and inference. OPER explores the potential of mitigating remote memory access latency in DLRM through fine-grained embedding table placement. Specifically, OPER proposes a theoretical modeling that builds up the relationship between EMT placement and the embedding communication latency in both training and inference. OPER proves the NP hardness of finding the optimal embedding table placement and proposes a heuristic algorithm that yields near optimal placement. OPER implements a SHMEM-based embedding table training system and a unified embedding index mapping to support fine-grained embedding table sharding and placement. Comprehensive experiments reveal that OPER achieves on average 3.4× and 5.1× speedup on training and inference respectively over state-of-the-art DLRM frameworks.

Wang, Zheng↗
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 OSTI2025

A resolution independent neural operator

The Deep operator network (DeepONet) is a powerful yet simple neural operator architecture that utilizes two deep neural networks to learn mappings between infinite-dimensional function spaces. This architecture is highly flexible, allowing the evaluation of the solution field at any location within the desired domain. However, it imposes a strict constraint on the input space, requiring all input functions to be discretized at the same locations; this limits its practical applications. Here, in this work, we introduce a general framework for operator learning from input–output data with arbitrary number and locations of sensors. This begins by introducing a resolution-independent DeepONet (RI-DeepONet), enabling it to handle input functions that are arbitrarily, but sufficiently finely, discretized. To this end, we propose two dictionary learning algorithms to adaptively learn a set of appropriate continuous basis functions, parameterized as implicit neural representations (INRs), from correlated signals defined on arbitrary point cloud data. These basis functions are then used to project arbitrary input function data as a point cloud onto an embedding space (i.e., a vector space of finite dimensions) with dimensionality equal to the dictionary size, which can be directly used by DeepONet without any architectural changes. In particular, we utilize sinusoidal representation networks (SIRENs) as trainable INR basis functions. The introduced dictionary learning algorithms are then used in a similar way to learn an appropriate dictionary of basis functions for the output function data, which defines a new neural operator architecture referred to as the R esolution I ndependent N eural O perator (RINO). In the RINO, the operator learning task simplifies to learning a mapping from the coefficients of input basis functions to the coefficients of output basis functions. We demonstrate the robustness and applicability of RINO in handling arbitrarily (but sufficiently richly) sampled input and output functions during both training and inference through several numerical examples.

Deep operator network (DeepONet)↗