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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Findings on Subtask 3.1 - Bakken Rich Gas Enhanced Oil Recovery Project

Total in-place oil for the Bakken petroleum system (BPS) (which includes the Bakken and Three Forks Formations) has been estimated to be 600 billion barrels (bbl). However, BPS wells have decline rates as high as 85% over the first 3 years of their lives, and primary recovery factors typically range from 3% to 10% of original oil in place. Given the low initial recovery rates, even small incremental productivity improvements could dramatically increase technically recoverable oil in the BPS. One potential solution is enhanced oil recovery (EOR) using gas injection, such as carbon dioxide (CO2) or hydrocarbon (HC) gases. While commonly used in conventional reservoirs, CO2 EOR in unconventional tight oil reservoirs has been limited to pilot tests. EOR using rich gas (mixture of methane, ethane, and propane) has also been employed in numerous pilots in several unconventional plays and has recently been successfully applied in the Eagle Ford play. If successful, large-scale gas-based EOR in the BPS could dramatically increase oil productivity and recovery factors and extend the life of the play for decades. While CO2 may be a technically suitable working fluid for EOR in the BPS, supplies are limited and costs for using CO2 in EOR pilots are prohibitively high. Meanwhile, produced gas flaring has presented challenges for BPS operators in North Dakota. Analysis conducted by the North Dakota Pipeline Authority indicates that the current gas-gathering infrastructure in North Dakota is insufficient to accommodate all of the associated gas that is produced from the BPS. The geographically isolated location of North Dakota relative to large natural gas markets, combined with suppressed natural gas prices, has made it economically challenging for industry to invest capital in expanding gas-gathering infrastructure in the state. These circumstances led to a research program conducted by the Energy & Environmental Research Center (EERC) in partnership with Liberty Resources Management Company LLC (LR) to examine the potential to use rich gas injection for EOR and mitigate flaring. A rich gas EOR pilot test was designed and executed by LR at its Stomping Horse development area in Williams County, North Dakota. From July 2018 through May 2019, a total of 160 million standard cubic feet (MMscf) of rich produced gas was injected into the BPS using five different wells in a sequential injection strategy. LR’s Leon–Gohrick drill spacing unit (DSU) was used as the test site. Regulatory oversight was provided by the North Dakota Industrial Commission (NDIC). Technical support was provided by the EERC through a series of laboratory, modeling, and field-based activities, and additional post-pilot research activities incorporated learnings from the test, developed new laboratory data, improved fracture modeling methods, and developed machine learning and big data analytics. The results from the Stomping Horse rich gas EOR pilot activities indicate that developing an effective, economical EOR approach for the BPS will require more field tests. Another key lesson learned from the Stomping Horse tests is that detailed pre- and posttest data on reservoir conditions and fluids production are essential. Robust reservoir characterization provides information that is crucial to creating realistic geomodels and conducting valid dynamic simulations of potential EOR scenarios. A detailed understanding of the completions and production history of offset wells is also necessary for valid test result interpretations. This knowledge is essential to designing the operational parameters of injectivity tests and interpreting the results. A conformance control strategy is also essential to success. Laboratory-based examinations of rich gas interactions with reservoir fluids and rocks were conducted, with an emphasis on determining the ability to mobilize oil in the tight reservoir rocks and shales of the BPS. Injection fluid composition was shown to have a positive impact on reducing reservoir oil minimum miscibility pressure (MMP), reducing interfacial tension (IFT), and altering wettability. IFT and contact angle measurements demonstrated that wettability can be altered in the presence of rich gas, suggesting the potential to improve oil recovery. Iterative modeling of surface infrastructure and reservoir performance using data generated by the various project activities was conducted. A geologic model of the Stomping Horse area was built; history-matched oil, gas, and water production was used in simulations of various EOR scenarios. Early programmatic modeling results were used to support LR’s design and operation of the EOR pilot and to provide insight regarding optimization of future commercial-scale BPS EOR design and operations. Post-pilot modeling focused on alternative methods of understanding complex fracture networks and accelerating simulation time. These led to improved simulation run times and provide excellent history-matching results. Several of these iterative models were used as the bases for developing algorithms into machine learning and big data analytics. History matching in reservoir simulation is time-consuming and computer processing-intensive. Machine learning algorithms were created, and an automated history-matching tool was developed. A large set of synthetic reservoir simulations were created to generate well responses (oil, gas, and water production, well bottomhole pressure [BHP], and tracer or propane breakthrough) for a set of EOR operating parameters that included offset well status (open or closed), injectate (rich gas or propane), injection rate, and injection well BHP. A user interface was developed to provide real-time visualization. Machine learning-based models were developed to provide rapid forecasting of well performance given a set of user-defined EOR operating parameters. These predictive models allow the user to modify the offset well status, injection rate, and injection well BHP and rapidly forecast future production performance. The combination of real-time visualization tools with real-time forecasting tools provides a framework for real-time control—operational changes that the EOR site operator can enact (e.g., changing gas injection rates) to affect the observed performance and potentially improve the EOR outcome. There is great reason to be optimistic about the future of EOR in the Bakken. The results of the laboratory studies suggest significant potential for high rates of oil mobilization using produced field gas injection under the right conditions. The results of the lab studies, combined with rigorous statistical analysis of well production data and associated modeling efforts, confirm the notion that fluid mobility within the reservoir is controlled by fractures. As more knowledge is gained about the nature and distribution of fracture networks in the Bakken, the industry will be in a better position to predict and, ultimately, influence fluid mobility. New field tests are necessary to develop a more complete understanding of those conditions. Thoughtful and creatively engineered field tests within a well-characterized geologic setting will yield the fundamental knowledge needed to take Bakken oil production to the next level. This subtask was cofunded through the EERC–U.S. Department of Energy Joint Program on Research and Development for Fossil Energy-Related Resources Cooperative Agreement No. DE-FE0024233. Nonfederal funding was provided by the North Dakota Industrial Commission’s Oil and Gas Research Program and Computer Modelling Group.

04 OIL SHALES AND TAR SANDS↗
DOE OSTI2024

Federated Machine Learning-Based Anomaly Detection System for Synchrophasor Network Using Heterogeneous Data Sets: Preprint

Synchrophasor technology is widely deployed in the energy management system to monitor the grid health at micro level and perform necessary corrective actions in real time; however, integrated phasor devices and data aggregators are exposed to several cybersecurity threats. This paper proposes a federated ML(FML)-based ADS to detect several data integrity attacks in the synchrophasor network. The proposed approach integrates the horizontal FML technique and consists of substation-based local models and a control center-based global model. The proposed methodology includes training local models using heterogeneous data sets that include network and grid information and updating the global model through multiple iterations by sharing model gradients. Finally, the trained global model is applied to identify cyberattacks, normal operation, and physical events. To validate the proof of concept, we used synthetic data sets generated by Mississippi State University and Oak Ridge National Laboratory for training and testing the classification models using the National Renewable Energy Laboratory's high performance computing resources. Our experimental results, computed through several performance measures, reveal that the proposed approach shows consistent performance during the binary, three-class, and multiclass classifications while ensuring privacy of synchrophasor data.

anomaly detection system↗
DOE OSTI2022

Optimization of Water-Alternating-CO2 Injection Field Operations Using a Machine-Learning-Assisted Workflow

Summary This paper will present a robust workflow to address multiobjective optimization (MOO) of carbon dioxide (CO2)-enhanced oil recovery (EOR)-sequestration projects with a large number of operational control parameters. Farnsworth unit (FWU) field, a mature oil reservoir undergoing CO2 alternating water injection (CO2-WAG) EOR, will be used as a field case to validate the proposed optimization protocol. The expected outcome of this work would be a repository of Pareto-optimal solutions of multiple objective functions, including oil recovery, carbon storage volume, and project economics. FWU’s numerical model is used to demonstrate the proposed optimization workflow. Because using MOO requires computationally intensive procedures, machine-learning-based proxies are introduced to substitute for the high-fidelity model, thus reducing the total computation overhead. The vector machine regression combined with the Gaussian kernel (Gaussian-SVR) is used to construct proxies. An iterative self-adjusting process prepares the training knowledge base to develop robust proxies and minimizes computational time. The proxies’ hyperparameters will be optimally designed using Bayesian optimization to achieve better generalization performance. Trained proxies will be coupled with multiobjective particle swarm Optimization (MOPSO) protocol to construct the Pareto-front solution repository. The outcomes of this workflow will be a repository containing Pareto-optimal solutions of multiple objectives considered in the CO2-WAG project. The proposed optimization workflow will be compared with another established methodology using a multilayer neural network (MLNN) to validate its feasibility in handling MOO with a large number of parameters to control. Optimization parameters used include operational variables that might be used to control the CO2-WAG process, such as the duration of the water/gas injection period, producer bottomhole pressure (BHP) control, and water injection rate of each well included in the numerical model. It is proved that the workflow coupling Gaussian-SVR proxies and the iterative self-adjusting protocol is more computationally efficient. The MOO process is made more rapid by squeezing the size of the required training knowledge base while maintaining the high accuracy of the optimized results. The outcomes of the optimization study show promising results in successfully establishing the solution repository considering multiple objective functions. Results are also verified by validating the Pareto fronts with simulation results using obtained optimized control parameters. The outcome from this work could provide field operators an opportunity to design a CO2-WAG project using as many inputs as possible from the reservoir models. The proposed work introduces a novel concept that couples Gaussian-SVR proxies with a self-adjusting protocol to increase the computational efficiency of the proposed workflow and to guarantee the high accuracy of the obtained optimized results. More importantly, the workflow can optimize a large number of control parameters used in a complex CO2-WAG process, which greatly extends its utility in solving large-scale MOO problems in various projects with similar desired outcomes.

Energy & Fuels↗
DOE OSTI2026

Surrogates for Valve-Controlled Pipe Flow: Accelerating Nuclear Reactor Design

Neural surrogate models are developed to replace expensive steady-state RANS CFD simulations for valve-controlled pipe flow in nuclear reactor design. Using parametric CFD data generated with MOOSE Pronghorn across a range of valve geometry and flow conditions, three approaches are compared: a POD-based reduced-order model, a structured UNet on a cylindrical grid, and unstructured models (DeepONet and BiStride MeshGraphNet) on nondimensionalized point clouds. POD achieves the highest accuracy (99%) with fast inference but requires storing all solution snapshots, while the DeepONet and BSMS-GNN both achieve ~89% accuracy at sub-second inference, with the BSMS-GNN offering superior geometric generalizability. These surrogates enable rapid ranking of candidate valve designs and can warm-start CFD solvers to accelerate convergence, supporting agentic design iteration on the Prometheus platform.

42 - ENGINEERING↗
DOE OSTI2022

Network Reconfiguration for Enhanced Operational Resilience Using Reinforcement Learning

This paper proposes a reinforcement learning-based approach for distribution network reconfiguration(DNR) to enhance the resilience of the electric power supply. Resilience enhancements usually require solving large-scale stochastic optimization problems that are computationally expensive and sometimes infeasible. The exceptional performance of reinforcement learning techniques has encouraged their adoption in various power system control studies, specifically resilience-based real-time applications. In this paper, a single agent framework is developed using an Actor-Critic algorithm (ACA) to determine statuses of tie-switches in a distribution feeder impacted by an extreme weather event. The proposed approach provides a fast-acting control algorithm that reconfigures the feeder topology to reduce or even avoid load shedding. The problem is formulated as a discrete Markov decision process in such a way that a system state captures the system topology and its operational characteristics. An action is made to open or close a specific set of tie-switches after which a reward is calculated to evaluate the practicality and advantage of that action. The iterative Markov process is used to train the proposed ACA under diverse failure scenarios and is demonstrated on the 33-node distribution feeder system. Results show the capability of the proposed ACA to determine proper switching action of tie-switches with accuracy exceeding 93%.

actor critic↗
DOE OSTI2024

Integrate Latimer Controls' Solution into RTAC (CRADA Final Report, CRD-23-24672)

Latimer Controls, Inc. was awarded two vouchers under the Department of Energy's American-Made Solar Prize Round 6 to conduct collaborative research at a national laboratory. The National Renewable Energy Laboratory (NREL) was selected as a partner to assist Latimer Controls in the performance evaluation of its photovoltaic (PV) control software. This collaboration focuses on developing a hardware-in-the-loop (HIL) testbed at NREL, which will be used to test and validate the Latimer PV control technology in a realistic yet de-risked environment. Both Latimer and NREL teams will work together to analyze the collected test data, derive insights, and disseminate the scientific findings. Recent studies underscore the potential of solar energy as a zero-marginal-cost and zero-emission flexibility resource within the bulk power system, particularly when integrated with advanced control systems. To enhance the performance of such systems, Latimer Controls has developed leading-edge technologies, including machine learning (ML) algorithms and hierarchical inverter set-point allocation methods. These innovations are designed to estimate the operational headroom of large PV plants for grid integration and control. However, comprehensive validation under real-world conditions remains necessary. To address this gap, the concurrent CRADA project proposes the real-world application and validation of the Latimer Control solution within a HIL environment. Initially, the Latimer algorithm was developed and tested within MATLAB Simulink, a platform suitable for research-level simulations and iterative development. However, transitioning this technology to a real solar site as an industry-ready solution necessitates implementation in a format compatible with widely used solar power plant controllers. In this additional CRADA work, the MATLAB Simulink-based logic will be translated into Structured Text, a programming language compliant with IEC 61131 standards, which is commonly used for custom logic implementations in industry-leading programmable logic controllers (PLCs), such as the Schweitzer SEL real-time automation controller (RTAC). This transition will facilitate the deployment of the Latimer Control solution in real-world solar power plants, thereby advancing the technology towards commercialization.

14 SOLAR ENERGY↗
DOE OSTI2022

Data Curation for Machine Learning Applied to Geothermal Power Plant Operational Data for GOOML: Geothermal Operational Optimization with Machine Learning: Preprint

Geothermal Operational Optimization with Machine Learning (GOOML) is a transferable and extensible component-based geothermal asset modeling framework that considers complex steamfield relationships and identifies optimization prospects using a data-driven approach to physics-guided, data-centric machine learning. This framework has been used to develop digital twins that provide steamfield operators with operational environments to analyze and understand historical and forecasted power production, explore new steamfield configuration possibilities, and seek optimal asset management in real world applications. To create, test, and apply the GOOML framework, diverse time-series datasets spanning multiple years were sourced from various geothermal power plant components within several complex real-world geothermal operations. These operations are based in the United States and New Zealand and include a variety of technologies, end-uses and configurations, collectively covering nearly all relevant operating conditions for modern geothermal fields. Datasets were acquired from multiple sources to ensure that machine learning experiments generalized properly to various operating conditions. It was found that the data varied in quality, format, and completeness. To ensure consistency between the various datasets, a standardized data curation process was developed to reliably streamline data preparation. This paper will discuss best practices as learned from the GOOML data curation process which takes the following steps: 1) acquisition of large quantities of data from power plant operators, 2) digestion of data to gain an initial understanding of what is included, 3) data transformation, which includes converting the data into a standardized machine-readable format so that they can be visualized, quality checked, and cleaned, 4) quality assurance and quality control, involving identification of significant data gaps and apparent anomalies through mapping of data features to real world componentry via the GOOML historical model, followed by discussion with modelers and power plant operators to identify additional data needs and to resolve issues, 5) use in machine learning algorithms, and 6) repetition of steps one through five until all data needs are met and data are deemed suitable for producing trustworthy modeling results which may be disseminated, ideally along with the curated dataset. This iterative process is focused on improving the quality of the data rather than tuning machine learning model parameters and supports a shift towards data-centric AI as a means to improving real-world applicability of geothermal machine learning projects.

access↗
DOE OSTI2023

Reinforcement learning for real-time process control in high-temperature superconductor manufacturing

With high efficiency and low energy loss, high-temperature superconductors (HTS) have demonstrated their profound applications in various fields, such as medical imaging, transportation, accelerators, microwave devices, and power systems. The high-field applications of HTS tapes have raised the demand for producing cost-effective tapes with long lengths in superconductor manufacturing. However, achieving the uniform and enhanced performance of a long HTS tape is challenging due to the unstable growth conditions in the manufacturing process. Although it is confirmed that the process parameters during the advanced metal organic chemical vapor deposition (A-MOCVD) process influence the uniformity of the produced HTS tapes, the high-dimensional process parameter signals and their complicated interactions make it difficult to develop an effective control policy. In this paper, we propose a local measure for the uniformity of HTS tapes to provide instant feedback for our control policy. Then, we model the manufacturing of HTS tapes as a Markov decision process (MDP) with continuous state and action spaces to assess the instant reward in real time in our feedback control model. As our MDP involves continuous and high-dimensional state and action spaces, a neural fitted Q-iteration (NFQ) algorithm is adopted to solve the MDP with artificial neural network (ANN) function approximation. The collinearity of process parameters can restrict our capability of adjusting the process parameters, which is addressed by the principal component analysis (PCA) in our method. The control policy adjusts the PCA of process parameters using the NFQ algorithm. In conclusion, based on our case studies on real A-MOCVD dataset, the obtained control policy increases the average uniformity of tapes by 5.6% and performs especially well on sample HTS tapes with a low uniformity.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

mystic : software for autonomous discovery and design under uncertainty

Throughout the diverse range of science and engineering applications, there is a growing desire to develop computational methods that can reliably predict the behavior of complex systems. Specifically, there is a strategic need for tools that can robustly forecast the behavior of complex physical systems, where data may be high-dimensional, noisy, or sparse, and models of the system may be time-dependent or include uncertainty. We use mystic to build tools that leverage statistical learning, physics-informed learning, and active learning in the efficient generation of reliably predictive surrogates for complex physical systems. mystic is a robust, proven, open-source optimization and uncertainty quantification toolkit with over a decade of use in the design and optimization of neutron instrumentation, solar-powered drones, and gasguns, and in iterative tuning of models for Raman spectroscopy and elastoplastic materials strength. Recent developments have focused on automated learning of statistically robust surrogates under uncertainty, with applications in materials in extreme environments, nanostructures, materials simulations and strength models, and the failure of shielding under particle radiation. In 2020, McKerns demonstrated active learning of optimally robust surrogates with respect to new simulated data for molecular dynamics simulations of materials mixing in warm dense matter, and is currently applying active learning to the automated steering of particle accelerator beams and the optimal design and control of quantum optical sensor instrumentation.

42 ENGINEERING↗
DOE OSTI2026

Micro-architected material design for mechanical response

Rapid advances in additive manufacturing (AM) have enabled the creation of micro-architected materials—also known as mechanical metamaterials—with unprecedented control over fine-scale geometries and arrangements of multiple material constituents. These “materials” can achieve unique and extraordinary effective mechanical properties through their complex architectures rather than composition alone. A key challenge is to design for these bespoke effective mechanical responses within the constraints of available AM techniques (i.e., given a set of desired effective properties), identify a (often nonunique) micro-architecture and selection of material constituents that achieves them. Two main strategies have emerged. Gradient-based methods use sensitivity analysis to iteratively refine candidate designs, while data-driven methods learn micro-architecture-constituent relationships from existing examples to propose new designs. This article reviews these design approaches for micro-architected materials with tailored mechanical responses that can be fabricated by AM as well as their applications.

Spadaccini, Christopher M [Lawrence Livermore Nati↗
DOE OSTI2022

Multifidelity multiobjective optimization for wake-steering strategies

Abstract. Wake steering is an emerging wind power plant control strategy where upstream turbines are intentionally yawed out of perpendicular alignment with the incoming wind, thereby “steering” wakes away from downstream turbines. However, trade-offs between the gains in power production and fatigue loads induced by this control strategy are the subject of continuing investigation. In this study, we present a multifidelity multiobjective optimization approach for exploring the Pareto front of trade-offs between power and loading during wake steering. A large eddy simulation is used as the high-fidelity model, where an actuator line representation is used to model wind turbine blades and a rainflow-counting algorithm is used to compute damage equivalent loads. A coarser simulation with a simpler loads model is employed as a supplementary low-fidelity model. Multifidelity Bayesian optimization is performed to iteratively learn both a surrogate of the low-fidelity model and an additive discrepancy function, which maps the low-fidelity model to the high-fidelity model. Each optimization uses the expected hypervolume improvement acquisition function, weighted by the total cost of a proposed model evaluation in the multifidelity case. The multifidelity approach is able to capture the logit function shape of the Pareto frontier at a computational cost only 30 % that of the single-fidelity approach. Additionally, we provide physical insights into the vortical structures in the wake that contribute to the Pareto front shape.

17 WIND ENERGY↗
DOE OSTI2025

Derivative-free stochastic optimization via adaptive sampling strategies

In this paper, we present a novel derivative-free framework for solving unconstrained stochastic optimization problems. Many problems in fields ranging from simulation optimization to reinforcement learning to quantum computing involve settings where only stochastic function values are obtained via a zeroth-order oracle, which has no available gradient information and necessitates the usage of derivative-free optimization methodologies. Our approach includes estimating gradients using stochastic function evaluations and integrating adaptive sampling techniques to control the accuracy in these stochastic approximations. Our framework encapsulates several gradient estimation techniques, including standard finite-difference, Gaussian smoothing, sphere smoothing, randomized coordinate finite-difference, and randomized subspace finite-difference methods. We provide theoretical convergence guarantees for our framework and analyze the worst-case iteration and sample complexities associated with each gradient estimation method. Finally, we demonstrate the empirical performance of the methods on logistic regression and nonlinear least squares problems.

Adaptive sampling↗
DOE OSTI2025

Digital Safety Analysis for Small Modular Nuclear Reactors (SMRs)

A Documented Safety Analysis (DSA) is a Department of Energy (DOE) construct that defines the extent to which a nuclear facility can be operated safely. It includes a description of hazards, safe boundaries, and hazard controls. The authors assert that a Digital Safety Analysis (DgSA) is far superior to a legacy DSA for several reasons: • The underling database is structured such that it is possible to perform a comprehensive design review and safety analysis by iterating systematically across a hierarchy of linked objects versus a redundant and spotty review by entities of various abilities under unknown resource and schedule constraints. • The analysis of a new design can discover elements that are similar to elements in previous designs. The discovery of similarities is made possible by using the same structure for the underlying database for each new DgSA. The “prior learning” from previous designs is then applied automatically to new designs. • Outputs from the DgSA are from a single source to ensure consistency among various views of the same information. After the DgSA is released, the continued use of a single source implements a configuration management program to ensure consistency between the design basis, the design, the built system, and system procedures. • The development of the DgSA is agile in that any change in a linked object triggers an analysis of impacts on other linked objects and updates of linked objects are made accordingly. After the DgSA is released, the continued maintenance of these links and objects automates the “unreviewed safety question” process.

22 - GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2025

Multigene engineering in plants: Technologies, applications, and future prospects

The emerging bioeconomy presents a promising solution to both economic and environmental challenges. Within the bioeconomy, plants serve as a renewable, sustainable, and cost-effective source of foods, fuels, chemicals, and materials. However, traditional breeding and single-gene engineering approaches fall short in addressing complex traits (e.g., drought tolerance, disease resistance, yield, nutrient use efficiency) which are controlled by multiple genes. The complexity of plant biology often necessitates the use of multigene engineering (MGE), which involves simultaneous ectopic expression, up/down-regulation, or editing of multiple genes, to enhance plant traits relevant to the bioeconomy. These genes may be associated with distinct traits or function as components of specific metabolic and regulatory pathways. This review summarizes current technologies for MGE within the synthetic biology-driven Design-Build-Test-Learn (DBTL) framework, detailing its four key stages: Design – gene construct development; Build – DNA assembly and plant transformation; Test – the molecular, biochemical, and physiological characterization of engineered plants; and Learn – computational modeling to refine, multiplex and iterate the process. Despite good progress in the applications of MGE in biofortification, metabolic engineering, and stress resilience, challenges remain in construct stability, coordinated gene expression, and regulatory predictability. We identified optimization paths and future directions to accelerate MGE deployment in sustainable agriculture, with possible societal benefits including reduced production costs, increased yield, and improved food and nutritional security.

AI-aided plant engineering↗
DOE OSTI2026

Divertor detachment and heat exhaust mitigation control in KSTAR with tungsten divertor

KSTAR has recently undergone an upgrade to use a new tungsten divertor to run experiments in ITER-relevant scenarios. Even with a high melting point of tungsten, it is important to control the heat flux impinging on tungsten divertor targets to minimize sputtering and contamination of the core plasma. Heat flux on the divertor is often controlled by increasing the degree of detachment of scrape-off layer plasma from the target plates. In this work, we have demonstrated successful divertor detachment and heat exhaust dissipation control experiments using two different methods. The first method uses attachment fraction as a control variable which is estimated using ion saturation current measurements from embedded Langmuir probes in the divertor. The second method uses a novel machine-learning-based surrogate model of 2D UEDGE simulation database, DivControlNN. We demonstrated running inference operation of DivControlNN in realtime to estimate heat flux at the divertor and use it as the control variable in a feedback loop with impurity gas flow. We present interesting insights from these experiments including a systematic approach to tuning controllers and discuss future improvements in the control infrastructure and control variables for future burning plasma experiments.

KSTAR tungsten divertor operations↗
DOE OSTI2021

A persistent adjoint method with dynamic time-scaling and an application to mass action kinetics

In this article, we consider an optimization problem where the objective function is evaluated at the fixed-point of a contraction mapping parameterized by a control variable, and optimization takes place over this control variable. Since the derivative of the fixed-point with respect to the parameter can usually not be evaluated exactly, an adjoint dynamical system can be used to estimate gradients. Using this estimation procedure, the optimization algorithm alternates between derivative estimation and an approximate gradient descent step. We analyze a variant of this approach involving dynamic time-scaling, where after each parameter update the adjoint system is iterated until a convergence threshold is passed. Here, we prove that, under certain conditions, the algorithm can find approximate stationary points of the objective function. We demonstrate the approach in the settings of an inverse problem in chemical kinetics, and learning in attractor networks.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Equation-Free Coarse Control of Distributed Parameter Systems via Local Neural Operators

The control of high-dimensional distributed parameter systems (DPS) remains a challenge when explicit coarse-grained equations are unavailable. Classical equation-free (EF) approaches rely on fine-scale simulators treated as black-box timesteppers. However, repeated simulations for steady-state computation, linearization, and control design are often computationally prohibitive, or the microscopic timestepper may not even be available, leaving us with data as the only resource. We propose a data-driven alternative that uses local neural operators, trained on spatiotemporal microscopic/mesoscopic data, to obtain efficient short-time solution operators. These surrogates are employed within Krylov subspace methods to compute coarse steady and unsteady-states, while also providing Jacobian information in a matrix-free manner. Krylov-Arnoldi iterations then approximate the dominant eigenspectrum, yielding reduced models that capture the open-loop slow dynamics without explicit Jacobian assembly. Both discrete-time Linear Quadratic Regulator (dLQR) and pole-placement (PP) controllers are based on this reduced system and lifted back to the full nonlinear dynamics, thereby closing the feedback loop.

93B52, 93C20, 47N70, 65J15, 65M32, 68T07, 68T20, 6↗
DOE OSTI2021

An adaptive Hessian approximated stochastic gradient MCMC method

Bayesian approaches have been successfully integrated into training deep neural networks. One popular family is stochastic gradient Markov chain Monte Carlo methods (SG-MCMC), which have gained increasing interest due to their ability to handle large datasets and the potential to avoid overfitting. Although standard SG-MCMC methods have shown great performance in a variety of problems, they may be inefficient when the random variables in the target posterior densities have scale differences or are highly correlated. Here, we present an adaptive Hessian approximated stochastic gradient MCMC method to incorporate local geometric information while sampling from the posterior. The idea is to apply stochastic approximation (SA) to sequentially update a preconditioning matrix at each iteration. The preconditioner possesses second-order information and can guide the random walk of a sampler efficiently. Instead of computing and saving the full Hessian of the log posterior, we use limited memory of the samples and their stochastic gradients to approximate the inverse Hessian-vector multiplication in the updating formula. Moreover, by smoothly optimizing the preconditioning matrix via SA, our proposed algorithm can asymptotically converge to the target distribution with a controllable bias under mild conditions. To reduce the training and testing computational burden, we adopt a magnitude-based weight pruning method to enforce the sparsity of the network. Our method is user-friendly and demonstrates better learning results compared to standard SG-MCMC updating rules. The approximation of inverse Hessian alleviates storage and computational complexities for large dimensional models. Numerical experiments are performed on several problems, including sampling from 2D correlated distribution, synthetic regression problems, and learning the numerical solutions of heterogeneous elliptic PDE. The numerical results demonstrate great improvement in both the convergence rate and accuracy.

97 MATHEMATICS AND COMPUTING↗