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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

StOKeDMD: Streaming Occupation kernel dynamic mode decomposition

Dynamic mode decomposition (DMD) has become a common technique for constructing surrogate models for dynamical systems from observed system states. The Occupation Kernel DMD (OKDMD) method proposed in (Rosenfeld et al., 2022) and (Rosenfeld et al., 2024) is a Liouville operator based method that builds surrogate models from system state trajectories. Here, this paper proposes an extension of OKDMD to the case when the system states are observed in a streaming fashion, i.e., only a small fraction of the state trajectory is available at a given time. The developed method, Streaming Occupation Kernel DMD (StOKeDMD), accommodates the streaming data input by leveraging properties of specific choices of kernel functions and occupation kernels. We apply the StoKeDMD method as a compression method for streaming data, analyze the memory complexity, and demonstrate the performance of StoKeDMD in the compression of streaming data generated from a Lorenz system and a fluid flow simulation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Dynamic mode decomposition for gyrokinetic eigenmode analysis

Dynamic mode decomposition (DMD) is a post-processing approach to decompose a complex time series into a set of modes via spectral analysis. DMD provides a new and powerful method to recover gyrokinetic drift-wave eigenfrequencies and eigenfunctions based only on the solution of the gyrokinetic-Maxwell initial value problem with almost no added cost to the initial value solver. In the present paper, DMD is applied to the CGYRO gyrokinetic code using a newly-developed CGYRO-DMD post-processor. CGYRO-DMD is numerically efficient, even on a single CPU. It does not set any restrictions on the plasma shape, beta (ratio of the plasma pressure to the magnetic field pressure), collisionality or number of species, and allows one to resolve numerous eigenmodes, even of comparable growth rates. In addition, DMD is not limited to unstable modes, but rather can capture stable and unstable branches simultaneously. In this work, we illustrate the accuracy of DMD through gyrokinetic analysis of mode transition for electromagnetic drift wave instabilities.

drift-wave eigenmodes↗
DOE OSTI2025

Efficient Streaming Dynamic Mode Decomposition

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

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

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↗
DOE OSTI2025

Online Dynamic Mode Decomposition Based System Identification of Multi-Zone Building HVAC Systems

Many works have recently been conducted to reduce the electricity consumption of smart buildings and allow them to support various grid services. Most of these works require accurate system models for the various appliances in the building including heating, ventilation, and air conditioning (HVAC) units. In this paper, we investigate a recursive data-driven system identification strategy to construct the thermal model for a time-varying building with a multi-zone HVAC unit. The online dynamic mode decomposition (DMD)-based strategy is employed to identify the multi-zone thermal building dynamics, where a simple information update (rank-1) is selected to avoid computational complexity. The DMD-based identification strategy is validated using a real gymnasium building equipped with a 4-zone HVAC unit, and its performance is compared with that of the traditional nuclear-norm subspace identification (N2SID) strategy.

Wu, Tumin [University of Tennessee, Knoxville (UTK↗
DOE OSTI2026

Efficient Measurement-Driven Eigenenergy Estimation with Classical Shadows

Quantum algorithms exploiting real-time evolution under a target Hamiltonian have demonstrated remarkable efficiency in extracting key spectral information. However, the broader potential of these methods, particularly beyond ground-state calculations, is underexplored. In this work, we introduce the framework of multiobservable dynamic mode decomposition (MODMD), which combines the observable dynamic mode decomposition (DMD), a measurement-driven eigensolver tailored for near-term implementation, with classical shadow tomography. MODMD leverages random scrambling in the classical shadow technique to construct, with exponentially reduced resource requirements, a signal subspace that encodes rich spectral information. Notably, we replace typical Hadamard-test circuits with a protocol designed to predict low-rank observables, thereby broadening the use of classical shadow tomography for predicting many low-rank observables. We establish theoretical guarantees on the spectral approximation from MODMD, taking into account distinct sources of error. In the ideal case, we prove that the spectral error scales as exp (−Δ⁢𝐸⁢𝑡 max ), where Δ⁢𝐸 is the Hamiltonian spectral gap and 𝑡 max is the maximal simulation time. This analysis provides a rigorous justification of the rapid convergence observed across simulations. To demonstrate the utility of our framework, we consider its application to fundamental tasks, such as determining the low-lying, i.e., ground or excited, energies of representative many-body systems. Our work paves the path for efficient designs of measurement-driven algorithms on near-term and early fault-tolerant quantum devices.

quantum algorithms & computation↗
DOE OSTI2025

Heterogeneous Mixtures of Dictionary Functions to Approximate Subspace Invariance in Koopman Operators: Why Deep Koopman Operators Work

Abstract Koopman operators model nonlinear dynamics as a linear dynamic system acting on a nonlinear function as the state. This nonstandard state is often called a Koopman observable and is usually approximated numerically by a superposition of functions drawn from a dictionary . In a widely used algorithm, extended dynamic mode decomposition (EDMD), the dictionary functions are drawn from a fixed class of functions. Deep learning combined with EDMD has been used to learn novel dictionary functions in an algorithm called deep dynamic mode decomposition (deepDMD). The learned representation both (1) accurately models and (2) scales well with the dimension of the original nonlinear system. In this paper, we analyze the learned dictionaries from deepDMD and explore the theoretical basis for their strong performance. We explore State-Inclusive Logistic Lifting (SILL) dictionary functions to approximate Koopman observables. Error analysis of these dictionary functions show they satisfy a property of subspace approximation, which we define as uniform finite approximate closure. Typically, a Koopman dictionary’s nonlinear functions are homogeneous. In this paper, we discover that structured mixing of heterogeneous dictionary functions drawn from different classes of nonlinear functions achieve the same accuracy and dimensional scaling as the deep-learning-based deepDMD algorithm Yeung et al. ( In: 2019 American Control Conference (ACC), 2019). We specifically show this by building a heterogeneous dictionary comprised of SILL functions and conjunctive radial basis functions (RBFs). This mixed dictionary achieves similar accuracy and dimensional scaling to deepDMD with an order of magnitude reduction in parameters, while maintaining geometric interpretability. These results strengthen the viability of dictionary-based Koopman models to solving high-dimensional nonlinear learning problems.

Johnson, Charles A.↗
DOE OSTI2025

Estimating Eigenenergies from Quantum Dynamics: A Unified Noise-Resilient Measurement-Driven Approach

Ground state energy estimation in physical, chemical, and materials sciences is one of the most promising applications of quantum computing. In this work, we introduce a new hybrid approach that finds the eigenenergies by collecting real-time measurements and post-processing them using the machinery of dynamic mode decomposition (DMD). From the perspective of quantum dynamics, we establish that our approach can be formally understood as a stable variational method on the function space of observables available from a quantum many-body system. We also provide strong theoretical and numerical evidence that our method converges rapidly even in the presence of a large degree of perturbative noise, and show that the method bears an isomorphism to robust matrix factorization methods developed independently across various scientific communities. Our numerical benchmarks on spin and molecular systems demonstrate an accelerated convergence and a favorable resource reduction over state-of-the-art algorithms. The DMD-centric strategy can systematically mitigate noise and stands out as a leading hybrid quantum-classical eigensolver.

Shen, Yizhi↗
DOE OSTI2024

Weighted Composition Operators for Learning Nonlinear Dynamics

Operator theoretic methods in dynamical system have been dominated by the use of Koopman operators and their continuous time counterparts, such as Koopman Generators and Liouville Operators. The advantage gained from their use primarily stems from the ability to extract subspaces and eigenfunctions within a space of observables that are invariant with respect to the Koopman operator over that space. When this occurs, a dynamic mode decomposition of the systems state provides a linear model for the dynamical system. Not all Koopman operators have eigenfunctions that may be exploited in this manner. However, the framework can still be leveraged for approximations using other operators. In this setting, we present a different operator for the study of dynamical systems, the weighted composition operator. These operators are compact for a wide range of dynamics and spaces, and through their interactions with occupation kernels and vector valued kernels, they admit an estimation of the underlying dynamics. Here, this manuscript presents a new algorithm for the data driven study of dynamical systems from data, and also provides two numerical experiments where convergence is achieved as a proof of concept.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Towards Improving luminosity using optics tuning and data-driven methods

The results of Run 24 experiments at Relativistic Heavy Ion Collider (RHIC) for improving luminosity using optics tuning are presented in this study. In the first experiment, MADx matching was used to output magnet strengths corresponding to specific s star movements around Interaction Region 8 (IR8). The corresponding Zero Degree Calorimeter (ZDC) signal was measured in place of luminosity, and Bayesian Optimization aids search of optimal movements. It was found that values retrieved from matching were inaccurate, resulting in negative feedback loops. The second experiment focused on calculating accurate s star movements. The matching method was replaced with a linear sensitivity matrix, directly relating optics to power supply, and its null space was used to fit constraints such as hysteresis effects. At the experiment, beam losses were observed at collimators around boundary of IR8, which were fixed for the third experiment. Dynamic mode decomposition was also introduced to improve quality of turn-by-turn (TBT) data as well as accuracy and consistency of optics measurements at IR8. These improvements will be tested in the experiment of next RHIC run for luminosity optimization.

Accelerator Physics↗
DOE OSTI2025

Harnessing on-machine metrology data for prints with a surrogate model for laser powder directed energy deposition

In this study, we leverage the massive amount of multi-modal on-machine metrology data generated from Laser Powder Directed Energy Deposition (LP-DED) to construct a comprehensive surrogate model of the 3D printing process. By employing Dynamic Mode Decomposition with Control (DMDc), a data-driven technique, we capture the complex physics inherent in this extensive dataset. This physics-based surrogate model emphasizes thermodynamically significant quantities, enabling us to accurately predict key process outcomes. The model ingests 21 process parameters, including laser power, scan rate, and position, while providing outputs such as melt pool temperature, melt pool size, and other essential observables. Furthermore, it incorporates uncertainty quantification to provide bounds on these predictions, enhancing reliability and confidence in the results. We then deploy the surrogate model on a new, unseen part and monitor the printing process as validation of the method. Our experimental results demonstrate that the predictions align with actual measurements with high accuracy, confirming the effectiveness of our approach. Furthermore, this methodology not only facilitates real-time predictions but also operates at process-relevant speeds, establishing a basis for implementing feedback control in LP-DED.

Digital twins↗
DOE OSTI2025

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↗
DOE OSTI2026

Temporal Convolutional Network Using Empirical Mode Decomposition to Detect Faults in Grid Connected Systems

Grid-connected power electronic systems require timely and reliable fault detection to prevent equipment damage and reduce downtime. This paper presents a forecasting-based anomaly detection pipeline that decomposes voltage and current measurements into intrinsic mode functions (IMFs) using empirical mode decomposition (EMD), then trains a causal temporal convolutional network (TCN) on normal-operation IMF data to predict short-horizon future dynamics. Deviations between forecasts and observations are summarized as reliability-weighted residual scores and thresholded per sensor using robust statistics with temporal persistence constraints to suppress false positives. To reduce runtime, EMD is performed on downsampled signals for detection, while raw-rate EMD is applied only within a short region of interest for high-frequency interpretability near detected events. Results on a simulated grid-connected converter system demonstrate that IMF-domain forecasting improves anomaly separability relative to raw-signal forecasting and provides interpretable evidence of faults across decomposition channels.

Sutton, Elizabeth [ORNL] (ORCID:0009000078885935)↗
DOE OSTI2026

Local reduced-order modeling for electrostatic plasmas by physics-informed solution manifold decomposition

Despite advancements in high-performance computing and modern numerical algorithms, computational cost remains prohibitive for multi-query kinetic plasma simulations. Here, in this work, we develop data-driven reduced-order models (ROMs) for collisionless electrostatic plasma dynamics, based on the kinetic Vlasov-Poisson equation. Our ROM approach projects the equation onto a linear subspace defined by the proper orthogonal decomposition (POD) modes. We introduce an efficient tensorial method to update the nonlinear term using a precomputed third-order tensor. We capture multiscale behavior with a minimal number of POD modes by decomposing the solution manifold into multiple time windows and creating temporally local ROMs. We consider two strategies for decomposition: one based on the physical time and the other based on the electric field energy. Applied to the 1D1V Vlasov–Poisson simulations, that is, prescribed E-field, Landau damping, and two-stream instability, we demonstrate that our ROMs accurately capture the total energy of the system both for parametric and time extrapolation cases. The temporally local ROMs are more efficient and accurate than the single ROM. In addition, in the two-stream instability case, we show that the energy-windowing reduced-order model (EW-ROM) is more efficient and accurate than the time-windowing reduced-order model (TW-ROM). With the tensorial approach, EW-ROM solves the equation approximately 90 times faster than Eulerian simulations while maintaining a maximum relative error of 7.5% for the training data and 11% for the testing data.

Electrostatic plasmas↗
DOE OSTI2025

Voltage cycling as a dynamic operation mode for high temperature electrolysis solid oxide cells

Solid Oxide Electrolysis Cells (SOECs) have emerged as a promising technology for the efficient production of H2 via high-temperature electrolysis. However, power input from dynamic energy sources remains a significant challenge for their long-term stability. It is important to analyze the tolerance of cells under dynamic operation conditions. This study focuses on evaluating the impact of voltage cycling on the performance and durability of electrode-supported SOECs. We explore the operational limits and degradation mechanisms of SOECs subjected to various voltage conditions and find that the cells have high tolerance for dynamic voltage. Voltage cycling between 1.3 V and 1.5 V for 9000 cycles does not damage the cell. Conversely, cycling to higher voltages (≥1.7 V) results in accelerated degradation. Advanced characterization is used to screen for various degradation modes post operation. Within the oxygen electrode, XRD and STEM EDS find compositional and phase evolution in all voltage cycled samples including increased decomposition of the air electrode resulting in cation migration. Microstructural analysis of the fuel electrode from nano-CT data shows minimal change throughout the sample set and no evidence of Ni migration, indicating the fuel electrode is stable and not impacted by cycling to higher voltages within the timeframe studied.

Zhu, Zhikuan↗
DOE OSTI2024

Geometry-aware training of factorized layers in tensor Tucker format

Reducing parameter redundancies in neural network architectures is crucial for achieving feasible computational and memory requirements during train and inference of large networks. Given its easy implementation and flexibility, one promising approach is layer factorization, which reshapes weight tensors into a matrix format and parameterizes it as the product of two rank-r matrices. However, this family of approaches often requires an initial full-model warm-up phase, prior knowledge of a feasible rank, and it is sensitive to parameter initialization.In this work, we introduce a novel approach to train the factors of a Tucker decomposition of the weight tensors. Our training proposal proves to be optimal in locally approximating the original unfactorized dynamics and stable for the initialization. Furthermore, the rank of each mode is dynamically updated during training.We provide a theoretical analysis of the algorithm, showing convergence, approximation and local descent guarantees. The method's performance is further illustrated through a variety of experiments, showing remarkable training compression rates and comparable or even better performance than the full baseline and alternative layer factorization strategies.

Zangrando, Emanuele [Gran Sasso Science Institute ↗