Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting

• URL: http://arxiv.org/abs/2308.13727v1
• Date: Sat, 26 Aug 2023 01:48:29 GMT
• Title: Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: II. dynamics forecasting
• Authors: Farbod Faraji, Maryam Reza, Aaron Knoll, J. Nathan Kutz
• Abstract summary: We develop a variant of the Dynamic Mode Decomposition (DMD) algorithm based on variable projection optimization, called Optimized Dynamic Mode Decomposition (OPT-DMD) We extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics. Despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven reduced-order models.
• Score: 3.203036813451742
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: In part I of the article, we demonstrated that a variant of the Dynamic Mode Decomposition (DMD) algorithm based on variable projection optimization, called Optimized DMD (OPT-DMD), enables a robust identification of the dominant spatiotemporally coherent modes underlying the data across various test cases representing different physical parameters in an ExB simulation configuration. As the OPT-DMD can be constrained to produce stable reduced-order models (ROMs) by construction, in this paper, we extend the application of the OPT-DMD and investigate the capabilities of the linear ROM from this algorithm toward forecasting in time of the plasma dynamics in configurations representative of the radial-azimuthal and axial-azimuthal cross-sections of a Hall thruster and over a range of simulation parameters in each test case. The predictive capacity of the OPT-DMD ROM is assessed primarily in terms of short-term dynamics forecast or, in other words, for large ratios of training-to-test data. However, the utility of the ROM for long-term dynamics forecasting is also presented for an example case in the radial-azimuthal configuration. The model's predictive performance is heterogeneous across various test cases. Nonetheless, a remarkable predictiveness is observed in the test cases that do not exhibit highly transient behaviors. Moreover, in all investigated cases, the error between the ground-truth and the reconstructed data from the OPT-DMD ROM remains bounded over time within both the training and the test window. As a result, despite its limitation in terms of generalized applicability to all plasma conditions, the OPT-DMD is proven as a reliable method to develop low computational cost and highly predictive data-driven reduced-order models in systems with a quasi-periodic global evolution of the plasma state.

Related papers

• Analysis and Forecasting of the Dynamics of a Floating Wind Turbine Using Dynamic Mode Decomposition [0.0]
  This article presents a data-driven equation-free modeling of the dynamics of a hexafloat floating offshore wind turbine based on the Dynamic Mode Decomposition (DMD) A forecasting algorithm for the motions, accelerations, and forces acting on the floating system is developed. Results show the approach's capability for short-term future estimates of the system's state, which can be used real-time prediction and control.
  arXiv  Detail & Related papers  (2024-11-08T18:38:29Z)
• Parsimonious Dynamic Mode Decomposition: A Robust and Automated Approach for Optimally Sparse Mode Selection in Complex Systems [0.40964539027092917]
  This paper introduces the Parsimonious Dynamic Mode Decomposition (parsDMD) ParsDMD is a novel algorithm designed to automatically select an optimally sparse subset of dynamic modes for both temporal and purely temporal data. It is validated on a diverse range of datasets, including standing wave signals, identifying hidden dynamics, fluid dynamics simulations, and atmospheric sea-surface temperature (SST) data.
  arXiv  Detail & Related papers  (2024-10-22T03:00:11Z)
• Diffusion posterior sampling for simulation-based inference in tall data settings [53.17563688225137]
  Simulation-based inference ( SBI) is capable of approximating the posterior distribution that relates input parameters to a given observation. In this work, we consider a tall data extension in which multiple observations are available to better infer the parameters of the model. We compare our method to recently proposed competing approaches on various numerical experiments and demonstrate its superiority in terms of numerical stability and computational cost.
  arXiv  Detail & Related papers  (2024-04-11T09:23:36Z)
• Synthetic location trajectory generation using categorical diffusion models [50.809683239937584]
  Diffusion models (DPMs) have rapidly evolved to be one of the predominant generative models for the simulation of synthetic data. We propose using DPMs for the generation of synthetic individual location trajectories (ILTs) which are sequences of variables representing physical locations visited by individuals.
  arXiv  Detail & Related papers  (2024-02-19T15:57:39Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Generative Modeling with Phase Stochastic Bridges [49.4474628881673]
  Diffusion models (DMs) represent state-of-the-art generative models for continuous inputs. We introduce a novel generative modeling framework grounded in textbfphase space dynamics Our framework demonstrates the capability to generate realistic data points at an early stage of dynamics propagation.
  arXiv  Detail & Related papers  (2023-10-11T18:38:28Z)
• Dynamic Mode Decomposition for data-driven analysis and reduced-order modelling of ExB plasmas: I. Extraction of spatiotemporally coherent patterns [3.203036813451742]
  We evaluate the generalability of the Dynamic Mode Decomposition (DMD) algorithm for data-driven analysis and reduced-order modelling of plasma dynamics.
  arXiv  Detail & Related papers  (2023-08-26T01:37:52Z)
• Mixed Effects Neural ODE: A Variational Approximation for Analyzing the Dynamics of Panel Data [50.23363975709122]
  We propose a probabilistic model called ME-NODE to incorporate (fixed + random) mixed effects for analyzing panel data. We show that our model can be derived using smooth approximations of SDEs provided by the Wong-Zakai theorem. We then derive Evidence Based Lower Bounds for ME-NODE, and develop (efficient) training algorithms.
  arXiv  Detail & Related papers  (2022-02-18T22:41:51Z)
• Bagging, optimized dynamic mode decomposition (BOP-DMD) for robust, stable forecasting with spatial and temporal uncertainty-quantification [2.741266294612776]
  Dynamic mode decomposition (DMD) provides a framework for learning a best-fit linear dynamics model over snapshots of temporal, or-temporal, data. The majority of DMD algorithms are prone to bias errors from noisy measurements of the dynamics, leading to poor model fits and unstable forecasting capabilities. The optimized DMD algorithm minimizes the model bias with a variable projection optimization, thus leading to stabilized forecasting capabilities.
  arXiv  Detail & Related papers  (2021-07-22T18:14:20Z)
• Deep neural network enabled corrective source term approach to hybrid analysis and modeling [0.0]
  Hybrid Analysis and Modeling (HAM) is an emerging modeling paradigm which aims to combine physics-based modeling and data-driven modeling. We introduce, justify and demonstrate a novel approach to HAM -- the Corrective Source Term Approach (CoSTA)
  arXiv  Detail & Related papers  (2021-05-24T20:17:13Z)
• Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations [58.720142291102135]
  Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract coherent schemes. This paper proposes a strategy to enable DMD to extract from observations with different mesh topologies and dimensions.
  arXiv  Detail & Related papers  (2021-04-28T22:14:25Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.