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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 145 records · Page 8
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

A Modified Maximum Entropy Inverse Reinforcement Learning Approach for Microgrid Energy Scheduling

Increasing popularity of integrating distributed energy resources (DERs) into the power system brings a challenge to optimize the microgrid dispatch policy. The reinforcement learning methods suffer from a long-time problem with the theoretical assumption of the objective/reward function for the microgrid system. Although the traditional inverse reinforcement learning (IRL) approaches can solve this problem to some extent, they encounter a limitation of complex computations for state visitation frequency in the large and continuous state space. To alleviate this limitation, we propose a modified maximum entropy IRL (MMIRL) method to extract the reward function from the expert demonstrations for solving the microgrid energy scheduling problem. The proposed MMIRL algorithm is promising in recovering the reward function and learning the dispatch policy compared to conventional approaches. Case studies are performed in an energy arbitrage problem and a microgrid system with DERs. Results substantiate that the proposed MMIRL approach can learn the dispatch policy with more than 99% efficiency and outperforms other comparative methods.

artificial intelligence, reinforcement learning, m↗
DOE OSTI2026

Unlocking the Future of Aircraft Manufacturing: The Environmental Benefits of Laser Patterning for Surface Enhancement of Aircraft-Certified Alloys

Surface protection and functional modification of aircraft-certified aluminum alloys are essential for corrosion resistance, durability, and long-term airworthiness. At the same time, increasingly restrictive environmental regulations motivate the development of alternatives to legacy wet-chemical surface treatments. This study presents an integrated assessment of ultrafast femtosecond laser surface texturing as a surface functionalization approach for Aluminum 6061 alloys within an aerospace manufacturing and sustainability context. Ultrashort-pulse laser processing enables controlled micro- and nano-scale surface topographical modification with limited thermal impact, allowing adjustment of wettability and surface functionality while preserving bulk material integrity. As a dry and contactless process, femtosecond laser treatment eliminates the use of hazardous chemicals, reduces consumable inputs, and generates minimal secondary waste. A streamlined cradle-to-gate life cycle assessment conducted in accordance with ISO 14040/14044 indicates a lower global-warming potential per functional unit compared with conventional surface treatments, including anodization, plasma-assisted coatings, and organic coating systems. Complementary qualitative analyses addressing environmental health and safety, supply-chain risk, and ESG alignment indicate potential advantages related to occupational safety, regulatory compliance, waste management, and end-of-life recyclability. The investigation is performed on planar Aluminum 6061 reference surfaces with a treated area of 25 mm 2 , providing a controlled laboratory-scale basis for analyzing process behavior, functional surface modification, and associated environmental metrics. Within this defined scope, the results support further evaluation of femtosecond laser surface texturing as a surface engineering option for future aerospace manufacturing.

corrosion resistance↗
DOE OSTI2021

Human adipose-derived mesenchymal stromal cells from face and abdomen undergo replicative senescence and loss of genetic integrity after long-term culture

Body fat depots are heterogeneous concerning their embryonic origin, structure, exposure to environmental stressors, and availability. Thus, investigating adipose-derived mesenchymal stromal cells (ASCs) from different sources is essential to standardization for future therapies. In vitro amplification is also critical because it may predispose cell senescence and mutations, reducing regenerative properties and safety. Here, we evaluated long-term culture of human facial ASCs (fASCs) and abdominal ASCs (aASCs) and showed that both met the criteria for MSCs characterization but presented differences in their immunophenotypic profile, and differentiation and clonogenic potentials. The abdominal tissue yielded more ASCs, and these had higher proliferative potential, but facial cells displayed fewer mitotic errors at higher passages. However, both cell types reduced clonal efficiency over time and entered replicative senescence around P12, as evaluated by progressive morphological alterations, reduced proliferative capacity, and SA-β-galactosidase expression. Loss of genetic integrity was detected by a higher proportion of cells showing nuclear alterations and γ-H2AX expression. Our findings indicate that the source of ASCs can substantially influence their phenotype and therefore should be carefully considered in future cell therapies, avoiding, however, long-term culture to ensure genetic stability.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2026

Advanced Facility Design and AI/ML Enabled Safeguards to Establish Secure, Economical Recycling of Fast Reactor Fuels (Final Scientific/Technical Report)

The project, "Advanced Facility Design and AI/ML Enabled Safeguards to Establish Secure, Economical Recycling of Fast Reactor Fuels," represents a significant advancement in nuclear fuel recycling technology. It integrates cutting-edge multimodal sensor fusion, machine learning (ML), and digital twin (DT) technologies to address challenges in material safeguarding, process optimization, and regulatory compliance for pyroprocessing facilities. This research has significantly enhanced the understanding of pyrochemical fuel recycling processes by developing innovative tools and methodologies. The Multimodal Safeguards Monitoring Unit (MSMU) combines electroanalytical techniques, Raman spectroscopy, and differential thermal analysis (DTA) to enable high-fidelity, near-real-time material accountancy measurements. Machine learning techniques, such as Long Short-Term Memory (LSTM) autoencoders, are utilized to detect anomalies in material balances and sensor data, improving the reliability of safeguards monitoring. Additionally, digital twin technology has been established to provide real-time system-level monitoring and diagnostics, integrating physics-based models with sensor data to optimize process safety and efficiency.

11 NUCLEAR FUEL CYCLE AND FUEL MATERIALS↗
DOE OSTI2021

Stochastic social behavior coupled to COVID-19 dynamics leads to waves, plateaus, and an endemic state

It is well recognized that population heterogeneity plays an important role in the spread of epidemics. While individual variations in social activity are often assumed to be persistent, that is, constant in time, here we discuss the consequences of dynamic heterogeneity. By integrating the stochastic dynamics of social activity into traditional epidemiological models, we demonstrate the emergence of a new long timescale governing the epidemic, in broad agreement with empirical data. Our stochastic social activity model captures multiple features of real-life epidemics such as COVID-19, including prolonged plateaus and multiple waves, which are transiently suppressed due to the dynamic nature of social activity. The existence of a long timescale due to the interplay between epidemic and social dynamics provides a unifying picture of how a fast-paced epidemic typically will transition to an endemic state.

77 NANOSCIENCE AND NANOTECHNOLOGY↗
DOE OSTI2021

First detection of VHE gamma-ray emission from TXS 1515–273, study of its X-ray variability and spectral energy distribution

ABSTRACT We report here on the first multiwavelength (MWL) campaign on the blazar TXS 1515–273, undertaken in 2019 and extending from radio to very-high-energy gamma-rays (VHE). Up until now, this blazar had not been the subject of any detailed MWL observations. It has a rather hard photon index at GeV energies and was considered a candidate extreme high-synchrotron-peaked source. MAGIC observations resulted in the first-time detection of the source in VHE with a statistical significance of 7.6σ. The average integral VHE flux of the source is 6 ± 1 per cent of the Crab nebula flux above 400 GeV. X-ray coverage was provided by Swift-XRT, XMM–Newton, and NuSTAR. The long continuous X-ray observations were separated by ∼9 h, both showing clear hour scale flares. In the XMM–Newton data, both the rise and decay time-scales are longer in the soft X-ray than in the hard X-ray band, indicating the presence of a particle cooling regime. The X-ray variability time-scales were used to constrain the size of the emission region and the strength of the magnetic field. The data allowed us to determine the synchrotron peak frequency and classify the source as a flaring high, but not extreme synchrotron-peaked object. Considering the constraints and variability patterns from the X-ray data, we model the broad-band spectral energy distribution. We applied a simple one-zone model, which could not reproduce the radio emission and the shape of the optical emission, and a two-component leptonic model with two interacting components, enabling us to reproduce the emission from radio to VHE band.

Acciari, V. A.↗
DOE OSTI2023

Long plasma duration operation analyses with an international multi-machine (tokamaks and stellarators) database

Combined high-fusion performance and long-pulse operation is one of the key integration challenges for fusion energy development in magnetic devices. Addressing these challenges requires an integrated vision of physics and engineering aspects with the purpose of simultaneously increasing time duration and fusion performance. Significant progress has been made in tokamaks and stellarators, including very recent achievement in duration and/or performance. This progress is reviewed by analyzing the experimental data (109 plasma pulses with a total of 3200 data points, i.e. on average 29 data per pulse) provided by ten tokamaks (in alphabetical order: Axially Symmetric Divertor Experiment Upgrade, DIII-D, Experimental Advanced Superconducting Tokamak, Joint European Torus, JT-60 Upgrade, Korea Superconducting Tokamak Advanced Research, tokamak à configuration variable, Tokamak Fusion Test Reactor, Tore Supra, W Environment in Steady-State Tokamak) and two stellarators (Large Helical Device and Wendelstein 7-X) expanding the pioneering work of Kikuchi (Kikuchi M. and Azumi M. 2015 Frontiers in Fusion Research II: Introduction to Modern Tokamak Physics (Springer)). Data have been gathered up to January 2022 and coordination has been provided by the recently created International Energy Agency-International Atomic Energy Agency international Coordination on International Challenges on Long duration OPeration group. By exploiting the multi-machine international database, recent progress in terms of injected energies (e.g. 1730 MJ in L-mode, 425 MJ in H-mode), durations (1056 s in L-mode, 101 s in H-mode), injected powers, and sustained performance will be reviewed. Progress has been made to sustain long-pulse operation in tokamaks and stellarators with superconducting coils, actively cooled components, and/or with metallic walls. The graph of the fusion triple products as a function of duration shows a dramatic reduction of, at least two orders of magnitude when increasing the plasma duration from less than 1 s to 100 s. Indeed, long-pulse operation is usually reached in dominant electron-heating modes at reduced density (current drive optimization) but with low ion temperatures ranging from 1 to 3 keV for discharges above 100 s. Difficulties in extending the duration may arise from coupling high heating powers over long durations and the evolving plasma-wall interaction towards an unstable operational domain. Possible causes limiting the duration and critical issues to be addressed prior to ITER operation and DEMO design are reported and analyzed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2023

Summary of Consolidated Interim Storage Advantages and Disadvantages from an Integrated Systems Perspective from Prior Reports and Studies

The question of whether centralized storage of civilian spent nuclear fuel (SNF) should be part of the federal waste management system as an intermediate step before permanent disposal has been debated for more than four decades. Centralized storage facilities were included as a potential component of the U.S. spent fuel management system in the Nuclear Waste Policy Act of 1982 (NWPA), but these facilities were not identified as being essential. When the NWPA was passed, it was expected that a permanent repository would be available around the turn of the century to meet the commitments that were made to start accepting waste by that time. For a number of reasons, a permanent repository was not available at that stage. This report summarizes the advantages and disadvantages of including an ISF as part of an integrated waste management system that have been identified in numerous analyses of the impacts of a consolidated interim storage facility (ISF), previously discussed as monitored retrievable storage, the form of ISF authorized in the NWPA) by the U.S. Department of Energy (DOE) and independent groups. Storing SNF before disposal is a functional requirement for an integrated waste management system. As described below, the studies reviewed in this report have identified a range of benefits that could be obtained by adding a consolidated ISF to the waste management system, including (1) earlier acceptance of fuel by the federal government, (2) reduction in the number of unintended long-term storage sites, (3) added system flexibility and opportunity for better integration, and (4) near-term development and demonstration of institutional and technical infrastructures for large-scale management of SNF. At the same time, these studies have identified potential drawbacks to deployment of an ISF, including (1) potential adverse impacts on development of a repository, (2) additional transportation of SNF, and (3) a large upfront economic investment to establish the consolidated storage capability. In general, the studies that have considered the positive and negative impacts of consolidated storage most comprehensively have concluded that in light of these considerations, the benefits of including an ISF as part of an integrated waste management system can outweigh any real or perceived disadvantages.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

Metocean Reference Station Best Practices: MORS-1 Case Study

The goal of a Metocean Reference Station should be to aid both near-term development of the offshore wind energy industry as well as long-term climate and energy research. Capitalizing on existing shared-use facilities wherever possible, reference stations should provide data valued by industry users as well as research users in a cost-effective way. Cost-effectiveness is a critical component of developing a reference site, as the real value of the site's data collection efforts is the length of the time series it is able to sustain. This report seeks to lay out the best practices toward developing and maintaining metocean reference stations in the United States. The best practices described here focus on suitable platforms, sensor integration, and long-term operations of the reference station itself, as best practices of operations for individual sensors for the research community or validation enterprises focused on industrial use of metocean data are well described in the literature. This work focuses on potential stations in the United States because the market for reference data and validation facilities is less well defined in the United States, given the young age of the rapidly emerging offshore wind energy industry here.

17 WIND ENERGY↗
DOE OSTI2025

Rapid wavefield forecasting for earthquake early warning via deep sequence to sequence learning

We propose a deep learning model, WaveCastNet, to forecast high-dimensional wavefields. WaveCastNet integrates a convolutional long expressive memory architecture into a sequence-to-sequence forecasting framework, enabling it to model long-term dependencies and multiscale patterns in both space and time. By sharing weights across spatial and temporal dimensions, WaveCastNet requires significantly fewer parameters than more resource-intensive models such as transformers, resulting in faster inference times. Crucially, WaveCastNet also generalizes better than transformers to rare and critical seismic scenarios, such as high-magnitude earthquakes. Here, we show the ability of the model to predict the intensity and timing of destructive ground motions in real time, using simulated data from the San Francisco Bay Area. Furthermore, we demonstrate its zero-shot capabilities by evaluating WaveCastNet on real earthquake data. Our approach does not require estimating earthquake magnitudes and epicenters, steps that are prone to error in conventional methods, nor does it rely on empirical ground-motion models, which often fail to capture strongly heterogeneous wave propagation effects.

Geophysics↗
DOE OSTI2025

Predicting nonequilibrium Green’s function dynamics and photoemission spectra via nonlinear integral operator learning

Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of large-scale nonequilibrium phenomena in realistic materials face serious challenges due to intrinsic high-dimensionality of quantum many-body problems and the absence of time-invariance. The nonequilibrium properties of many-body systems can be described by the dynamics of the correlator, or the Green's function of the system, whose time evolution is given by a high-dimensional system of integro-differential equations, known as the Kadanoff–Baym equations (KBEs). The time-convolution term in KBEs, which needs to be recalculated at each time step, makes it difficult to perform long-time numerical simulation. In this paper, we develop an operator-learning framework based on recurrent neural networks (RNNs) to address this challenge. We utilize RNNs to learn the nonlinear mapping between Green's functions and convolution integrals in KBEs. By using the learned operators as a surrogate model in the KBE solver, we obtain a general machine-learning scheme for predicting the dynamics of nonequilibrium Green's functions. Besides significant savings per each time step, the new methodology reduces the temporal computational complexity from $O(N_t^3)$ to $O(N_t)$ where N t is the number of steps taken in a simulation, thereby making it possible to study large many-body problems which are currently infeasible with conventional KBE solvers. Through various numerical examples, we demonstrate the effectiveness of the operator-learning based approach in providing accurate predictions of physical observables such as the reduced density matrix and time-resolved photoemission spectra. Moreover, our framework exhibits clear numerical convergence and can be easily parallelized, thereby facilitating many possible further developments and applications.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Lithium-niobate-on-insulator waveguide-integrated superconducting nanowire single-photon detectors

Here, we demonstrate waveguide-integrated superconducting nanowire single-photon detectors on thin-film lithium niobate (LiNbO 3 , LN). Using a 250 μm-long NbN superconducting nanowire lithographically defined on top of a 125 μm-long LN nanowaveguide, an on-chip detection efficiency of 46% is realized with simultaneous high performance in dark count rates and timing jitter. As LN possesses high χ (2) second-order nonlinear and electro-optic properties, an efficient single-photon detector on thin-film LN opens up the possibility to construct a small-scale fully integrated quantum photonic chip, which includes single-photon sources, filters, tunable quantum gates, and detectors.

42 ENGINEERING↗
DOE OSTI2022

Modeling Needs to Support the Reconstruction Strategy of Ukraine

Ukraine has been facing difficult times. Russia started a full-scale invasion on February 24, 2022, and has caused huge human and infrastructure losses. As a result of the invasion, more than 8 million people left their homes. The Russian army has targeted Ukrainian energy sources, destroying or damaging over 50% of thermal power generation capacity (coal and gas), 30% of solar generation, and 90% of wind generation. The Russians are also threatening Ukrainian energy security, as they currently control the Zaporizhzhia nuclear power plant – Europe’s largest. In addition, Russia has destroyed 121,000 buildings, including 5,300 multistory buildings - more buildings than Ukraine built during the past five years. The occupiers destroyed or damaged 343 district heat boiler stations (destroyed 12 / damaged 331) and 8 CHPs (destroyed 4/ damaged 4). There is no doubt that Ukraine will be able to protect its sovereignty and restore its territorial integrity; however, this will be a long process. The Government of Ukraine needs to simultaneously focus on many issues, from waging war to the restoration of electricity, water, and heat supply in the territories close to the front line. In addition to these time-sensitive issues, the government also needs to plan a long term multi-sector strategy for the reconstruction of Ukraine’s economy. Ukraine initiated a broad-based political process for recovery at the International Ukraine Recovery Conference (URC 2022) in Lugano, Switzerland. Prior to URC 2022, Ukraine applied for EU membership on February 28 and was granted the status of candidate country by the European Council on June 23, 2022. More than 40 nations are fully committed to supporting Ukraine throughout its path from early to long-term recovery. In addition, these countries link a successful recovery to Ukraine’s European future (URC, 2022a). The reconstruction process will be long. The government also recognizes that it is not enough to build energy infrastructure back – it should be built back better. The government is committed to building a more sustainable and cleaner energy sector. Energy modeling can provide important insights into paths to decarbonize Ukraine’s economy while rebuilding it after the war. Pacific Northwest National Laboratory (PNNL) and the Institute for Economics and Forecasting of the National Academy of Sciences of Ukraine (IEF) work on modeling decarbonization scenarios in the energy sector of Ukraine. The teams focus on the heat sector, which includes district heat, autonomous and individual heating, and energy consumption by final energy consumption sectors, including buildings. Since the teams use world-class integrated assessment models, other sectors will be analyzed as well. The purpose of the document is to describe the needs of key Ukrainian ministries in modeling the reconstruction process. The scope of this document is limited to modeling energy consumption by the power and heat sectors, final energy consumption by buildings, and GHG emissions from these two sectors. The rest of this policy memo is organized as follows. After this introduction, Chapter 2 discusses key provisions of the reconstruction strategy with a focus on energy, buildings, heat supply, environment, and European integration aspirations. Section 3 provides an overview of recent developments and key decisions of the Government of Ukraine in the area of energy efficiency and decarbonization. Finally, Section 4 provides key suggestions on how PNNL and IEF can help the Government of Ukraine in developing strategic documents.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗
DOE OSTI2022

Studies of BONuS12 Radial GEM Detector and TCS Beam Spin Asymmetry in CLAS12

The Barely Offshell Nucleon Structure (BONuS12) experiment adopted the concept of spectator tagging technique to study the nearly-free neutron structure function Fn2 in the CLAS12 of Jefferson Lab. A novel Radial Time Projection Chamber (RTPC) detector was built, tested and integrated into the CLAS12 system to detect a back-moving low momentum tagged proton in d(e,ep)X deep-inelastic scattering. It was a 40 cm long gaseous detector consisting of 3 layers of cylindrical GEM foils for the charge amplification, with the data readout directly from the surrounding padboard. The RTPC detected the recoiling spectator proton, in coincidence with the scattered electron in the CLAS12. Nucleon structure functions are directly related to the partonic functions, quarks momentum distribution in one dimension. A Generalized Parton Distribution (GPD) came to the lime-light as it encodes the information of both longitudinal momentum and transverse position of partons inside the nucleons. Factorization of hard process such as DVCS allows to access GPDs. Timelike Compton Scattering (TCS), ?p ? ??p, is another process that allows to access the GPDs. TCS is studied experimentally in the CLAS12 of Jefferson lab using the quasi-real photoproduction of time-like photon which eventually decays to lepton pair. This dissertation presents the concept of spectator tagging in BONuS12, and the research and development efforts during the BONuS12 preparation leading up to the successful data-taking during spring and summer 2020. In addition, analysis framework to extract the beam spin asymmetry of TCS events through the CLAS12 Run group A data is presented.

Poudel, Jiwan↗
DOE OSTI2021

Charge Transfer Properties of Heterostructures Formed by Bi 2 O 2 Se and Transition Metal Dichalcogenide Monolayers

Atomically thin bismuth oxyselenide (Bi 2 O 2 Se) exhibits attractive properties for electronic and optoelectronic applications, such as high charge-carrier mobility and good air stability. Recently, the development of Bi 2 O 2 Se-based heterostructures have attracted enormous interests with promising prospects for diverse device applications. Although the electrical properties of Bi 2 O 2 Se-based heterostructures have been widely studied, the interlayer charge transfer in these heterostructures remains elusive, despite its importance in harnessing their emergent functionalities. Here, a comprehensive experimental investigation on the interlayer charge transfer properties of two heterostructures formed by Bi 2 O 2 Se and representative transition metal dichalcogenides (namely, WS 2 /Bi 2 O 2 Se and MoS 2 /Bi 2 O 2 Se) is reported. In this work, Kelvin probe force microscopy is used to measure the work functions of the samples, which are further employed to establish type-II band alignment of both heterostructures. Photoluminescence quenching is observed in each heterostructure, suggesting high charge transfer efficiency. Time-resolved and layer-selective pump–probe measurements further prove the ultrafast interlayer charge transfer processes and formation of long-lived interlayer excitons. These results establish the feasibility of integrating 2D Bi 2 O 2 Se with other 2D semiconductors to fabricate heterostructures with novel charge transfer properties and provide insight for understanding the performance of optoelectronic devices based on such 2D heterostructures.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Reaction–drift–diffusion models from master equations: application to material defects

We present a general method to produce well-conditioned continuum reaction–drift–diffusion equations directly from master equations on a discrete, periodic state space. We assume the underlying data to be kinetic Monte Carlo models (i.e. continuous-time Markov chains) produced from atomic sampling of point defects in locally periodic environments, such as perfect lattices, ordered surface structures or dislocation cores, possibly under the influence of a slowly varying external field. Our approach also applies to any discrete, periodic Markov chain. Here, the analysis identifies a previously omitted non-equilibrium drift term, present even in the absence of external forces, which can compete in magnitude with the reaction rates, thus being essential to correctly capture the kinetics. To remove fast modes which hinder time integration, we use a generalized Bloch relation to efficiently calculate the eigenspectrum of the master equation. A well conditioned continuum equation then emerges by searching for spectral gaps in the long wavelength limit, using an established kinetic clustering algorithm to define a proper reduced, Markovian state space.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Slow thermalization and subdiffusion in $U$(1) conserving Floquet random circuits

Random quantum circuits are paradigmatic models of minimally structured and analytically tractable chaotic dynamics. We study a family of Floquet unitary circuits with Haar random U(1) charge conserving dynamics; the minimal such model has nearest-neighbor gates acting on spin-1/2 qubits, and a single layer of even/odd gates repeated periodically in time. We find that this minimal model is not robustly thermalizing at numerically accessible system sizes, and displays slow subdiffusive dynamics for long times. We map out the thermalization dynamics in a broader parameter space of charge conserving circuits, and understand the origin of the slow dynamics in terms of proximate localized and integrable regimes in parameter space. In contrast, we find that small extensions to the minimal model are sufficient to achieve robust thermalization; these include (i) increasing the interaction range to three-site gates, (ii) increasing the local Hilbert space dimension by appending an additional unconstrained qubit to the conserved charge on each site, or (iii) using a larger Floquet period comprised of two independent layers of gates. Furthermore, our results should inform future studies of charge conserving circuits, which are relevant for a wide range of topical theoretical questions.

1-dimensional spin chains↗
DOE OSTI2025

Multi-scale, Multi-disciplinary, and Multi-agent Explainable AI with Koopman-Undergirded Learning, Prediction, and Analysis (M3EA KULPA) (Project Closeout Report)

The goal of this project was to develop and use domain-aware machine learning formulations, based on the Koopman Operator (KO), for modelling multi-scale, multi-disciplinary (e.g., multi-physics), and/or multi-agent systems. The project developed these formulations for the following cases: • Systems with dynamics at two separate time scales, • Systems with a bi-level hierarchical control structure, • Systems with bi-level hierarchical control and dynamics at two separate time scales (the lower level controls operating at the faster time scale), and • Systems with n separate but interacting agents/disciplines (with/without control, respectively); the controls for each agent could include bi-level hierarchical control and dynamics at two separate time scales as described above. The project then defined a set of dynamical systems consisting of different nonlinear oscillators that could be used to test these different formulations and then subsequently learned the KO models for those systems. With the KO models, we were able to do the following: • Quantify system stability, including both long-term and transient behavior, • Quantify the effects of feedbacks between the different time scales and agents/disciplines in terms of those feedbacks’ effects on system stability, • Replace a standard Proportional-Integral (PI) control in the hierarchical control structure with a KO-based Linear-Quadratic Regular (LQR), a form of optimal control, • Calculate optimal supervisory control policies a) with and without time scale separated dynamics at the lower level control levels and b) with both PI and KO-based LQR lower level control policies, and • Calculate dynamic Nash equilibria for multi-agent systems where each agent makes its own control decisions.

97 MATHEMATICS AND COMPUTING↗