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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Survey of Dynamic Mode Decomposition Methods

Dynamic mode decomposition (DMD) is a data-driven reduced order modeling (ROM) technique used for dynamic systems. The widely adopted algorithm was first introduced and demonstrated on fluid flow data by Schmid. In recent years, various other fields, such as nuclear engineering, have begun to adopt this method. For example, DMD has been used for estimating α-eigenvalues, as an ROM for pulsed neutron problems, for predicting isotopic composition in burnup calculations, as acceleration techniques for iterative methods, and in capturing dynamic behaviors in molten salt reactor transients. This report seeks to demonstrate the capabilities and limits of the standard DMD algorithm, and identify problem spaces where variants may be better suited. The primary variant this report considers is Multi-Resolution DMD (mrDMD). Because this serves as a survey, synthetically produced data is used in lieu of simulation results. The remainder of this report will go into detail on the DMD theory, outline the standard DMD and mrDMD algorithms, present test cases highlighting the applicability of each, and finally present a discussion on how to determine the best suited algorithm for a given problem. All calculations performed in this report are carried out using the open source DMD library, PyDMD.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Reduced-order modeling on a near-term quantum computer

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems of equations as well as systems of linear ordinary differential equations (ODEs) and partial differential equations (PDEs). Reducedorder modeling (ROM) algorithms for studying fluid dynamics have shown success in identifying linear operators that can describe flowfields, where dynamic mode decomposition (DMD) is a particularly useful method in which a linear operator is identified from data. In this work, DMD is reformulated as an optimization problem to propagate the state of the linearized dynamical system on a quantum computer. This reformulation was chosen as a means of facilitating implementation on a near-term quantum computer. Quadratic unconstrained binary optimization (QUBO), a technique for optimizing quadratic polynomials in binary variables, allows for quantum annealing algorithms to be applied. A quantum circuit model (quantum approximation optimization algorithm, QAOA) is utilized to obtain predictions of the state trajectories. Results are shown for the quantum-ROM predictions for flow over a 2D cylinder at Re = 220 and flow over a NACA0009 airfoil at Re = 500 and α = 15°. The quantum-ROM predictions are found to depend on the number of bits utilized for a fixed point representation and the truncation level of the DMD model. Comparisons with DMD predictions from a classical computer algorithm are made, as well as an analysis of the computational complexity and prospects for future, more fault-tolerant quantum computers.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

DRIPS: A framework for dimension reduction and interpolation in parameter space

Reduced-order models are often used to describe the behavior of complex systems, whose simulation with a full model is too expensive, or to extract salient features from the full model’s output. We introduce a new model-reduction framework DRIPS (dimension reduction and interpolation in parameter space) that combines the offline local model reduction with the online parameter interpolation of reduced-order bases (ROBs). The offline step of this framework relies on dynamic mode decomposition (DMD) to build a low-rank linear surrogate model, equipped with a local ROB, for quantities of interest derived from the training data generated by repeatedly solving the (nonlinear) high-fidelity model for multiple parameter points. The online step consists of the construction of a parametric reduced-order model for each target/test point in the parameter space, with the interpolation of ROBs done on a Grassman manifold and the interpolation of reduced-order operators done on a matrix manifold. The DMD component enables DRIPS to model (typically low-dimensional) quantities of interest directly, without having to access the (typically high-dimensional and possibly nonlinear) operators in a high-fidelity model that governs the dynamics of the underlying high-dimensional state variables, as required in projection-based reduced-order modeling. A series of numerical experiments suggests that DRIPS yields a model reduction, which is computationally more efficient than the commonly used projection-based proper orthogonal decomposition; it does so without requiring a prior knowledge of the governing equation for quantities of interest. Furthermore, for the nonlinear systems considered, DRIPS is more accurate than Gaussian-process interpolation (Kriging).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Higher order mode analysis of a 915 MHz 2-cell cavity for a prototype industrial accelerator

A possible solution to reduce the complexity posed by the cryogenic systems in a superconducting RF accelerator for industrial applications, is to capitalize on the advances achieved by the Nb3Sn superconducting RF technology, as well as the feasibility of a reliable 4 K cooling system, based on commercial cryocoolers. Following this philosophy, the conceptual design for a prototype, conduction-cooled, 4 MeV, 20 kW SRF electron linac, is being developed at Jefferson Lab. Such design is based on a 915 MHz two-cell Nb3Sn cavity. In this contribution, we present the proposed cavity design, including the fundamental power coupler, and the analysis of the Higher Order Modes, using numerical simulations to estimate the potentially dangerous modes and to provide the requirements for damping for reliable operations with a cryocooler.

Rimmer, Robert↗
DOE OSTI2020

Learning compact physics‐aware delayed photocurrent models using dynamic mode decomposition

Abstract Radiation‐induced photocurrent in semiconductor devices can be simulated using complex physics‐based models, which are accurate, but computationally expensive. This presents a challenge for implementing device characteristics in high‐level circuit simulations where it is computationally infeasible to evaluate detailed models for multiple individual circuit elements. In this work we demonstrate a procedure for learning compact delayed photocurrent models that are efficient enough to implement in large‐scale circuit simulations, but remain faithful to the underlying physics. Our approach utilizes dynamic mode decomposition (DMD), a system identification technique for learning reduced‐order discrete‐time dynamical systems from time series data based on singular value decomposition. To obtain physics‐aware device models, we simulate the excess carrier density induced by radiation pulses by solving numerically the ambipolar diffusion equation, then use the simulated internal state as training data for the DMD algorithm. Our results show that the significantly reduced‐order delayed photocurrent models obtained via this method accurately approximate the dynamics of the internal excess carrier density—which can be used to calculate the induced current at the device boundaries—while remaining compact enough to incorporate into larger circuit simulations.

Hanson, Joshua↗
DOE OSTI2021

Reduced-order modeling of advection-dominated systems with recurrent neural networks and convolutional autoencoders

A common strategy for the dimensionality reduction of nonlinear partial differential equations (PDEs) relies on the use of the proper orthogonal decomposition (POD) to identify a reduced subspace and the Galerkin projection for evolving dynamics in this reduced space. However, advection-dominated PDEs are represented poorly by this methodology since the process of truncation discards important interactions between higher-order modes during time evolution. In this study, we demonstrate that encoding using convolutional autoencoders (CAEs) followed by a reduced-space time evolution by recurrent neural networks overcomes this limitation effectively. We demonstrate that a truncated system of only two latent space dimensions can reproduce a sharp advecting shock profile for the viscous Burgers equation with very low viscosities, and a six-dimensional latent space can recreate the evolution of the inviscid shallow water equations. Additionally, the proposed framework is extended to a parametric reduced-order model by directly embedding parametric information into the latent space to detect trends in system evolution. Furthermore, our results show that these advection-dominated systems are more amenable to low-dimensional encoding and time evolution by a CAE and recurrent neural network combination than the POD-Galerkin technique.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2022

Direct Measurement of Ice-Ablator Interface Motion for Instability Mitigation in Indirect Drive ICF Implosions

In indirect drive inertial confinement fusion (ICF) implosions hydrodynamic instability growth at the imploding capsule ablator-DT fuel interface can reduce fuel compressibility and inject ablator into the hot spot hence reducing hot spot pressure and temperature. As a mitigation strategy, a gentle acceleration of this interface is predicted by simulations and theory to significantly reduce this instability growth in the early stage of the implosion. We have performed high-contrast, time-resolved x-ray refraction enhanced radiography (RER) to accurately measure the level of acceleration as a function of the initial laser drive time history for indirect-drive implosions on the National Ignition Facility. Here, we demonstrate a transition from no acceleration to 20 ± 1.8μm ns -2 acceleration by tweaking the drive that should reduce the initial instabilities by an order of magnitude at high modes.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

A Micromorphic Length-Scale Coupling Framework for the Determination of Higher-Order Constitutive Models and the Multi-Scale Simulation of Heterogeneous Materials [Thesis]

Heterogeneous materials and materials with complex microstructures pose a unique challenge in the development of accurate models of their response to external stimuli. These difficulties principally arise due to the difficulty in characterizing and modeling the constituents and their interactions. It is usually possible, though non-trivial, to construct an explicit representation of the microstructure (a direct numeric simulation or DNS) but the method by which the complex modes of deformation and other processes can be homogenized to a reduced-order approximation is frequently unclear. Many homogenization approaches are ad-hoc and lack a strong justification beyond ease of computation. Furthermore, the homogenization approach can, in some cases, not utilize the full breadth of information available in the computation of the macro-scale stresses and deformation measures. It is also noteworthy that homogenization, by its very nature, will tend to obfuscate details of processes occurring at the lower length-scale. It is therefore of interest to include as much information as possible in the construction of the reduced-order model so as to be predictive in a variety of loading environments. We here present a length-scale bridging technique based upon the micromorphic continuum mechanics of Eringen which incorporates volume and surface area averages as a part of its construction. This approach enforces the balance equations at the micro-scale and then studies the effect of the spatially varying nature on the macro-scale. This leads, naturally, to further balance equations which are solved at the macro-scale. This work details a homogenization framework which arises naturally from the micromorphic construction of Eringen attempting to introduce no definitions beyond which are justifiable from micro-structural considerations. One of the results of this effort is the so-called “micromorphic filter” which has been developed and applied to several DNS to demonstrate its effectively. In order to determine the macroscopic degrees of freedom we utilize the special case of an overlap coupling technique where the macro-scale is fully constrained to the micro-scale. This enables us to study the resulting material properties as expected but also allows us to further study the boundary conditions on the additional degrees of freedom at the macro-scale.

42 ENGINEERING↗
DOE OSTI2024

Parametric reduced-order modeling for component-oriented treatment and localized nonlinear feature inclusion

Abstract We propose coupling a physics-based reduction framework with a suited response decomposition technique to derive a component-oriented reduction (COR) approach, which is suitable for assembly systems featuring localized nonlinearities. Dependencies on influencing parameters are injected into the reduced-order model (ROM), thus ensuring robustness and validity over a domain of parametric inputs, while capturing nonlinear effects. The implemented approach employs individual component modes to capture localized features while additionally relying on reduced modes of a global nature to approximate the system’s dynamics accurately. The global modes are derived from a linear monolithic system, defined as a result of a coordinate separation scheme, which permits the proposed COR-ROM to naturally couple the response between linear and nonlinear subdomains. The derived low-order representation utilizes a proper orthogonal decomposition projection and is additionally reinforced with the inclusion of a hyper-reduction technique to capture the underlying high-fidelity model response while providing accelerated computations. The resulting approach is exemplified in the synthetic case studies of a four-story shear frame with multiple nonlinear regions driven by hysteresis and a large-scale kingpin connection featuring plasticity.

Vlachas, Konstantinos (ORCID:000000029124219X)↗
DOE OSTI2020

Shuffling mode competition leads to directionally anisotropic mobility of faceted Σ11 boundaries in fcc metals

Faceted grain boundaries can migrate in interesting and unexpected ways. For example, faceted Σ11 <110> tilt grain boundaries were observed to exhibit mobility values that could be strongly dependent on the direction of migration. In order to understand whether this directionally-anisotropic mobility is a general phenomenon and to isolate mechanistic explanations for this behavior, molecular dynamics simulations of bicrystals evolved under an artificial driving force are used to study interface migration for a range of boundary plane inclination angles and temperatures in multiple face centered cubic metals (Al, Ni, and Cu). We find that directionally anisotropic mobility is active in a large fraction of these boundaries in Ni and Cu and should therefore impact the coarsening of polycrystalline materials. On the other hand, no such anisotropy is observed in any of the Al boundaries, showing that this behavior is material-dependent. Migration of the faceted boundaries is accomplished through transformation events at facet nodes and incommensurate boundary plane facets, which are termed shuffling modes. Three major shuffling modes have been identified, namely Shockley shuffling, slip plane shuffling, and disordered shuffling. A shift from the first two ordered modes to the third disordered mode is found to be responsible for reducing or removing directionally-anisotropic mobility, especially at the highest temperatures studied.

36 MATERIALS SCIENCE↗
DOE OSTI2022

Machine-Learning Assisted Identification of Accurate Battery Lifetime Models with Uncertainty

Reduced-order battery lifetime models, which consist of algebraic expressions for various aging modes, are widely utilized for extrapolating degradation trends from accelerated aging tests to real-world aging scenarios. Identifying models with high accuracy and low uncertainty is crucial for ensuring that model extrapolations are believable, however, it is difficult to compose expressions that accurately predict multivariate data trends; a review of cycling degradation models from literature reveals a wide variety of functional relationships. Here, a machine-learning assisted model identification method is utilized to fit degradation in a stand-out LFP-Gr aging data set, with uncertainty quantified by bootstrap resampling. The model identified in this work results in approximately half the mean absolute error of a human expert model. Models are validated by converting to a state-equation form and comparing predictions against cells aging under varying loads. Parameter uncertainty is carried forward into an energy storage system simulation to estimate the impact of aging model uncertainty on system lifetime. The new model identification method used here reduces life-prediction uncertainty by more than a factor of three (86% ± 5% relative capacity at 10 years for human-expert model, 88.5% ± 1.5% for machine-learning assisted model), empowering more confident estimates of energy storage system lifetime.

25 ENERGY STORAGE↗
DOE OSTI2020

Characterizing magnetized plasmas with dynamic mode decomposition

Accurate and efficient plasma models are essential to understand and control experimental devices. Existing magnetohydrodynamic or kinetic models are nonlinear and computationally intensive and can be difficult to interpret, while often only approximating the true dynamics. In this work, data-driven techniques recently developed in the field of fluid dynamics are leveraged to develop interpretable reduced-order models of plasmas that strike a balance between accuracy and efficiency. In particular, dynamic mode decomposition (DMD) is used to extract spatio-temporal magnetic coherent structures from the experimental and simulation datasets of the helicity injected torus with steady inductive (HIT-SI) experiment. Three-dimensional magnetic surface probes from the HIT-SI experiment are analyzed, along with companion simulations with synthetic internal magnetic probes. A number of leading variants of the DMD algorithm are compared, including the sparsity-promoting and optimized DMD. Optimized DMD results in the highest overall prediction accuracy, while sparsity-promoting DMD yields physically interpretable models that avoid overfitting. These DMD algorithms uncover several coherent magnetic modes that provide new physical insights into the inner plasma structure. These modes were subsequently used to discover a previously unobserved three-dimensional structure in the simulation, rotating at the second injector harmonic. Finally, using data from probes at experimentally accessible locations, DMD identifies a resistive kink mode, a ubiquitous instability seen in magnetized plasmas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2020

Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network

Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a deep residual neural network (ResNet) closure learning framework for ROMs of nonlinear systems. The novel ResNet-ROM framework consists of two steps: (i) In the first step, we use ROM projection to filter the given nonlinear system and construct a spatially filtered ROM. This filtered ROM is low-dimensional, but is not closed. (ii) In the second step, we use ResNet to close the filtered ROM, i.e., to model the interaction between the resolved and unresolved ROM modes. We emphasize that in the new ResNet-ROM framework, data is used only to complement classical physical modeling (i.e., only in the closure modeling component), not to completely replace it. We also note that the new ResNet-ROM is built on general ideas of spatial filtering and deep learning and is independent of (restrictive) phenomenological arguments, e.g., of eddy viscosity type. The numerical experiments for the 1D Burgers equation show that the ResNet-ROM is significantly more accurate than the standard projection ROM. The new ResNet-ROM is also more accurate and significantly more efficient than other modern ROM closure models.

Xie, Xuping↗
DOE OSTI2026

Booster cavity damper redesign for PIP-II

A new Higher Order Mode (HOM) damper was designed and is undergoing testing for the Booster accelerator cavity at Fermilab. In anticipation of the PIP-II upgrade, it was discovered that the higher intensity of PIP-II may cause beam instability due to an excited mode at 106 MHz. This unfortunately corresponds with the cavity’s 2nd order harmonic mode, which will sweep from 86-105.7 MHz. The new damper is a modification of an existing damper that was designed to reduce an existing static HOM at 83 MHz, with the new design intending to cover the 2nd order HOM as well. The existing damper uses an inductive coupling loop to extract RF energy from the cavity which then goes through a filter in order to reflect the fundamental frequency back into the cavity while passing HOMs to a dump load. The new damper intends to replace the filter portion of the system with a wider band variant while also changing the topology from a coaxial cable loop filter to a componentized PCB-based design. Primary design challenges include bandwidth coverage, impedance matching of the various modes, long term thermal and mechanical stability, radiation hardness, and high voltage handling. Initial designs achieved the desired damping but were found to quickly succumb to destructive arcing due to the voltages present. More finalized designs intend to address this problem through circuit design modifications as well as the use of hardier components.

Pieper, Dustin [Fermilab]↗
DOE OSTI2025

Booster Cavity Damper Redesign for PIP-II

A new Higher Order Mode (HOM) damper was designed and tested for the Booster accelerator cavity at Fermilab. In anticipation of the PIP-II upgrade, it was discovered that the higher beam intensity of PIP-II may cause beam instability due to an excited mode at 106 MHz. This unfortunately corresponds with the cavity s 2nd order harmonic mode, which will sweep from 86-105.7 MHz. The new damper is a modification of an existing damper that was designed to reduce an existing static HOM at 83 MHz, with the new design intending to cover the 2nd order HOM as well. The existing damper uses an inductive coupling loop to extract RF energy from the cavity which then goes through a filter in order to reflect the fundamental frequency back into the cavity while passing HOMs to a dump load. The new damper intends to replace the filter portion of the system with a wider band variant while also changing the topology from a coaxial cable loop filter to a componentized PCB-based design. Primary design challenges include bandwidth coverage, impedance matching of the various modes, long term thermal and mechanical stability, radiation hardness, and high voltage handling. Initial designs achieved the desired damping but were found to quickly succumb to destructive arcing due to the voltages present. More finalized designs intend to address this problem through circuit design modifications as well as the use of hardier components.

Pieper, Dustin [Fermilab]↗
DOE OSTI2024

Extended dynamic mode decomposition for model reduction in fluid dynamics simulations

High computational cost and storage/memory requirements of fluid dynamics simulations constrain their usefulness as a predictive tool. Reduced-order models (ROMs) provide a viable solution to this challenge by extracting the key underlying dynamics of a complex system directly from data. We investigate the efficacy and robustness of an extended dynamic mode decomposition (xDMD) algorithm in constructing ROMs of three-dimensional cardiovascular computations. Focusing on the ROMs' accuracy in representation and interpolation, we relate these metrics to the truncation rank of singular value decomposition, which underpins xDMD and other approaches to ROM construction. Our key innovation is to relate the truncation rank to the singular values of the original flow problem. This result establishes a priori guidelines for the xDMD deployment and its likely success as a means of data compression and reconstruction of the system's dynamics from dominant spatiotemporal structures present in the data.

Mechanics↗
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 OSTI2025

Tropical Cyclone Super Resolution using conditional diffusion denoising probabilistic model from mesoscale simulation to LES

Accurate modeling of tropical cyclone wind fields is essential for the design, risk assessment, and operational planning of offshore energy infrastructure. While mesoscale simulations are widely used thanks to their computational efficiency, they lack the necessary resolution to capture key features such as wind shear and veer profiles as well as the distribution turbulent kinetic energy (TKE). High-fidelity large-eddy simulation (LES) models on the other hand, can resolve turbulent structures and provide a more accurate representation of the complex wind field, albeit at a higher computational cost. To address this modeling gap, we introduce a two-part generative framework to enhance the resolution and physics-capturing ability of mesoscale simulations. First, a reduced-order model based on Karhunen–Loève (KL) decomposition is used to extract dominant spatial modes from one-dimensional mean wind profiles. A multilayer perceptron (MLP) is trained to map mesoscale mode weights to their LES counterparts, enabling accurate reconstruction of vertical velocity profiles. Second, a conditional Diffusion Denoising Probabilistic Model (DDPM) is developed to super-resolve coarse and low-fidelity mesoscale velocity fields, recovering fine-scale turbulence structures and stress distributions. The framework is evaluated across different tropical cyclone intensity categories defined by the Saffir–Simpson scale and demonstrates strong performance in both interpolation and extrapolation tasks. The generated fields accurately reproduce spatial coherence, stress distributions, and spectral energy characteristics observed in LES data. By bridging the fidelity gap between mesoscale and LES outputs, this approach offers a scalable, data-driven solution for enhancing the representation of tropical cyclone wind fields, enabling more robust offshore energy infrastructure systems design in tropical-cyclone-prone areas.

17 WIND ENERGY↗