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DOE OSTI2024

A structure-preserving machine learning framework for accurate prediction of structural dynamics for systems with isolated nonlinearities

The nonlinearities present in structural systems are often found in isolated regions within the structure, such as those containing joints or interfaces. However, despite the localized nature of these nonlinearities their presence serves to couple together the modes of the underlying linear system and significantly complicate the development of appropriate reduced-order models; the localized nonlinearities have a global effect on the dynamics of the system. Further, in the presence of evolving structural health the nonlinearities can arise from accumulating damage, with dynamics distinct from those observed in the healthy state. The present work develops a data-driven formulation to identify and include the contributions of the isolated nonlinearities on the dynamics of the underlying linear structure. A novel coordinate separation is developed that decomposes those nonlinearities restricted to the isolated subdomain from the known linear system defined over the entire domain, and the influence of the isolated nonlinearities is reintroduced as an appropriately identified traction at the boundary of the isolated subdomain, referred to as the deviatoric force. In the region exterior to the nonlinear subdomain the response of the ideal linear system recovers that of the original nonlinear system. In this work, the deviatoric force component is predicted using a structure-preserving multilayer perceptron, based only on measured responses at the boundary of the isolated subdomain. Therefore introduction of the perceptron is able to bypass the direct numerical simulation of the nonlinearities within the isolated subdomain. This approach is illustrated through a simple structural system in which an interior region contains cubic nonlinearities and hysteretic damping. Once trained, the machine learning system is able to accurately predict the deviatoric force so that the ideal system recovers the response of the original system in the region outside the isolated nonlinear subdomain. Moreover, the data-driven approach is able to accurately predict the response when the system is subject to differing initial conditions and external excitation without the need for retraining, so that the proposed approach provides a robust description of the structural dynamics of the overall system.

Machine learning↗

DOE OSTI2022

Microscopic dynamics underlying the stress relaxation of arrested soft materials

Arrested soft materials such as gels and glasses exhibit a slow stress relaxation with a broad distribution of relaxation times in response to linear mechanical perturbations. Although this macroscopic stress relaxation is an essential feature in the application of arrested systems as structural materials, consumer products, foods, and biological materials, the microscopic origins of this relaxation remain poorly understood. Here, we elucidate the microscopic dynamics underlying the stress relaxation of such arrested soft materials under both quiescent and mechanically perturbed conditions through X-ray photon correlation spectroscopy. By studying the dynamics of a model associative gel system that undergoes dynamical arrest in the absence of aging effects, we show that the mean stress relaxation time measured from linear rheometry is directly correlated to the quiescent superdiffusive dynamics of the microscopic clusters, which are governed by a buildup of internal stresses during arrest. We also show that perturbing the system via small mechanical deformations can result in large intermittent fluctuations in the form of avalanches, which give rise to a broad non-Gaussian spectrum of relaxation modes at short times that is observed in stress relaxation measurements. These findings suggest that the linear viscoelastic stress relaxation in arrested soft materials may be governed by nonlinear phenomena involving an interplay of internal stress relaxations and perturbation-induced intermittent avalanches.

36 MATERIALS SCIENCE↗

DOE OSTI2021

Reservoir Computing as a Tool for Climate Predictability Studies

Reduced-order dynamical models play a central role in developing our understanding of predictability of climate irrespective of whether we are dealing with the actual climate system or surrogate climate models. In this context, the linear inverse modeling (LIM) approach, by capturing a few essential interactions between dynamical components of the full system, has proven valuable in providing insights into predictability of the full system. We demonstrate that reservoir computing (RC), a form of learning suitable for systems with chaotic dynamics, provides an alternative nonlinear approach that improves on the predictive skill of the LIM approach. We do this in the example setting of predicting sea surface temperature in the North Atlantic in the preindustrial control simulation of a popular earth system model, the Community Earth System Model so that we can compare the performance of the new RC-based approach with the traditional LIM approach both when learning data are plentiful and when such data are more limited. The improved predictive skill of the RC approach over a wide range of conditions—larger number of retained EOF coefficients, extending well into the limited data regime, etc.—suggests that this machine-learning technique may have a use in climate predictability studies. While the possibility of developing a climate emulator—the ability to continue the evolution of the system on the attractor long after failing to be able to track the reference trajectory—is demonstrated in the Lorenz-63 system, it is suggested that further development of the RC approach may permit such uses of the new approach in more realistic predictability studies.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2026

Data-Driven Modeling and Correction of Vehicle Dynamics

We develop a data-driven framework for learning and correcting nonautonomous vehicle dynamics. Physics-based vehicle models are often simplified for tractability and therefore exhibit inherent model-form uncertainty, motivating the need for data-driven correction. Moreover, nonautonomous dynamics are governed by time-dependent control inputs, which pose challenges in learning predictive models directly from temporal snapshot data. To address these, we reformulate the vehicle dynamics via a local parameterization of the time-dependent inputs, yielding a modified system composed ofa sequence of local parametric dynamical systems. Here, we approximate these parametric systems using two complementary approaches. First, we employ the dimension reduction and interpolation in parameter space (DRIPS) methodology to construct efficient linear surrogate models, equipped with lifted observable spaces and manifold-based operator interpolation. This enables data-efficient learning of vehicle models whose dynamics admit accurate linear representations in the lifted spaces. Second, for more strongly nonlinear systems, we employ flow map learning (FML), a deep neural network (DNN) approach that approximates the parametric evolution map without requiring special treatment of nonlinearities. We further extend FML with a transfer-learning-based model correction procedure, enabling the correction of misspecified prior models using only a sparse set of high-fidelity or experimental measurements, without assuming a prescribed form for the correction term. Through a suite of numerical experiments on unicycle, simplified bicycle, and slip-based bicycle models, we demonstrate that DRIPS offers robust and highly data-efficient learning of nonautonomous vehicle dynamics, while FML provides expressive nonlinear modeling and effective correction of model-form errors under severe data scarcity.

data-driven modeling↗

DOE OSTI2026

Control Parameter Sensitivity Study for Inverter-Based-Resource Dominated Grids: A Small Signal Stability Approach and Framework

The growing adoption of renewable energy is driving the prevalence of inverter-based resources (IBRs) within power grids. Future power grids will integrate both grid-following IBRs (GFM-IBRs) and grid-forming IBRs (GFL-IBRs) alongside synchronous generators. Therefore, it is crucial to perform stability studies that account for all components and especially control interactions related to IBRs. Extensive research has performed to study the IBR-related stability, however, the sensitivity study of IBRs' control parameters on system stability has not been adequately studied yet, especially from a systematic way. Therefore, this paper conducts a small signal stability analysis for a generic grid with multiple types of resources and develops an analytical framework for assessing the sensitivity of control parameters affecting stability margins. To achieve that, the non-autonomous reduced-order non-linear dynamic model is developed for a generic power system with multiple synchronous generator-based resources (SGBRs), GFM-IBRs, and GFL-IBRs. Based on the analytic model, a systematic framework for parametric sensitivity on systems' asymptotic stability is developed. A parameter sensitivity analysis based on eigenvalue methods is proposed. The impact of the droop controllers of GFM-IBRs, PQ-dispatch and the PLL controller of GFL-IBR on the system asymptotic stability is discussed. This sensitivity study is aiming to provide deep insights on control parameters' impact on system stability, and gives direction for parameter tuning in case of instability.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2023

Adaptively Learned Modeling for a Digital Twin of Hydropower Turbines with Application to a Pilot Testing System

In the development of a digital twin (DT) for hydropower turbines, dynamic modeling of the system (e.g., penstock, turbine, speed control) is crucial, along with all the necessary data interface, virtualization, and dashboard designs. Since the DT must mimic the actual dynamics of the hydropower turbine accurately, adaptive learning is required to train these dynamic models online so that the models in the DT can effectively follow the representation of the actual hydropower turbine dynamics accurately and reliably. This study presents an adaptive learning method for obtaining the hydropower turbine models for DT development of hydropower systems using the recursive least squares algorithm. To simplify the formulation, the hydropower turbine under consideration was assumed to operate near a fixed operating point, where the system dynamics can be well represented by a set of linear differential equations with constant parameters. In this context, the well-known six-coefficient model for the Francis turbine was formulated as the starting point to obtain input and output models for the turbine. Then, an adaptive learning mechanism was developed to learn model parameters using real-time data from a hydropower turbine testing system. This led to semi-physical modeling, in which first principles and data-driven modeling are integrated to produce dynamic models for DT development. Applications to a pilot system at the Norwegian University of Science and Technology (NTNU) were made, and the models learned adaptively using the data collected from the university’s pilot system. Desired modeling and validation results were obtained.

13 HYDRO ENERGY↗

DOE OSTI2025

Frequency-domain modeling of floating wind arrays with shared mooring lines

A frequency-domain model for floating wind turbine dynamics has been extended to model floating wind farms with couplings from shared mooring systems. The model, called RAFT, could previously calculate the mean offsets and wave-induced response spectra for single floating wind turbines. Now, the model supports multiple floating wind turbines, each with their own properties and responses, along with mooring lines that run directly between floating wind turbines in the array, meaning that shared mooring lines or fully suspended dynamic power cables can be included. This capability is achieved by setting up an array-level solution of the system mean offsets and assembling the full system matrices for solving the dynamic response. The quasi-static mooring model MoorPy is used to linearize the mooring system properties. To compute the floating wind turbine relative motions, phase offsets are applied to each turbine's response as a function of wave frequency based on the wavelength and relative positions in the array. These differential motions are then applied to mooring system tension Jacobians to compute the tension loads in the shared mooring lines. Overall, the capability provides a frequency-domain analog to the modeling capabilities of the floating support structure in FAST.Farm. Mean offsets and power spectral density plots of responses are compared between RAFT and FAST.Farm to verify the implementation. The results indicate good agreement within the expectations of a frequency-domain modeling approach and suggest correct implementation of the shared mooring aspects. Additionally, a unique comb-like frequency response in the shared mooring line tensions has been observed. This phenomenon has a clear physical basis and may be an important design consideration for future shared mooring systems.

17 WIND ENERGY↗

DOE OSTI2024

Convergence of Weak-SINDy Surrogate Models

In this paper, we give an in-depth error analysis for surrogate models generated by a variant of the Sparse Identification of Nonlinear Dynamics (SINDy) method. We start with an overview of a variety of nonlinear system identification techniques, namely SINDy, weak-SINDy, and the occupation kernel method. Under the assumption that the dynamics are a finite linear combination of a set of basis functions, these methods establish a linear system to recover coefficients. We illuminate the structural similarities between these techniques and establish a projection property for the weak-SINDy technique. Following the overview, we analyze the error of surrogate models generated by a simplified version of weak-SINDy. In particular, under the assumption of boundedness of a composition operator given by the solution, we show that (i) the surrogate dynamics converges towards the true dynamics and (ii) the solution of the surrogate model is reasonably close to the true solution. Finally, as an application, we discuss the use of a combination of weak-SINDy surrogate modeling and proper orthogonal decomposition (POD) to build a surrogate model for partial differential equations (PDEs).

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

FTL: Transfer Learning Nonlinear Plasma Dynamic Transitions in Low Dimensional Embeddings (FTL) v1.0

Fusion Transfer Learning (FTL) model provides a new paradigm to study high-dimensional dynamical behaviors, such as those in fusion plasma systems. The knowledge transfer process leverages a pre-trained neural encoder-decoder network, initially trained on linear simulations, to effectively capture nonlinear dynamics. The low-dimensional embeddings extract the coherent structures of interest, while preserving the inherent dynamics of the complex system. Experimental results highlight FTL's capacity to capture transitional behaviors and dynamical features in plasma dynamics -- a task often challenging for conventional methods. The model developed in this study is generalizable and can be extended broadly through transfer learning to address various magnetohydrodynamics (MHD) modes.

Bai, Zhe↗

DOE OSTI2024

Oscillating surge wave energy converter using a novel above-water power takeoff with belt-arc speed amplification

We investigate the performance of a novel power takeoff (PTO) featuring belt-arc speed amplification for oscillating surge wave energy converters (OSWECs), aiming to address the challenges of extremely low rotary speed and large torque under the low-frequency ocean wave excitations. The belt-arc design significantly increases the rotary speed of the generator, enabling generator downsizing and decreasing the powertrain friction losses. The design also allows for placing the generator above water, eliminating the need for high Ingress Protection ratings for the generator and powertrain, and potentially leading to substantial reductions in capital and maintenance costs. Using the linear potential wave theory, the dynamics of the integrated system are analyzed, and key parameters are identified. To validate the numerical analysis, a 1:10 scale model is designed, fabricated, and tested in a wave tank. Performance evaluations are conducted under regular and irregular wave conditions, with quantified effects of parameter tuning. The results reveal an optimal wave-to-electric efficiency of 48% under regular wave excitation and 20% under irregular excitation. Furthermore, these findings underscore the effectiveness of the proposed novel PTO design in addressing the challenges of low rotation speed and large torque inherent in OSWECs, demonstrating its ability to efficiently convert wave power into electricity.

16 TIDAL AND WAVE POWER↗

DOE OSTI2022

Koopman Model Predictive Control for Eco-Driving of Automated Vehicles

In this paper, we develop a data-driven process for building a model predictive control (MPC) for eco-driving of automated vehicles. The process involves performing system identification in which the non-linear vehicle dynamics model is approximated by the Koopman operator, a linear predictor of higher state-dimension, in a data-driven framework. This approach allows us to formulate the eco-driving problem in a constrained quadratic program that leads to a computationally fast MPC. The MPC is then implemented as a closed-loop control of an electric vehicle in numerical simulations for demonstration.

autonomous vehicle↗

DOE OSTI2023

Assessing complexity and dynamics in epidemics: geographical barriers and facilitators of foot-and-mouth disease dissemination

Introduction: Physical and non-physical processes that occur in nature may influence biological processes, such as dissemination of infectious diseases. However, such processes may be hard to detect when they are complex systems. Because complexity is a dynamic and non-linear interaction among numerous elements and structural levels in which specific effects are not necessarily linked to any one specific element, cause-effect connections are rarely or poorly observed. Methods: To test this hypothesis, the complex and dynamic properties of geo-biological data were explored with high-resolution epidemiological data collected in the 2001 Uruguayan foot-and-mouth disease (FMD) epizootic that mainly affected cattle. County-level data on cases, farm density, road density, river density, and the ratio of road (or river) length/county perimeter were analyzed with an open-ended procedure that identified geographical clustering in the first 11 epidemic weeks. Two questions were asked: (i) do geo-referenced epidemiologic data display complex properties? and (ii) can such properties facilitate or prevent disease dissemination? Results: Emergent patterns were detected when complex data structures were analyzed, which were not observed when variables were assessed individually. Complex properties–including data circularity–were demonstrated. The emergent patterns helped identify 11 counties as ‘disseminators’ or ‘facilitators’ (F) and 264 counties as ‘barriers’ (B) of epidemic spread. In the early epidemic phase, F and B counties differed in terms of road density and FMD case density. Focusing on non-biological, geographical data, a second analysis indicated that complex relationships may identify B-like counties even before epidemics occur. Discussion: Geographical barriers and/or promoters of disease dispersal may precede the introduction of emerging pathogens. If corroborated, the analysis of geo-referenced complexity may support anticipatory epidemiological policies.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Online Output-Based Inertia Estimation of Modern Power Systems

The overall inertia of modern power systems is drastically impacted by the penetration level of converter-based resources (CBRs). The intermittent output of CBRs and their dependence on the weather conditions affirm the need for a realtime inertia estimation approach. This can help the transmission system operators(TSOs) to be continuously aware of the changes in the system inertia and to take suitable control actions. This paper is a step forward to a totally data-driven framework for power system inertia estimation using the available measurements from the phasor measurement units (PMUs). This inertia estimation is done based on the spectral analysis of the so-called Koopman linear operator. Koopman operator considers the relationship between the system's inertia and its dynamical response to slight disturbances in the load. Simulation results show that Koopman operator can approximate the system behavior in a reconstructed linear space hence inertia constant is estimated accurately.

data-driven↗

DOE OSTI2026

Fermionic mean-field dynamics for spin systems beyond free fermions

We introduce the fermionized time-dependent Hartree–Fock (fTDHF), a real-time quantum dynamics method for spin-1/2 Hamiltonians following their mapping to fermions via the Jordan-Wigner transformation. fTDHF is formally equivalent to exact dynamics in the case of free fermions, and can efficiently handle non-local string operators arising from long-range interactions via transition matrix elements between non-orthogonal Slater determinants. We show that the fTDHF method can be implemented on a classical computer with a cost that scales polynomially with system size, and linearly with the time steps. We benchmark fTDHF against exact dynamics on three separate spin-1/2 models, representing adiabatic preparation of states with long-range correlations, disorder-driven observation of many-body localization, and particle production in the Schwinger model. For each of these systems, fTDHF is shown to reproduce the qualitative dynamics generated by the exact evolutions, while maintaining a simple physical picture due to its mean-field nature.

Dutta, Rishab↗

DOE OSTI2024

Optimal Control of SOEC-Based Hydrogen Production Systems for Demand Response Using Deep Reinforcement Learning in Smart Grids

Solid oxide electrolysis cell (SOEC) hydrogen production technology can range in size from small, appliance-size equipment to large-scale, central production facilities that can be tied directly to renewable or non-greenhouse-gas-emitting forms of electricity production, making it an ideal resource for demand response (DR). The SOEC hydrogen production system is a complex integrated system that encompasses fluid dynamics, electrical dynamics, and electrochemical and thermal dynamics, all of which involve non-linearity and non-convexity. Proper control of the SOEC hydrogen production system is crucial to enable its participation in the DR program. Here, to overcome the difficulty of designing an explicit control law for such nonlinear systems with nonconvex optimization features in DR applications, deep reinforcement learning (DRL) is explored to achieve the optimal control of the SOEC system for DR participation. Specifically, a twin delayed deterministic policy gradient (TD3) control framework is applied to achieve optimal response performance during DR events by considering power tracking error and hydrogen production efficiency with a suitable reward function. Two case studies with grid connections for tracking different DR commands were investigated. The first case study involved operating conditions reaching the boundaries, while the second involved operating conditions within the boundaries. The results showed that the proposed DRL-based control for SOEC can track the DR signal in a timely manner while maintaining high energy efficiency.

08 HYDROGEN↗

DOE OSTI2022

Spectral density reconstruction with Chebyshev polynomials

Accurate calculations of the spectral density in a strongly correlated quantum many-body system are of fundamental importance to study its dynamics in the linear response regime. Typical examples are the calculation of inclusive and semiexclusive scattering cross sections in atomic nuclei and transport properties of nuclear and neutron star matter. Integral transform techniques play an important role in accessing the spectral density in a variety of nuclear systems. However, their accuracy is in practice limited by the need to perform a numerical inversion which is often ill-conditioned. Here, in the present work we extend a recently proposed quantum algorithm which circumvents this problem. We show how to perform controllable reconstructions of the spectral density over a finite energy resolution with rigorous error estimates. An appropriate expansion in Chebyshev polynomials allows for efficient simulations also on classical computers. We apply our idea to obtain the local density of states for graphene in a magnetic field as a proof of principle. This paves the way for future applications in nuclear and condensed matter physics.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2021

Synergistic data analytics for electromechanical oscillation in electric power systems

Accurate real-time estimation of the four electromechanical oscillation properties, i.e., dominant oscillation modes, mode shapes, participation factors, and coherent groups, is of great importance to assess and mitigate potential electromechanical oscillations in interconnected power systems. While eigenvalue analysis can realize such estimation, it requires precise linearized dynamic models and accurate parameters, which are highly difficult to obtain in practice. Data fusion-based modal estimation methods can extract the properties of electromechanical oscillations from measurement data without the power system model and parameters, but most of the time only one or two property assessments can be accomplished each time. To overcome this challenge, this paper presents a synergistic data analytics solution to characterize the dynamic behaviors of electromechanical oscillations from real-time measurement data. Here, the proposed method uses optimized variable projection, and it is capable of estimating all four electromechanical oscillation behavior properties from measured responses. Case studies are performed using the simulated measurement data of a 16-generator 68-bus test system and the field measurements collected by the PMUs deployed in the Yunnan Power Grid. The results demonstrate that the proposed synergistic data analytics solution can achieve satisfactory performance in capturing the properties of electromechanical oscillations from measurement data and exhibit strong robustness against measurement noise when compared with existing measurement-based methods.

42 ENGINEERING↗

DOE OSTI2024

The Cauchy Problem for Boltzmann Bi-linear Systems: The Mixing of Monatomic and Polyatomic Gases

Abstract From a unified vision of vector valued solutions in weighted Banach spaces, this paper establishes the existence and uniqueness for space homogeneous Boltzmann bi-linear systems with conservative collisional forms arising in complex gas dynamical structures. This broader vision is directly applied to dilute multi-component gas mixtures composed of both monatomic and polyatomic gases. Such models can be viewed as extensions of scalar Boltzmann binary elastic flows, as much as monatomic gas mixtures with disparate masses and single polyatomic gases, providing a unified approach for vector valued solutions in weighted Banach spaces. Novel aspects of this work include developing the extension of a general ODE theory in vector valued weighted Banach spaces, precise lower bounds for the collision frequency in terms of the weighted Banach norm, energy identities, angular or compact manifold averaging lemmas which provide coerciveness resulting into global in time stability, a new combinatorics estimate for p -binomial forms producing sharper estimates for the k -moments of bi-linear collisional forms. These techniques enable the Cauchy problem improvement that resolves the model with initial data corresponding to strictly positive and bounded initial vector valued mass and total energy, in addition to only a $$2^+$$ 2 + moment determined by the hard potential rates discrepancy, a result comparable in generality to the classical Cauchy theory of the scalar homogeneous Boltzmann equation.

Physics↗