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DOE OSTI2026

Identifying stochastic dynamics via finite expression methods

Modeling stochastic differential equations (SDEs) is crucial for understanding complex dynamical systems in various scientific fields. Recent methods often employ neural network-based models, which typically represent SDEs through a combination of deterministic and stochastic terms. However, these models usually lack interpretability and have difficulty in generalizing beyond their training domain. Here, this paper introduces the Finite Expression Method (FEX), a symbolic learning approach designed to derive interpretable mathematical representations of the deterministic component of SDEs. For the stochastic component, we integrate FEX with advanced generative modeling techniques to provide a comprehensive representation of SDEs. The numerical experiments on linear, nonlinear, and multidimensional SDEs demonstrate that FEX generalizes well beyond the training domain and delivers more accurate long-term predictions compared to neural network-based methods. The symbolic expressions identified by FEX not only improve prediction accuracy but also offer valuable scientific insights into the underlying dynamics of the systems.

Complex dynamical systems↗

DOE OSTI2026

Dynamical Downscaling of Earth System Model Data for Energy System Analysis

Assessing energy resources (e.g., solar, wind, and hydro) under future scenarios requires datasets with sufficient spatial and temporal detail to capture variability and extreme events. While global-scale Earth System Model (ESM) projections are widely used, their coarse resolution limits direct application to regional energy system analyses. Dynamical downscaling offers a robust approach to generate physically consistent, fine-scale datasets that better represent local atmospheric processes impacting energy resources. In this work, we present a two-stage approach for producing high-resolution historical and future projections over the contiguous United States (CONUS). First, we optimize the Weather Research and Forecasting (WRF) model configuration for energy-relevant variables - solar irradiance, wind speed, and precipitation - by conducting ERA5-driven simulations at 8-km and 28-km resolution. Multiple physics schemes and model configurations within the WRF are evaluated against observational datasets including the National Solar Radiation Database (NSRDB), the Parameter-elevation Regressions on Independent Slopes Model (PRISM), and the Stage IV multi-radar/multi-sensor precipitation product for the CONUS domain. Using the best-performing configuration, we dynamically downscale MPI-ESM1-2-HR simulations for 2000-2060 under SSP2-4.5 and SSP5-8.5 scenarios at 4-km spatial and hourly temporal resolution. This presentation will provide a comprehensive analysis of the results from multiple numerical experiments and high-resolution ESM projections. In addition, we will discuss potential applications of our high-resolution datasets within the energy sector and outline future research avenues dedicated to evaluating how extreme weather events influence system performance and resilience.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Modeling COVID-19 Impacts on Prison Population

The goal of this project was to develop a unique, high-level, concept model that will (1) help examine the consequences COVID-19 has had on prison population and flow dynamics in Illinois and (2) explore (to the extent possible) how that will unfold in the short- and mid-term future. Argonne has unique expertise in dynamic systems modeling and highly specialized simulation capabilities, which will be helpful in developing such a model. The ultimate objective of this CRADA is to develop with the Illinois Public Sentencing Policy Advisory Council (SPAC) the capability to identify and understand factors and interactions associated with prison population and flow dynamics in Illinois. This understanding will then potentially lead to improvements in the allocation of various resources and services. This approach would also be useful to other states.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2024

Energy Analysis of Combi Heat Pump System Configurations for Space Conditioning and Domestic Hot Water Heating in Residential Buildings

Combi heat pump systems, also referred to multifunctional variable refrigerant flow heat recovery (MF-VRFHR) systems, are specifically designed for residential applications to manage both space conditioning and domestic hot water (DHW). They have attracted attention due to their potential for energy conservation through heat recovery. The incorporation of a hot water tank introduces various system configurations, each characterized by distinct pros and cons related to energy efficiency, system stability, and maintenance. Despite this, a critical gap exists as the specific energy performance remains unquantified under diverse operational modes (e.g., heating mode and heat recovery mode). This paper aims to bridge this gap by conducting a comprehensive comparative analysis of two prevalent system configurations while considering feasible proposed control logics. Configuration 1 integrates a separate hot water tank and a refrigerant-to-water heat exchanger (HEX), also known as a Hydro Kit while Configuration 2 incorporates a refrigerant-wrapped hot water tank. To facilitate this analysis, we developed high-fidelity system models for both configurations in Modelica, capturing system dynamics and detailed control sequences effectively. These system models were built upon the TIL library for HVAC equipment components and the Buildings library for residential building thermal load calculations. The validation of the simulation testbed utilized data from experiments conducted in the PNNL lab home for Configuration 1. To establish the simulation testbed for Configuration 2, we extended the modeling setup derived from Configuration 1. This extension specifically involved substituting the separate hot water tank and Hydro Kit with a refrigerant-wrapped hot water tank of similar sizing sourced from an actual product. The simulation analysis of heating-only and heat recovery modes reveals that Configuration 2 not only saves energy and maintains warmer tank temperatures but also demonstrates faster water heating capabilities. This is attributed to decreased energy loss and improved heat transfer. The study encompasses a wide range of scenarios, considering diverse thermal loads and water usage patterns across heating and heat recovery modes. Overall, the comprehensive results indicate that Configuration 2 achieves energy savings ranging from 3.5% to 12.2% compared to Configuration 1, depending on factors such as water usage patterns, thermal loads, and operational modes.

Configuration, Comparison, Multi-functional, Resid↗

DOE OSTI2025

Efficient Streaming Dynamic Mode Decomposition

We propose a reformulation of the streaming dynamic mode decomposition method that requires maintaining a single orthonormal basis, thereby reducing computational redundancy. The proposed efficient streaming dynamic mode decomposition method results in a constant-factor reduction in computational complexity and memory storage requirements. Numerical experiments on representative canonical dynamical systems show that the enhanced computational efficiency does not compromise the accuracy of the proposed method.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Scenario storyline discovery for complex multi-actor human-natural systems

This poster was presented at the AGU Fall Meeting 2024. Abstract:Scenario analysis is a useful tool for assessing the impacts of future conditions or alternative strategies. However, the common practice of focusing on a small number of predetermined scenarios can limit our understanding of key uncertainties, and fail to represent diverse stakeholder impacts. Exploratory modeling approaches have been developed to address these issues by simulating a wide range of possible futures and system perspectives. A challenge with these approaches is that they often involve large ensemble experiments which limit interpretability and usability. We recently introduced the FRamework for Narrative Storylines and Impact Classification (FRNSIC; pronounced ``forensic''), a scenario discovery framework that helps users identify scenario storylines that capture key system dynamics and as well as important outcomes. In this poster presentation, we present training materials to support the generalizable application of the framework to other multi-actor systems with complex dynamics. Specifically, we will present a step-by-step methodological typology of tools and methods that can be used to generate and classify plausible states of the world on key metrics and consequential dynamics. The typology will also discuss potential implications of these choices and their applicability to different systems.

Colorado River↗

DOE OSTI2024

Bayesian inference of structured latent spaces from neural population activity with the orthogonal stochastic linear mixing model

The brain produces diverse functions, from perceiving sounds to producing arm reaches, through the collective activity of populations of many neurons. Determining if and how the features of these exogenous variables (e.g., sound frequency, reach angle) are reflected in population neural activity is important for understanding how the brain operates. Often, high-dimensional neural population activity is confined to low-dimensional latent spaces. However, many current methods fail to extract latent spaces that are clearly structured by exogenous variables. This has contributed to a debate about whether or not brains should be thought of as dynamical systems or representational systems. Here, we developed a new latent process Bayesian regression framework, the orthogonal stochastic linear mixing model (OSLMM) which introduces an orthogonality constraint amongst time-varying mixture coefficients, and provide Markov chain Monte Carlo inference procedures. We demonstrate superior performance of OSLMM on latent trajectory recovery in synthetic experiments and show superior computational efficiency and prediction performance on several real-world benchmark data sets. We primarily focus on demonstrating the utility of OSLMM in two neural data sets: μ ECoG recordings from rat auditory cortex during presentation of pure tones and multi-single unit recordings form monkey motor cortex during complex arm reaching. We show that OSLMM achieves superior or comparable predictive accuracy of neural data and decoding of external variables (e.g., reach velocity). Most importantly, in both experimental contexts, we demonstrate that OSLMM latent trajectories directly reflect features of the sounds and reaches, demonstrating that neural dynamics are structured by neural representations. Together, these results demonstrate that OSLMM will be useful for the analysis of diverse, large-scale biological time-series datasets.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2026

Learning thermodynamic master equations for open quantum systems

The characterization of Hamiltonians and other components of open quantum dynamical systems plays a crucial role in quantum computing and other applications. Scientific machine learning techniques have been applied to this problem in a variety of ways, including by modeling with deep neural networks. However, the majority of mathematical models describing open quantum systems are linear, and the natural nonlinearities in learnable models have not been incorporated using physical principles. We present a data-driven model for open quantum systems that includes learnable, thermodynamically consistent terms. The trained model is interpretable, as it directly estimates the system Hamiltonian and linear components of coupling to the environment. We validate the model on synthetic two and three-level data, as well as experimental two-level data collected from a quantum device at Lawrence Livermore National Laboratory.

Mathematics and Computing↗

DOE OSTI2024

Modeling and Analysis of a Heat Pump Clothes Dryer with Thermal Energy Storage

Clothes drying is an energy-intensive process that causes significant electricity consumption and carbon emissions in the US. Approximately 83% of Households in the US own a tumble clothes dryer at home and 80% of dryers are electrical resistance dryers with low energy efficiency. Heat pump technology makes it possible for highly efficient and clean drying. Additionally, the ventless design of heat pump clothes dryers (HPCD) provides more installation flexibility. HPCD involves three primary mediums: wet clothes, a closed air loop, and a refrigerant circuit. The evaporator is used to dehumidify the wet air and the condenser is used to re-heat the dry air. One of the critical technological barriers to HPCD market penetration is its long drying time, primarily due to the relatively low discharging temperature and the slow response during the warm-up period. In this study, the thermal energy storage (TES) technology is adopted to address this challenge by providing pre-heating of air prior to the condenser to increase the operating temperature of the process air. The heat pump will charge the phase change material (PCM) in the TES device with heating energy during clothes washing and the PCM will discharge the stored heat to facilitate air heating during clothes drying. To analyze the optimal design and potential for energy saving and drying time reduction, a mathematical model of the HPCD system was developed. The HPCD is a highly dynamic system with a coupled heat and mass transfer and heat pumping cycle. This paper provides solutions to simulate the transient behavior of the system while maintaining low computational cost. The modeling result indicates reduced energy consumption and drying time by integrating TES with HPCD, as compared to electrical resistance dryers. The study can provide significant insights into improving building flexibility with TES and smart appliances.

Liu, Xiaoli↗

DOE OSTI2025

Dynamic probabilistic risk assessment and game theory for cyber security risk analysis in nuclear power plants

Nuclear Power Plants and energy systems have become more prone to cyber-attacks with their digitalization and the increased use of smart equipment. Hence, it is important to quantify the risk associated with cyber-attacks in such systems. Dynamic Probabilistic Risk Assessment which involves studying the evolution of a system due to random events and operator and attacker actions during a cyber-attack by employing a physics-based model of the system is a suitable framework to quantify cybersecurity risk in nuclear power plants. In addition to the plant dynamics, it is also important to model the strategies of the attackers and plant operators for an effective cybersecurity risk assessment. Game theory provides a set of necessary tools to model such strategic interactions. In this research, a framework that integrates dynamic probabilistic risk assessment with game theory for cybersecurity risk analysis in nuclear power plants is presented. The mathematical formulation is derived based on the theory of continuous event trees. We propose a game theory based action model, that utilizes physics-based rewards to define the strategies of attackers and operators at every decision epoch. As a case study, the risk associated with cyber-attacks on the digital components in the secondary side of a pressurized water reactor is studied using a reduced order model. A set of attacker actions and a set of operator actions are defined for the system. The operator and attacker interactions were modelled using simultaneous game, their action policies were computed using the concept of mixed strategy Nash equilibrium and the evolution of the system was studied.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

A Generation-Storage Coordination Dispatch Strategy for Power System Based on Causal Reinforcement Learning

In the backdrop of global energy transformation, power systems integrating high proportions of renewable energy sources are facing unprecedented challenges in operational stability and dispatch efficiency. To address these challenges, this study introduces a generation-storage coordination real-time dispatch strategy based on Causal Power System Dynamic Reinforcement Learning (CPSDRL). Diverging from traditional reinforcement learning approaches, CPSDRL innovatively incorporates causal inference within the state prediction model - the crux of model-based reinforcement learning - thereby establishing the Power Causal Dynamic Model (PCDM). Assisted by the prior knowledge of power systems, the model significantly enhances prediction accuracy and reliability through a two-stage training process. Utilizing PCDM, this study further applies a direct policy search algorithm to optimize the real-time dispatch strategy. Experimental results indicate that the proposed method improves the stability of generation-storage coordination real-time dispatch and exhibits competitive advantages in sample efficiency and computational speed, compared to traditional model-based and model-free reinforcement learning algorithms. This method is expected to enhance the practicality and adaptability of causal reinforcement learning techniques in power system scheduling and control.

causal reinforcement learning↗

DOE OSTI2026

Latent Twins

Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex systems. From inverse problems to numerical partial differential equations (PDEs), dynamical systems, and model reduction, these advances have pushed the boundaries of what can be simulated. Yet they have often progressed in parallel, with representation learning and algorithmic solution methods evolving largely as separate pipelines. With Latent Twins, we propose a unifying mathematical framework that creates a hidden surrogate in latent space for the underlying equations. Whereas digital twins mirror physical systems in the digital world, Latent Twins mirror mathematical systems in a learned latent space governed by operators. Through this lens, classical modeling, inversion, model reduction, and operator approximation all emerge as special cases of a single principle. We establish the fundamental approximation properties of Latent Twins for both ordinary differential equations (ODEs) and PDEs and demonstrate the framework across three representative settings: (i) canonical ODEs, capturing diverse dynamical regimes; (ii) a PDE benchmark using the shallow-water equations, contrasting Latent Twin simulations with deep operator network and forecasts with a four-dimensional variational method baseline; and (iii) a challenging real-data geopotential reanalysis dataset, reconstructing and forecasting from sparse, noisy observations. Latent Twins provide a compact, interpretable surrogate for solution operators that evaluate across arbitrary time gaps in a single-shot, while remaining compatible with scientific pipelines such as assimilation, control, and uncertainty quantification. Looking forward, this framework offers scalable, theory-grounded surrogates that bridge data-driven representation learning and classical scientific modeling across disciplines.

Latent Twins↗

DOE OSTI2024

Mixed-mode oscillations in a three-timescale coupled Morris–Lecar system

Mixed-mode oscillations (MMOs) are complex oscillatory behaviors of multiple-timescale dynamical systems in which there is an alternation of large-amplitude and small-amplitude oscillations. It is well known that MMOs in two-timescale systems can arise either from a canard mechanism associated with folded node singularities or a delayed Andronov–Hopf bifurcation (DHB) of the fast subsystem. While MMOs in two-timescale systems have been extensively studied, less is known regarding MMOs emerging in three-timescale systems. In this work, we examine the mechanisms of MMOs in coupled Morris–Lecar neurons with three distinct timescales. We investigate two kinds of MMOs occurring in the presence of a singularity known as canard-delayed-Hopf (CDH) and in cases where CDH is absent. In both cases, we examine how features and mechanisms of MMOs vary with respect to variations in timescales. Our analysis reveals that MMOs supported by CDH demonstrate significantly stronger robustness than those in its absence. Moreover, we show that the mere presence of CDH does not guarantee the occurrence of MMOs. This work yields important insights into conditions under which the two separate mechanisms in two-timescale context, canard and DHB, can interact in a three-timescale setting and produce more robust MMOs, particularly against timescale variations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Hybrid Modeling of Three-Phase Grid-Supporting Inverters for Dynamic Studies

Grid technologies connected by power electronic converter (PEC) interfaces continually implement grid support functions mandated by grid codes and standards. The transition to converter-based generation demands precise PEC models to assess system dynamics, which have been previously overlooked in conventional power systems. This study proposes a hybrid method for analyzing grid-connected three-phase PEC dynamics with the IEEE standard 1547-2018 Volt-VAr mode that combines physics and data-driven techniques. The physics model reflects the PEC’s internal behavior, whereas the data-driven modeling technique evaluates the grid-supporting capabilities of the smart PEC. The system identification approach is used to generate dynamic PEC models based on changing grid voltage and measured current injected into the grid by the PEC. In the Volt-VAr support mode, a detailed topological model including switches is utilized to compare the goodness-of-fit of the extracted hybrid dynamic model. The results demonstrate that the hybrid PEC model in the Volt-VAr mode accurately matches the dynamics with the topological model.

Subedi, Sunil↗

DOE OSTI2024

Simultaneous optimal system and controller design for multibody systems with joint friction using direct sensitivities

Abstract Real-world multibody systems are often subject to phenomena like friction, joint clearances, and external events. These phenomena can significantly impact the optimal design of the system and its controller. This work addresses the gradient-based optimization methodology for multibody dynamic systems with joint friction using a direct sensitivity approach. The Brown–McPhee model has been used to characterize the joint friction in the system. This model is suitable for the study due to its accuracy for dynamic simulation and its compatibility with sensitivity analysis. This novel methodology supports codesign of the multibody system and its controller, which is especially relevant for applications like robotics and servo-mechanical systems, where the actuation and design are highly dependent on each other. Numerical results are obtained using a software package written in Julia with state-of-the-art libraries for automatic differentiation and differential equations. Three case studies are provided to demonstrate the attractive properties of simultaneous optimal design and control approach for certain applications.

Verulkar, Adwait↗

DOE OSTI2026

Causality-respecting adaptive refinement for PINNs: enabling precise interface evolution in phase field modeling

Physics-informed neural networks (PINNs) have emerged as a powerful tool for solving physical systems described by partial differential equations (PDEs). However, their accuracy in dynamical systems, particularly those involving sharp moving boundaries with complex initial morphologies, remains a challenge. Here, this study introduces an approach combining residual-based adaptive refinement (RBAR) with causality-informed training to enhance the performance of PINNs in solving spatio-temporal PDEs. Our method employs a three-step iterative process: initial causality-based training, RBAR-guided domain refinement, and subsequent causality training on the refined mesh. Applied to the Allen-Cahn equation, a widely-used model in phase field simulations, our approach demonstrates significant improvements in solution accuracy and computational efficiency over traditional PINNs. Notably, we observe an ‘overshoot and relocate’ phenomenon in dynamic cases with complex morphologies, showcasing the method’s adaptive error correction capabilities. This synergistic interaction between RBAR and causality training enables accurate capture of interface evolution, even in challenging scenarios where traditional PINNs fail. Our framework not only resolves the limitations of uniform refinement strategies but also provides a generalizable methodology for solving a broad range of spatio-temporal PDEs. The enhanced performance of the RBAR–causality combined framework demonstrates its strong potential for advancing PINN-based modeling of physical systems characterized by complex, evolving interfaces.

Allen-Cahn equations↗

DOE OSTI2025

Quantum simulation of charge and exciton transfer in multi-mode models using engineered reservoirs

Quantum simulation enables studies of open-system dynamics in non-perturbative regimes by programming electronic, vibrational, and environmental interactions on comparable energy scales. Trapped ions offer this capability, combining spins, phonons, and tunable dissipation on one platform. We demonstrate an open-system quantum simulation of charge and exciton transfer in a multi-mode linear vibronic coupling model. Using tailored spin-phonon interactions with reservoir engineering, we emulate a system with two dissipative vibrational modes coupled to donor and acceptor sites and track its non-equilibrium dynamics. We continuously tune the system from the charge transfer regime to the vibrationally assisted exciton transfer regime and find that degenerate modes enhance transfer rates at large energy gaps, while non-degenerate modes activate pathways that reduce the energy-gap dependence. Thus, the presence of one additional vibration introduces interfering pathways and reshapes non-perturbative excitation transfer. Our results establish a scalable, hardware-efficient route to simulate vibronic processes with engineered environments.

74 ATOMIC AND MOLECULAR PHYSICS↗

DOE OSTI2025

Open-Source Ambient-Signal-Based Inertia Monitoring Tool for Power systems [SWR-25-59]

This script, developed by NREL, implements an inertia estimation algorithm using a sliding window approach. The inertia (H) is estimated based on frequency deviations and active power deviations, utilizing the swing equation from power system dynamics. An example application is provided using the WECC 240-bus system.

Peng, Jiangkai [National Renewable Energy Laborato↗