Reduced-Order Finite-Difference Mode Solutions for Metal Cavities With Symmetry
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Wallace, Jon William [Sandia National Laboratories↗
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Accelerating particle-in-cell kinetic plasma simulations via reduced-order modeling of space-charge dynamics using dynamic mode decomposition
We present a data-driven reduced-order modeling of the space-charge dynamics for electromagnetic particle-in-cell (EMPIC) plasma simulations based on dynamic mode decomposition (DMD). The dynamics of the charged particles in kinetic plasma simulations such as EMPIC is manifested through the plasma current density defined along the edges of the spatial mesh. We showcase the efficacy of DMD in modeling the time evolution of current density through a low-dimensional feature space. Not only do such DMD based predictive reduced-order models help accelerate EMPIC simulations, they also have the potential to facilitate investigative analysis and control applications. Here, we demonstrate the proposed DMD-EMPIC scheme for reduced-order modeling of current density and speedup in EMPIC simulations involving electron beam under the influence of magnetic field, virtual cathode oscillations, and backward wave oscillator.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Micro–macro finite element modeling method for rub response in abradable coating materials
Gas turbine engines experience “rub” when the rotating blades come in contact with a static abradable coating. This results in extreme strain rates and dynamics inside a high-temperature/high-pressure environment. Current rub models are phenomenological and do not reflect the underlying microstructures, thus limiting their prediction accuracy. In this work, a microstructure-informed, reduced order modeling framework is introduced for simulating abradable coating “rub" behavior. This framework comprises a microscale model constructed based on digitized abradable microstructure and explicitly simulates the mechanical behavior of each constituent phases and their interactions. After calibration and validation with experiment data, the calibrated microscale model is used to generate data across a vast range of applied strain rates and temperature with various load paths. Then, the virtually generated data are used to fit the macroscopic-reduced order model, which enables fast component scale rub simulation without compromising the integrity of the complex material behavior. In conclusion, the proposed effort will address the technical challenge of predicting abradable material behavior during rub through the application of multiscale modeling from microstructure to engines behavior, effectively reducing the development costs and time of new abradable material for better “rub” properties.
36 MATERIALS SCIENCE↗
Novel Concepts for High Gradient Acceleration (Final Technical Report)
We have conducted an intensive, pioneering program to demonstrate novel concepts for achieving high gradient acceleration at frequencies from the conventional microwave bands up to the millimeter wave /THz bands. High gradient accelerators hold the promise of smaller and less costly accelerators for applications ranging from the largest scale accelerators used for discovery science down to the smallest accelerators used for industrial, homeland security and medical applications. The research consisted of two major research thrusts: 1.) Structure-based wakefield accelerator (SWFA) research in collaboration with the Argonne Wakefield Accelerator research group and 2.) Millimeter Wave / THz high gradient acceleration in collaboration with SLAC. The specific goals of the research program were: Design novel metallic metamaterial structures that increase the beam-wave coupling for the accelerator mode and reduce the effect of high order modes; test novel metamaterial structures to achieve higher output power, > 1 GW at X-Band (11.7 GHz), in test at the Argonne Wakefield Accelerator (AWA); determine the experimental breakdown threshold for nanosecond-scale pulses at X-Band in testing at the AWA; test a 110 GHz accelerator structure with a field emission electron gun, built at SLAC, using pulses from a 1 MW, 110 GHz gyrotron; design, build and test a 110 GHz quasi-optical, resonant-ring pulse compressor to compress microsecond pulses from the 1 MW gyrotron into > 20 MW, 5 ns output pulses for accelerator structure testing. The proposed research program built on our successes in our research program including: Generation of 510 MW, 2.1 ns (FWHM) pulses at 11.7 GHz from a metallic metamaterial structure in test at the Argonne Wakefield Accelerator using a train of eight 65 MeV electron bunches spaced at 1.3 GHz with a total charge of 280 nC. The metamaterial structure consisted of 100 copper unit cells each consisting of a “wagon-wheel” plate and a spacer plate with a total structure length of 0.2 m. The 510 MW pulse generated an on-axis wakefield of 130 MV/m that could be used to accelerate a trailing witness bunch. Demonstration of coupling of an unprecedented rf power level of 575kW into a 110 GHz accelerator structure using a quasi-optical setup. The standing structure consisted of a central copper cavity located between two matching cavities fed by a TM01 mode. The 6 ns input pulses were sliced from 3 microsecond pulses from the gyrotron using a laser-driven silicon switch. We obtained an unprecedented high gradient up to 230MV/m corresponding to a peak surface electric field of more than 520 MV/m.
43 PARTICLE ACCELERATORS↗
Nonlocal, Pattern-Aware Response and Feedback Framework for Regional Climate Response
We devise a pattern-aware feedback framework for representing the forced climate response using a suite of Green’s function experiments with solar radiation perturbations. By considering the column energy balance, a comprehensive linear response function (CLRF) for important climate variables and feedback quantities such as moist static energy, sea surface temperature, albedo, cloud optical depth, and lapse rate is learned from Green’s function data. The learned CLRF delineates the effects of the energy diffusion in both the ocean and atmosphere and the pattern-aware feedbacks from the aforementioned radiatively active processes. The CLRF can then be decomposed into forcing–response mode pairs, which are in turn used to construct a reduced-order model describing the dominant dynamics of climate responses. These mode pairs capture nonlocal effects and teleconnections in the climate and thus make the reduced-order model apt for capturing regional features of climate response. A key observation is that the CLRF captures the polar-amplified response as the most excitable mode of the climate system, and this mode is explainable in the data-learned pattern-aware feedback framework. The reduced-order model can be used for predicting the response for a given forcing and for reconstructing the forcing from a given response; we demonstrate these capabilities for multiple independent forcing scenarios.
Feedback↗
Data-scarce surrogate modeling of shock-induced pore collapse process
Understanding the mechanisms of shock-induced pore collapse is of great interest in various disciplines in sciences and engineering, including materials science, biological sciences, and geophysics. However, numerical modeling of the complex pore collapse processes can be costly. To this end, a strong need exists to develop surrogate models for generating economic predictions of pore collapse processes. Here, in this work, we study the use of a data-driven reduced-order model, namely dynamic mode decomposition, and a deep generative model, namely conditional generative adversarial networks, to resemble the numerical simulations of the pore collapse process at representative training shock pressures. Since the simulations are expensive, the training data are scarce, which makes training an accurate surrogate model challenging. To overcome the difficulties posed by the complex physics phenomena, we make several crucial treatments to the plain original form of the methods to increase the capability of approximating and predicting the dynamics. In particular, physics information is used as indicators or conditional inputs to guide the prediction. In realizing these methods, the training of each dynamic mode composition model takes only around 30 s on CPU. In contrast, training a generative adversarial network model takes 8 h on GPU. Moreover, using dynamic mode decomposition, the final-time relative error is around 0.3% in the reproductive cases. We also demonstrate the predictive power of the methods at unseen testing shock pressures, where the error ranges from 1.3 to 5% in the interpolatory cases and 8 to 9% in extrapolatory cases.
97 MATHEMATICS AND COMPUTING↗
Data-Driven Analysis of Multipactor Dynamics via Dynamic Mode Decomposition
Multipactor effect is a performance-limiting kinetic plasma effect that can occur in high-power microwave and radio frequency (RF) devices. Multipactor effect is of special concern in vacuum or near-vacuum conditions such as those in particle accelerators and spaceborne devices. In this work, we present a data-driven reduced-order model (ROM) based on dynamic mode decomposition (DMD) for modeling of multipactor effects. We study multipactor effects and the resulting nonlinear harmonic generation by processing high-fidelity data generated from electromagnetic particle-in-cell (EMPIC) simulations using the DMD algorithm. We also investigate time-delay embedding extensions of DMD with improved generalizability and accuracy for modeling the electron plasma current density behavior. Here, the results show that DMD provides valuable insights into multipactor phenomena by extracting relevant modal spatiotemporal patterns and frequencies. In addition, DMD offers the potential to time extrapolate EMPIC simulations at a minimal cost, thereby reducing overall simulation time.
43 PARTICLE ACCELERATORS↗
Machine learning without a processor: Emergent learning in a nonlinear analog network
Standard deep learning algorithms require differentiating large nonlinear networks, a process that is slow and power-hungry. Electronic contrastive local learning networks (CLLNs) offer potentially fast, efficient, and fault-tolerant hardware for analog machine learning, but existing implementations are linear, severely limiting their capabilities. These systems differ significantly from artificial neural networks as well as the brain, so the feasibility and utility of incorporating nonlinear elements have not been explored. Here, we introduce a nonlinear CLLN—an analog electronic network made of self-adjusting nonlinear resistive elements based on transistors. We demonstrate that the system learns tasks unachievable in linear systems, including XOR (exclusive or) and nonlinear regression, without a computer. We find our decentralized system reduces modes of training error in order (mean, slope, curvature), similar to spectral bias in artificial neural networks. The circuitry is robust to damage, retrainable in seconds, and performs learned tasks in microseconds while dissipating only picojoules of energy across each transistor. This suggests enormous potential for fast, low-power computing in edge systems like sensors, robotic controllers, and medical devices, as well as manufacturability at scale for performing and studying emergent learning.
Science & Technology - Other Topics↗
Modal dynamics of wind turbine wake meandering from lidar observations
Horizontal scans from nacelle-mounted lidars provide time series measurements of wind turbine wakes across diverse atmospheric conditions, enabling analysis of coherent turbulent structures that influence wake meandering through proper orthogonal decomposition (POD). While low-order modes capture the most energetic turbulent structures, our analysis reveals that they do not necessarily dominate wake meandering dynamics. We evaluate more than 16,000 combinatorial reconstructions of the flow field for each inflow case, demonstrating that mode relevance depends on mode symmetry, turbulent kinetic energy content, and inflow characteristics. Cases with low turbulence intensity and large integral timescales show stronger correlations between POD modes and wake meandering, whereas higher turbulence conditions (turbulence intensity > 7%) are less effectively described by reduced-order models. However, the qualitative similarity of POD modes across varied atmospheric conditions suggests the potential existence of a semi-universal basis for representing wind turbine wakes, with implications for improving engineering wake models.
17 WIND ENERGY↗
Train small, model big: Scalable physics simulators via reduced order modeling and domain decomposition
Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the pilot-scale model, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. The ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. Here this method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about 15–40 times faster with only ~1% relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
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↗
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)↗
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]↗
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]↗
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↗
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↗
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↗
Towards Universal Non-Dimensional Characterization of the Oscillatory Dynamics of Wind Turbine Rotors of Multiple Sizes
One concern in the field of Horizontal Axis Wind Turbines (HAWTs) is what control strategies are needed to handle gust pulses in the wind to prevent extreme oscillations of the blades to reduce fatigue stress, prevent blade rupture, and extend the turbine’s operational life. In order to design innovative control strategies to modify the blade’s oscillatory response, it is crucial to establish the fundamental vibrational behavior of the blades when excited by gust pulses of different frequencies and amplitudes present in the fluctuating wind inflow. In a series of previous works, the authors presented a novel Reduced-Order Characterization (ROC) technique that provided an energy-based characterization of the fundamental modes of oscillation of wind turbine rotors when excited by combinations of wind gust pulses of different frequencies and amplitudes. The main focus of the present work is to extend these original notions of energy-based ROC to a universal technique expressed in terms of non-dimensional quantities that could be applied to turbines of any size, operating in any set of wind conditions, as long as they share geometrical and material similarity. The ROC technique provides a simple formula that is capable of predicting the dominant vibrational modes of a blade with sufficient precision to be useful in the determination of a control decision that can be computed in real time, an aspect of fundamental importance in dealing with rapid fluctuations in wind conditions.
Yates, North (ORCID:000900052204261X)↗