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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 OSTI2024

Replica symmetry breaking in spin glasses in the replica-free Keldysh formalism

We show that the algebra of Parisi ultrametric matrices is recovered by the real-time, replica-free, Dyson-Keldysh equations of infinite-range quantum spin glasses in the late time glassy limit. This connects to earlier results on classical and quantum systems showing how ultrametricity emerges from the persistent slow aging dynamics of the glass phase. The stationary spin glass state thereby spontaneously breaks thermal symmetry, or the Kubo-Martin-Schwinger relation of a state in global thermal equilibrium. We describe the Keldysh path integral of the infinite-range Ising model in transverse and longitudinal fields, and in the context of the Landau expansion of the action functional, show how the long-time limit connects to the full replica symmetry breaking obtained in the equilibrium formalism. We also illustrate our formalism by applying it to the spherical quantum p p -spin model, which only exhibits one-step replica symmetry breaking.

Lang, Johannes (ORCID:0000000283533392)↗

DOE OSTI2022

Physics-constrained deep learning of nonlinear normal modes of spatiotemporal fluid flow dynamics

In this study, we present a physics-constrained deep learning method to discover and visualize from data the invariant nonlinear normal modes (NNMs) which contain the spatiotemporal dynamics of the fluid flow potentially containing strong nonlinearity. Specifically, we develop a NNM-physics-constrained convolutional autoencoder (NNM-CNN-AE) integrated with a multi-temporal-step dynamics prediction block to learn the nonlinear modal transformation, the NNMs containing the spatiotemporal dynamics of the flow, and reduced-order reconstruction and long-time future-state prediction of the flow fields, simultaneously. In test cases, we apply the developed method to analyze different flow regimes past a cylinder, including laminar flows with low Reynolds number in transient and steady states (RD = 100) and high Reynolds number flow (RD = 1000), respectively. The results indicate that the identified NNMs are able to reveal the nonlinear spatiotemporal dynamics of these flows, and the NNMs-based reduced-order modeling consistently achieves better accuracy with orders of magnitudes smaller errors in construction and prediction of the nonlinear velocity and vorticity fields, compared to the linear proper orthogonal decomposition (POD) method and the Koopman-constrained-CNN-AE using the same number or dimension of modes. We perform an analysis of the modal energy distribution of NNMs and find that compared to POD modes, the few fundamental NNMs capture a very high level of total energy of the flow, which is advantageous for reduced-order modeling and representation of the complex flows. Finally, we discuss the potentials and limitations of the presented method.

Mechanics↗

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 OSTI2024

Structure preserving and energy dissipative contact approaches for implicit dynamics

In this work, several structure preserving and energy dissipative contact approaches are proposed and evaluated. The time integration schemes considered are general with regard to the version of constraint type, but here the emphasis was on mortar contact. The proposed mortar contact approach conserves both linear and angular momentum for mortar contact in a novel way. The proposed time integration scheme can conserve energy or provide strict contact dissipation. In addition, the proposed scheme enforces both gap constraints and gap velocity constraints (i.e., persistency). Using a midstep time integrator often causes energy dissipation during initial impact, here this energy can be recovered in a novel way. Enforcing the gap velocity constraint mitigates the contact chatter of the contact pressure and nodes in many problems. Whereas some approaches enforce the persistency condition and gap constraints simultaneously during the solution of the equations of motion (EOM) requiring multipliers for both constraints included in the equation set, here the gap constraint is solved through the equations of motion and the persistency condition is satisfied in the time integration scheme by the velocity update after the equations of motion. It is shown that this approach is strictly dissipative in that a plastic contact condition can be achieved. Analogous to a coefficient of restitution for rigid bodies, any dissipated energy can then be returned upon release if energy conservation is desired. Structure preserving methods are good for long-time dynamics simulations and energy conserving and strictly dissipative methods can overcome stability issues associated with standard time integration algorithms such as the Newmark method.

42 ENGINEERING↗

DOE OSTI2021

Maximum bound principle preserving integrating factor Runge–Kutta methods for semilinear parabolic equations

A large class of semilinear parabolic equations satisfy the maximum bound principle (MBP) in the sense that the time-dependent solution preserves for any time a uniform pointwise bound imposed by its initial and boundary conditions. Here, the MBP plays a crucial role in understanding the physical meaning and the well-posedness of the mathematical model. Investigation on numerical algorithms with preservation of the MBP has attracted increasingly attentions in recent years, especially for the temporal discretizations, since the violation of MBP may lead to nonphysical solutions or even blow-ups of the algorithms. In this paper, we study high-order MBP-preserving time integration schemes by means of the integrating factor Runge-Kutta (IFRK) method. Beginning with the space-discrete system of semilinear parabolic equations, we present the IFRK method in general form and derive the sufficient conditions for the method to preserve the MBP. In particular, we show that the classic four-stage, fourth-order IFRK scheme is MBP preserving for some typical semilinear systems although not strong stability preserving, which can be instantly applied to the Allen-Cahn type of equations. To our best knowledge, this is the first time to present a fourth-order linear numerical method preserving the MBP. In addition, convergence of these numerical schemes is proved theoretically and verified numerically, as well as their efficiency by simulations of 2D and 3D long-time evolutional behaviors. Numerical experiments are also carried out for a model which is not a typical gradient flow as the Allen-Cahn type of equations.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Computational assessment of smooth and rough parameter dependence of statistics in chaotic dynamical systems

An assumption of smooth response to small parameter changes, of statistics or long-time averages of a chaotic system, is generally made in the field of sensitivity analysis, and the parametric derivatives of statistical quantities are critically used in science and engineering. In this paper, we propose a numerical procedure to assess the differentiability of statistics with respect to parameters in chaotic systems. Here, we numerically show that the existence of the derivative depends on the Lebesgue integrability of a certain density gradient function, which we define as the derivative of logarithmic SRB density along the unstable manifold. We develop a recursive formula for the density gradient that can be efficiently computed along trajectories, and demonstrate its use in determining the differentiability of statistics. Our numerical procedure is illustrated on low-dimensional chaotic systems whose statistics exhibit both smooth and rough regions in parameter space.

42 ENGINEERING↗

DOE OSTI2023

Topology induced crossover between Langevin, subdiffusion, and Brownian diffusion regimes in supercooled water

Despite extensive studies of supercooled water, it remains challenging to understand its peculiar dynamic anomalous properties. In this work, we integrated full atomistic simulations of supercooled water over the temperature range of room temperature to 200 K using a quantum-mechanics-based polarizable force field with the dressed dynamics method that couples fast collision events and slow reorganization dynamics of hydrogen-bond networks. Our analysis unveils the salient multiscale features in the transient relaxation dynamics of supercooled water. A classical Langevin behavior dominates at fast timescales, while long-time relaxations unveil two different activation barriers in two temperature regions: below and above 230 K. The modulation of the entropy spectrum by temperature is elucidated in terms of a three-state model underlined by the complexity of the water dynamics associated with a topological transition of a strong hydrogen-bond network. This state-dependent network topology is quantitatively characterized by power-law exponents of inverse network connectivity from 200 to 298 K. Finally, this work provides valuable guidance for further studies on the transient relaxation dynamics of supercooled water.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2024

A new method for solving the linearized 1D Vlasov–Poisson system yielding a new class of solutions

We describe a new method for solving the linearized 1D Vlasov–Poisson system by using properties of Cauchy-type integrals. Our method remedies critical flaws of the two standard methods, reveals a previously unrecognized Gaussian-in-time-like decay, and can also account for an externally applied electric field. The Landau approximation involves deforming the Bromwich contour around the poles closest to the real axis due to the analytically continued dielectric function, finding the long-time behavior for a stable system: Landau damping. Jackson's generalization encircles all poles while sending the contour to infinity, assuming its contribution vanishes, which is not true in general. This gives incorrect solutions for physically reasonable configurations and can exhibit pathological behavior, of which we show examples. The van Kampen method expresses the solution for a stable equilibrium as a continuous superposition of waves, resulting in an opaque integral. Case's generalization includes unstable systems and predicts a decaying discrete mode for each growing discrete mode, an apparent contradiction to both the Jackson solution and ours. We show, without imposing additional constraints, that the decaying modes are never present in the time evolution due to an exact cancellation with part of the continuum. Our solution is free of integral expressions, is obtained using algebra and Laurent series expansions, does not rely on analytic continuations, and results in a correct asymptotically convergent form in the case of infinite sums. The analysis used can be readily applied in higher-dimensional, electromagnetic systems and also provides a new technique for evaluating certain inverse Laplace transforms.

Physics↗

DOE OSTI2023

Demonstrate FARM supervisory capabilities for a thermal energy storage problem for the DETAIL facility: IES Simulation Ecosystem Control System Development

The goal of the power dispatch problem for an Integrated Energy System (IES) is to adjust the power output and the heat flow of each component to maximize the profitability of the whole unit. Facilities that can integrate real-time digital signals, mock nuclear power, thermal energy storage and industrial heat use via high-temperature electrolysis were constructed at INL to support the research activities. The Dynamic Energy Technology and Integration Laboratory (DETAIL) houses the Microreactor Agile Non-nuclear Experimental Test Bed (MAGNET) and the Thermal Energy Distribution System (TEDS). In this report, the hierarchical control system architecture proposed in June 2023 milestone for the flexible operation of DETAIL facility is finalized and demonstrated. A brief description of the components and the corresponding Dymola models from the HYRBID repository is first provided. Then, the current control strategy is presented. In particular, the approach for generating the set-point trajectories to be fed to the PI controllers is analyzed, and its limits were identified. To preserve safe operation over both long-time and real-time horizons, the integration of a Supervisory Control layer embedding a modified version of FARM (Feasible Actuator Range Modifier) module is proposed. FARM is a component of the RAVEN-based FORCE framework designed to support HERON module at optimizing the operation of IES units. The proposed control system for DETAIL foresees FARM to be applied twice, i.e., the original version (“FARM-Validator”) aiding the solution of the power dispatch problem, and a modified version (“FARM-Supervisory”) coordinating the PID controllers. Despite the kernel of the two modules is the same, their tasks are quite different. The former intervenes at the beginning of each hour to prevent constraint violations over long time periods, the latter addresses real-time control tasks and monitors the response of constrained variables at a much finer time resolution. A tentative procedure for training the embedded Digital Twins with the experimental data is also proposed. Finally, the capabilities of the designed architecture and the impact of the added Supervisory Control layer are demonstrated by simulating a representative power dispatch scenario.

25 ENERGY STORAGE↗

DOE OSTI2025

Mitigation for roof alterations to building 06-cp-65 at the area 6 control point, nevada national security site, nye county, nevada

Building 06-CP-65 has been determined to be a contributing element to the Area 6 Control Point Historic District (O’Neill et al. 2021; Reed 2022). It contributes to the significance of the historic district under Criterion A as one of the principal buildings that supported timing and firing operations for nuclear testing on the NNSS from 1966 to 1992. As such, the building served as a major warehouse with office space within the district. It was used by both REECo, a long-time general contractor at the NNSS, as well as EG&G, which provided technical support to the national laboratories and the DOD. The building served as an important staging area and electrical power supply point for the NNSS diagnostic trailer fleet and its unique location immediately along Mercury Highway allowed easy accessibility to the forward areas of the NNSS. The building also contributes to the historic district under Criterion C as it is one of the large, unadorned, precast concrete buildings at the Control Point. These types of buildings were the prominent elements of the compound that convey the district’s overall utilitarian, military-industrial character. Building 06-CP-65 retains all aspects of integrity to a high degree and easily conveys its significance as a warehouse that supported Control Point operations. Building 06-CP-65 is not recommended eligible for listing in the NRHP as an individual resource. While it served an important support function as part of the Control Point Historic District, an archival and literature review did not reveal information linking it to any specific test, series of tests, programs, or for any specific role on the NNSS other than as a warehouse (Criterion A). It has no direct association with any important individual (Criterion B). It also is not architecturally significant in its own right beyond reflecting the overall aesthetic of the Control Point Historic District (Criterion C), and it does not have potential to yield information important to the history of nuclear testing beyond what can be learned from historic texts, drawings, and other documents (Criterion D).

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2020

Nature of the nonequilibrium phase transition in the non-Markovian driven Dicke model

The Dicke model famously exhibits a phase transition to a superradiant phase with a macroscopic population of photons and is realized in multiple settings in open quantum systems. In this paper, we study a variant of the Dicke model where the cavity mode is lossy due to the coupling to a Markovian environment while the atomic mode is coupled to a colored bath. We analytically investigate this model by inspecting its low-frequency behavior via the Schwinger-Keldysh field theory and carefully examine the nature of the corresponding superradiant phase transition. Integrating out the fast modes, we can identify a simple effective theory allowing us to derive analytical expressions for various critical exponents including the dynamical exponent. We find excellent agreement with previous numerical results when the non-Markovian bath is at zero temperature; however, contrary to these studies, our low-frequency approach reveals that the same exponents govern the critical behavior when the colored bath is at finite temperature unless the chemical potential is zero. Furthermore, we show that the superradiant phase transition is classical in nature, while it is genuinely nonequilibrium. In this work, we derive a fractional Langevin equation and conjecture the associated fractional Fokker-Planck equation that captures the system's long-time memory as well as its nonequilibrium behavior. Finally, we consider finite-size effects at the phase transition and identify the finite-size scaling exponents, unlocking a rich behavior in both statics and dynamics of the photonic and atomic observables.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Develop a weather-aware climate model to understand and predict extremes and associated power outages and renewable energy shortages with uncertainty-aware and physics-informed machine learning

Focal Area(s): The focus area is predictive modeling through the use of AI techniques and AI-derived model components with a particular emphasis on extreme weather in Atmospheric Science and power outages and shortages in Energy Science. Science Challenge: Predicting weather extremes (e.g., heavy precipitation, strong wind, and large hailstones), and weather-related power system outages and shortages can mitigate economic losses, save lives, support renewables integration, and improve power system resiliency. However, currently, the poor reliability and large uncertainty associated with the weather extreme prediction in the current climate models make the problem intractable. The key challenges are: (1) physical factors like green-house gases (GHGs), aerosols, and land use and land cover (LULC) can significantly impact extreme storms, but the understanding of these impacts is limited, particularly globally; (2) the convective permitting resolutions needed to model severe convective storms and their impacts are computationally prohibitive with global climate models (GCMs); (3) interactions between weather extremes and power system outages are complex and subject to great uncertainty. Current outage prediction models are short lead (~ 3 days), which do not allow for long-time planning of energy production and distribution. Moreover, we have limited capacity to predict weather events leading to sustained shortages in a renewable-energy-dominated power system. These challenges drive motivation for mechanistic understanding and reliable and efficient predictive modeling of extremes and their impacts from the sub-seasonal to long term projections.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2024

Quadrature Based Neural Network Learning of Stochastic Hamiltonian Systems

Hamiltonian Neural Networks (HNNs) provide structure-preserving learning of Hamiltonian systems. In this paper, we extend HNNs to structure-preserving inversion of stochastic Hamiltonian systems (SHSs) from observational data. We propose the quadrature-based models according to the integral form of the SHSs’ solutions, where we denoise the loss-by-moment calculations of the solutions. The integral pattern of the models transforms the source of the essential learning error from the discrepancy between the modified Hamiltonian and the true Hamiltonian in the classical HNN models into that between the integrals and their quadrature approximations. This transforms the challenging task of deriving the relation between the modified and the true Hamiltonians from the (stochastic) Hamilton–Jacobi PDEs, into the one that only requires invoking results from the numerical quadrature theory. Meanwhile, denoising via moments calculations gives a simpler data fitting method than, e.g., via probability density fitting, which may imply better generalization ability in certain circumstances. Numerical experiments validate the proposed learning strategy on several concrete Hamiltonian systems. The experimental results show that both the learned Hamiltonian function and the predicted solution of our quadrature-based model are more accurate than that of the corrected symplectic HNN method on a harmonic oscillator, and the three-point Gaussian quadrature-based model produces higher accuracy in long-time prediction than the Kramers–Moyal method and the numerics-informed likelihood method on the stochastic Kubo oscillator as well as other two stochastic systems with non-polynomial Hamiltonian functions. Moreover, the Hamiltonian learning error εH arising from the Gaussian quadrature-based model is lower than that from Simpson’s quadrature-based model. These demonstrate the superiority of our approach in learning accuracy and long-time prediction ability compared to certain existing methods and exhibit its potential to improve learning accuracy via applying precise quadrature formulae.

Mathematics↗

DOE OSTI2023

Face mask integrated with flexible and wearable manganite oxide respiration sensor

Face masks are key personal protective equipment for reducing exposure to viruses and other environmental hazards such as air pollution. Integrating flexible and wearable sensors into face masks can provide valuable insights into personal and public health. The advantages that a breath-monitoring face mask requires, including multi-functional sensing ability and continuous, long-term dynamic breathing process monitoring, have been underdeveloped to date. Here, we design an effective human breath monitoring face mask based on a flexible La 0.7 Sr 0.3 MnO 3 (LSMO)/Mica respiration sensor. The sensor’s capabilities and systematic measurements are investigated under two application scenes, namely clinical monitoring mode and daily monitoring mode, to monitor, recognise, and analyse different human breath status, i.e., cough, normal breath, and deep breath. This sensing system exhibits super-stability and multi-modal capabilities in continuous and long-time monitoring of the human breath. We determine that during monitoring human breath, thermal diffusion in LSMO is responsible for the change of resistance in flexible LSMO/Mica sensor. Both simulated and experimental results demonstrate good discernibility of the flexible LSMO/Mica sensor operating at different breath status. Our work opens a route for the design of novel flexible and wearable electronic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2021

Theory of the effect of external stress on the activated dynamics and transport of dilute penetrants in supercooled liquids and glasses

We generalize the self-consistent cooperative hopping theory for a dilute spherical penetrant or tracer activated dynamics in dense metastable hard sphere fluids and glasses to address the effect of external stress, the consequences of which are systematically established as a function of matrix packing fraction and penetrant-to-matrix size ratio. All relaxation processes speed up under stress, but the difference between the penetrant and matrix hopping (alpha relaxation) times decreases significantly with stress corresponding to less time scale decoupling. A dynamic crossover occurs at a critical “slaving onset” stress beyond which the matrix activated hopping relaxation time controls the penetrant hopping time. This characteristic stress increases (decreases) exponentially with packing fraction (size ratio) and can be well below the absolute yield stress of the matrix. Below the slaving onset, the penetrant hopping time is predicted to vary exponentially with stress, differing from the power law dependence of the pure matrix alpha time due to system-specificity of the stress-induced changes in the penetrant local cage and elastic barriers. An exponential growth of the penetrant alpha relaxation time with size ratio under stress is predicted, and at a fixed matrix packing fraction, the exponential relation between penetrant hopping time and stress for different size ratios can be collapsed onto a master curve. Direct connections between the short- and long-time activated penetrant dynamics and between the penetrant (or matrix) alpha relaxation time and matrix thermodynamic dimensionless compressibility are also predicted. The presented results should be testable in future experiments and simulations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Real-time evolution of Anderson impurity models via tensor network influence functionals

In this work, we present and analyze two tensor network-based influence functional approaches for simulating the real-time dynamics of quantum impurity models such as the Anderson model. Via comparison with recent numerically exact simulations, we show that such methods accurately capture the long-time nonequilibrium quench dynamics. The two parameters that must be controlled in these tensor network influence functional approaches are a time discretization (Trotter) error and a bond dimension (tensor network truncation) error. We show that the actual numerical uncertainties are controlled by an intricate interplay of these two approximations, which we demonstrate in different regimes. Our work opens the door to using these tensor network influence functional methods as general impurity solvers.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗