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Deep-Learning-Based Koopman Modeling for Online Control Synthesis of Nonlinear Power System Transient Dynamics
Power system stability and control have become more challenging due to the increasing uncertainty associated with renewable generation. Here, the performance of conventional control is highly driven by the physics-based offline-developed dynamic models that can deviate from the actual system characteristics under different operating conditions and/or configurations. Data-driven approaches based on online measurements can be a better solution to addressing these issues by capturing real-time operation conditions. This article describes a novel fully data-driven probabilistic framework to derive a linear representation of postcontingency grid dynamics and online prescribe control based on the derived model to enhance transient stability. The complex nonlinear power system dynamics is approximated by a linear model by using multiple neural network modules that infer distributions of the observations and introducing a Koopman layer to sample possible Koopman linear models from the inferred distributions. The trained model features linearity that can be easily incorporated into the existing linear control design paradigm and ease the controller design process. The effectiveness of Koopman-based control designs is validated through comparative case studies, which demonstrate increased prediction accuracy and control performance when applied to a power system with heterogeneous generator dynamics.
Semi-supervised Learning of Dynamical Systems with Neural Ordinary Differential Equations: A Teacher-Student Model Approach
Modeling dynamical systems is crucial for a wide range of tasks, but it remains challenging due to complex nonlinear dynamics, limited observations, or lack of prior knowledge. Recently, data-driven approaches such as Neural Ordinary Differential Equations (NODE) have shown promising results by leveraging the expressive power of neural networks to model unknown dynamics. However, these approaches often suffer from limited labeled training data, leading to poor generalization and suboptimal predictions. On the other hand, semi-supervised algorithms can utilize abundant unlabeled data and have demonstrated good performance in classification and regression tasks. We propose TS-NODE, the first semi-supervised approach to modeling dynamical systems with NODE. TS-NODE explores cheaply generated synthetic pseudo rollouts to broaden exploration in the state space and to tackle the challenges brought by lack of ground-truth system data under a teacher-student model. TS-NODE employs an unified optimization framework that corrects the teacher model based on the student's feedback while mitigating the potential false system dynamics present in pseudo rollouts. TS-NODE demonstrates significant performance improvements over a baseline Neural ODE model on multiple dynamical system modeling tasks.
Conin
SAND2025-07645O Conin is a Python library that supports constrained analysis of probabilistic graphical models (PGMs). It enables constrained inference and learning for hidden Markov models, Bayesian networks, dynamic Bayesian networks, and Markov networks. Conin interfaces with the pgmpy library to specify general probabilistic graphical models with a variety of optimization solvers to support learning and inference. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.
Matrix-Model Simulations Using Quantum Computing, Deep Learning, and Lattice Monte Carlo
Matrix quantum mechanics plays various important roles in theoretical physics, such as a holographic description of quantum black holes, and it underpins the only practical numerical approach to the study of complex high-dimensional supergravity theories. Understanding quantum black holes and the role of entanglement in a holographic setup is of paramount importance for the realization of a quantum theory of gravity. Moreover, a complete numerical understanding of the holographic duality and the emergence of geometric space-time features from microscopic degrees of freedom could pave the way for new discoveries in quantum information science. Euclidean lattice Monte Carlo simulations are the de facto numerical tool for understanding the spectrum of large matrix models and have been used to test the holographic duality. However, they are not tailored to extract dynamical properties or even the quantum wave function of the ground state of matrix models. Quantum computing and deep learning provide potentially useful approaches to study the dynamics of matrix quantum mechanics. If successful in the context of matrix models, these rapidly improving numerical techniques could become the new Swiss army knife of quantum gravity practitioners. In this paper, we perform the first systematic survey for quantum computing and deep-learning approaches to matrix quantum mechanics, comparing them to lattice Monte Carlo simulations. These provide baseline benchmarks before addressing more complicated problems. In particular, we test the performance of each method by calculating the low-energy spectrum.
Chemical evolution in nitrogen shocked beyond the molecular stability limit
Evolution of nitrogen under shock compression up to 100 GPa is revisited via molecular dynamics simulations using a machine-learned interatomic potential. The model is shown to be capable of recovering the structure, dynamics, speciation, and kinetics in hot compressed liquid nitrogen predicted by first-principles molecular dynamics, as well as the measured principal shock Hugoniot and double shock experimental data, albeit without shock cooling. Our results indicate that a purely molecular dissociation description of nitrogen chemistry under shock compression provides an incomplete picture and that short oligomers form in non-negligible quantities. Finally, this suggests that classical models representing the shock dissociation of nitrogen as a transition to an atomic fluid need to be revised to include reversible polymerization effects.
Seismicity-constrained fault detection and characterization with a multitask machine learning model
Geological fault detection and characterization are crucial for understanding subsurface dynamics across scales. While methods for fault delineation based on either seismicity location analysis or seismic image reflector discontinuity are well-established, a systematic approach that integrates both data types remains absent. We develop a novel machine learning model that unifies seismic reflector images and seismicity location information to automatically identify geological faults and characterize their geometrical properties. The model encodes a seismic image and a seismicity location image separately, and fuses the encoded features with a spatial-channel attention fusion module to improve the learning of important features in both inputs. We design an automated strategy to generate high-quality synthetic training data and labels. To improve the realism of the seismicity location image, we include random seismicity noise and missing seismicity location associated with some of the faults. We validate the model’s efficacy and accuracy using synthetic data examples and two field data examples. Moreover, we show that fine-tuning the trained model with a small, domain-specific dataset enhances its fidelity for field data applications. The results demonstrate that integrating seismicity location and seismic images into a unified framework allows the end-to-end neural network to achieve higher fidelity and accuracy in delineating subsurface faults and their geometrical properties compared with image-only fault detection methods. Our approach offers an adaptive data-driven tool for geological fault characterization and seismic hazard mitigation, bridging the gap between seismicity location and image-based fault detection methods.
Electrochemical Characterization of Molten Salt Chemistry During Atmospheric Ingressions
This report describes the salt chemistry and sedimentation studies that were completed in FY23 as part of the Pyrochemical Fuel Cycles – ANL project. The primary objective of these activities was to employ electrochemical methods in order to quantify and gain insights into the reaction mechanisms associated with the interaction of O2 and moisture impurities with the molten chloride salts used for the pyrochemical processing of nuclear materials. If not monitored and controlled, the ingression of these atmospheric impurities can lead to changes in the salt redox conditions and initiate the formation of oxide particles, potentially resulting in operational and safeguards challenges. By elucidating the mechanisms underlying the formation of oxide particles, we can effectively monitor the conditions of the salt and design systems to mitigate the influence of atmospheric O2 and H2O. To achieve these goals, we designed a test system that allowed for precisely controlled gas ingressions into the molten salt vessel. This system included on-line monitoring provided by electrochemical probes that enable near real-time measurements of the salt conditions throughout the course of the experiment. Using this system, we systematically varied experimental conditions, including O2/Ar flow rates and O2 concentrations, to comprehensively understand their impact on solid particle formation. We also used a particle size and shape analyzer to characterize the particles that were generated. Tests in FY23 concentrated on the formation of CeO2 particles, but we also prepared a separate apparatus targeting UO2 particles for use in FY24. We additionally conducted extensive modeling activities in support of this work. This included multiphysics simulations of the gas ingressions along with the development of a machine learning workflow to enable accelerated molecular dynamics modeling of the molten salt chemistry of LiCl-KCl-UCl3. The combination of experimental and modeling tools has allowed us to begin to get a more complete understanding of the reactions that occur when atmospheric ingressions occur in pyroprocessing systems.
Operator inference for non-intrusive model reduction with quadratic manifolds
This paper proposes a novel approach for learning a data-driven quadratic manifold from high-dimensional data, then employing this quadratic manifold to derive efficient physics-based reduced-order models. The key ingredient of the approach is a polynomial mapping between high-dimensional states and a low-dimensional embedding. This mapping consists of two parts: a representation in a linear subspace (computed in this work using the proper orthogonal decomposition) and a quadratic component. The approach can be viewed as a form of data-driven closure modeling, since the quadratic component introduces directions into the approximation that lie in the orthogonal complement of the linear subspace, but without introducing any additional degrees of freedom to the low-dimensional representation. Combining the quadratic manifold approximation with the operator inference method for projection-based model reduction leads to a scalable non-intrusive approach for learning reduced-order models of dynamical systems. Further, applying the new approach to transport-dominated systems of partial differential equations illustrates the gains in efficiency that can be achieved over approximation in a linear subspace.
Melting curves of ice polymorphs in the vicinity of the liquid–liquid critical point
The possible existence of a liquid–liquid critical point in deeply supercooled water has been a subject of debate due to the challenges associated with providing definitive experimental evidence. The pioneering work by Mishima and Stanley [Nature 392, 164–168 (1998)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected liquid–liquid transition and its associated critical point. Based on the continuous or discontinuous changes in the slope of the melting curves, Mishima [Phys. Rev. Lett. 85, 334 (2000)] suggested that the liquid–liquid critical point lies between the melting curves of ice III and ice V. Herein we explore this conjecture using molecular dynamics simulations with a machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII and find that all of them are supercritical and do not intersect the liquid–liquid transition locus. We also find a pronounced, yet continuous, change in the slope of the melting lines upon crossing of the liquid locus of maximum compressibility. Finally, we analyze the literature in light of our findings and conclude that the scenario in which the melting curves are supercritical is favored by the most recent computational and experimental evidence. Although the preponderance of evidence is consistent with the existence of a second critical point in water, the behavior of ice polymorph melting lines does not provide strong evidence in support of this viewpoint, according to our calculations.
Coding the Computing Continuum: Fluid Function Execution in Heterogeneous Computing Environments
Advances in network technologies have greatly decreased barriers to accessing physically distributed computers. This newfound accessibility coincides with increasing hardware specialization, creating exciting new opportunities to dispatch workloads to the best resource for a specific purpose, rather than those that are closest or most easily accessible. We present Delta, a service designed to intelligently schedule function-based workloads across a distributed set of heterogeneous computing resources. Delta implements an extensible architecture in which different predictors and scheduling algorithms can be integrated to provide dynamically evolving estimates of function execution times on different resources-estimates that can be used to determine the most appropriate location for execution. We describe predictors for function runtime, data transfer time, and cold-start resource provisioning and configuration delay; dynamic learning methods that update predictor models over time; and scheduling strategies that take into account both function and endpoint information. We show that these methods can halve workload makespan when compared with a strategy that selects the fastest resource, and decrease makespan by a factor of five when compared to a round robin strategy, when deployed on a heterogeneous testbed with resources ranging from a Raspberry Pi to a GPU node in an academic cloud.
Machine Learning-Based Regression Models for Ironmaking Blast Furnace Automation
Computational fluid dynamics (CFD)-based simulation has been the traditional way to model complex industrial systems and processes. One very large and complex industrial system that has benefited from CFD-based simulations is the steel blast furnace system. The problem with the CFD-based simulation approach is that it tends to be very slow for generating data. The CFD-only approach may not be fast enough for use in real-time decisionmaking. To address this issue, in this work, the authors propose the use of machine learning techniques to train and test models based on data generated via CFD simulation. Regression models based on neural networks are compared with tree-boosting models. In particular, several areas (tuyere, raceway, and shaft) of the blast furnace are modeled using these approaches. The results of the model training and testing are presented and discussed. The obtained R 2 metrics are, in general, very high. The results appear promising and may help to improve the efficiency of operator and process engineer decisionmaking when running a blast furnace.
Learning of networked spreading models from noisy and incomplete data
Recent years have seen a lot of progress in algorithms for learning parameters of spreading dynamics from both full and partial data. Some of the remaining challenges include model selection under the scenarios of unknown network structure, noisy data, missing observations in time, as well as an efficient incorporation of prior information to minimize the number of samples required for an accurate learning. Here, in this work, we introduce a universal learning method based on a scalable dynamic message-passing technique that addresses these challenges often encountered in real data. The algorithm leverages available prior knowledge on the model and on the data, and reconstructs both network structure and parameters of a spreading model. We show that a linear computational complexity of the method with the key model parameters makes the algorithm scalable to large network instances.
Data-driven recovery of hidden physics in reduced order modeling of fluid flows
In this article, we introduce a modular hybrid analysis and modeling (HAM) approach to account for hidden physics in reduced order modeling (ROM) of parameterized systems relevant to fluid dynamics. The hybrid ROM framework is based on using first principles to model the known physics in conjunction with utilizing the data-driven machine learning tools to model the remaining residual that is hidden in data. This framework employs proper orthogonal decomposition as a compression tool to construct orthonormal bases and Galerkin projection (GP) as a model to build the dynamical core of the system. Our proposed methodology hence compensates structural or epistemic uncertainties in models and utilizes the observed data snapshots to compute true modal coefficients spanned by these bases. The GP model is then corrected at every time step with a data-driven rectification using a long short-term memory (LSTM) neural network architecture to incorporate hidden physics. A Grassmannian manifold approach is also adopted for interpolating basis functions to unseen parametric conditions. The control parameter governing the system's behavior is thus implicitly considered through true modal coefficients as input features to the LSTM network. The effectiveness of the HAM approach is then discussed through illustrative examples that are generated synthetically to take hidden physics into account. Furthermore, our approach thus provides insights addressing a fundamental limitation of the physics-based models when the governing equations are incomplete to represent underlying physical processes.
Constrained Block Nonlinear Neural Dynamical Models
Neural network modules conditioned by known priors can be effectively trained and combined to represent systems with nonlinear dynamics. This work explores a novel formulation for data-efficient learning of deep control-oriented nonlinear dynamical models by embedding local model structure and constraints. The proposed method consists of neural network blocks that represent input, state, and output dynamics with constraints placed on the network weights and system variables. For handling partially observable dynamical systems, we utilize a state observer neural network to estimate the states of the system's latent dynamics. We evaluate the performance of the proposed architecture and training methods on system identification tasks for three nonlinear systems: a continuous stirred tank reactor, a two tank interacting system, and an aerodynamics body. Models optimized with a few thousand system state observations accurately represent system dynamics in open loop simulation over thousands of time steps from a single set of initial conditions. Experimental results demonstrate an order of magnitude reduction in open-loop simulation mean squared error for our constrained, block-structured neural models when compared to traditional unstructured and unconstrained neural network models.
Efficient learning of power grid voltage control strategies via model-based deep reinforcement learning
Here this article proposes a model-based deep reinforcement learning (DRL) method to design emergency control strategies for short-term voltage stability problems in power systems. Recent advances show promising results for model-free DRL-based methods in power systems control problems. But in power systems applications, these model-free methods have certain issues related to training time (clock time) and sample efficiency; both are critical for making state-of-the-art DRL algorithms practically applicable. DRL-agent learns an optimal policy via a trial-and-error method while interacting with the real-world environment. It is also desirable to minimize the direct interaction of the DRL agent with the real-world power grid due to its safety-critical nature. Additionally, the state-of-the-art DRL-based policies are mostly trained using a physics-based grid simulator where dynamic simulation is computationally intensive, lowering the training efficiency. We propose a novel model-based DRL framework where a deep neural network (DNN)-based dynamic surrogate model (SM), instead of a real-world power grid or physics-based simulation, is utilized within the policy learning framework, making the process faster and more sample efficient. However, having stable training in model-based DRL is challenging because of the complex system dynamics of large-scale power systems. We addressed these issues by incorporating imitation learning to have a warm start in policy learning, reward-shaping, and multi-step loss in surrogate model training. Finally, we achieved 97.5% reduction in samples and 87.7% reduction in training time for an application to the IEEE 300-bus test system.
Enhancement of Unsteady and 3D Aerodynamics Models using Machine Learning
Unsteady aerodynamics will be an important part of the floating wind turbines of the future operating under high shear across the rotor disk coupled with platform motion and atmospheric turbulence. We develop an unsteady aerodynamics and dynamic stall model using a long short-term memory variant of recurrent neural networks. The neural network model is trained using the oscillating airfoil data set from Ohio State University. The predictions from our machine learning (ML)-based model show good agreement with the experimental data and other state-of-the-art dynamic stall models for a wide range of airfoils, Reynolds numbers and reduced frequencies. In some cases the predictions are better than the Beddoes-Leishman model implementation in OpenFAST, when using the default coefficients. The ML-based model is also able to capture the key physics associated with dynamic stall, such as the precedence of moment stall before lift stall and cycle-to-cycle variations in the aerodynamic response. The new unsteady aerodynamics model is expected to improve prediction of fatigue loads for yaw-based wake-steering control scenarios in actuator-line and actuator-disc simulations of wind farms. Our methodology for training the ML-model provides a pathway for improving design level tools using high-fidelity computational fluid dynamics (CFD) simulations in the future.
Physics-informed machine learning modeling for predictive control using noisy data
Due to the occurrence of over-fitting at the learning phase, the modeling of chemical processes via artificial neural networks (ANN) by using corrupted data (i.e., noisy data) is an ongoing challenge. Therefore, this work investigates the effect of both Gaussian and non-Gaussian noise on the performance of process-structure based recurrent neural networks (RNN) models, which take the form of partially-connected RNN models in this work, that are used to approximate a class of multi-input-multi-outputs nonlinear systems. Furthermore, two different techniques, specifically Monte Carlo dropout and co-teaching, are utilized in the development of partially-connected RNN models. Here, these two techniques are employed to reduce the over-fitting in ANNs when noisy data is used in the training process and, hence, to improve the open-loop accuracy as well as the closed-loop performance under a Lyapunov-based model predictive controller (MPC). Aspen Plus Dynamics, a well-known high-fidelity process simulator, is used to simulate a large-scale chemical process application in order to demonstrate the anticipated improvements in both open-loop approximation and closed-loop controller performance in the presence of Gaussian and non-Gaussian noise in the data set using physics-informed RNNs.