Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations

• URL: http://arxiv.org/abs/2104.14034v1
• Date: Wed, 28 Apr 2021 22:14:25 GMT
• Title: Dynamic Mode Decomposition in Adaptive Mesh Refinement and Coarsening Simulations
• Authors: Gabriel F. Barros, Mal\'u Grave, Alex Viguerie, Alessandro Reali, Alvaro L. G. A. Coutinho
• Abstract summary: 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.
• Score: 58.720142291102135
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Dynamic Mode Decomposition (DMD) is a powerful data-driven method used to extract spatio-temporal coherent structures that dictate a given dynamical system. The method consists of stacking collected temporal snapshots into a matrix and mapping the nonlinear dynamics using a linear operator. The standard procedure considers that snapshots possess the same dimensionality for all the observable data. However, this often does not occur in numerical simulations with adaptive mesh refinement/coarsening schemes (AMR/C). This paper proposes a strategy to enable DMD to extract features from observations with different mesh topologies and dimensions, such as those found in AMR/C simulations. For this purpose, the adaptive snapshots are projected onto the same reference function space, enabling the use of snapshot-based methods such as DMD. The present strategy is applied to challenging AMR/C simulations: a continuous diffusion-reaction epidemiological model for COVID-19, a density-driven gravity current simulation, and a bubble rising problem. We also evaluate the DMD efficiency to reconstruct the dynamics and some relevant quantities of interest. In particular, for the SEIRD model and the bubble rising problem, we evaluate DMD's ability to extrapolate in time (short-time future estimates).

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• 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)
• Entropic Regression DMD (ERDMD) Discovers Informative Sparse and Nonuniformly Time Delayed Models [0.0]
  We present a method which determines optimal multi-step dynamic mode decomposition models via entropic regression. We develop a method that produces high fidelity time-delay DMD models that allow for nonuniform time space. These models are shown to be highly efficient and robust.
  arXiv  Detail & Related papers  (2024-06-17T20:02:43Z)
• Real-Time Motion Detection Using Dynamic Mode Decomposition [0.40964539027092906]
  We propose a simple and interpretable motion detection algorithm for streaming video data rooted in Dynamic Mode Decomposition (DMD) Our method leverages the fact that there exists a correspondence between the evolution of important video features, such as foreground motion, and the eigenvalues of the matrix which results from applying DMD to segments of video.
  arXiv  Detail & Related papers  (2024-05-08T13:52:14Z)
• Optimized Dynamic Mode Decomposition for Reconstruction and Forecasting of Atmospheric Chemistry Data [3.1484174280822845]
  We introduce the optimized dynamic mode decomposition for constructing an adaptive and efficient reduced order model and forecasting tool. We show that the DMD algorithm successfully extracts known features of atmospheric chemistry, such as summertime surface pollution and biomass burning activities.
  arXiv  Detail & Related papers  (2024-04-13T15:44:12Z)
• A Poisson-Gamma Dynamic Factor Model with Time-Varying Transition Dynamics [51.147876395589925]
  A non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time. A fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance.
  arXiv  Detail & Related papers  (2024-02-26T04:39:01Z)
• 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)
• Coupled and Uncoupled Dynamic Mode Decomposition in Multi-Compartmental Systems with Applications to Epidemiological and Additive Manufacturing Problems [58.720142291102135]
  We show that Dynamic Decomposition (DMD) may be a powerful tool when applied to nonlinear problems. In particular, we show interesting numerical applications to a continuous delayed-SIRD model for Covid-19.
  arXiv  Detail & Related papers  (2021-10-12T21:42:14Z)
• 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 Bayesian Active Learning for Accelerating Stochastic Simulation [74.58219903138301]
  Interactive Neural Process (INP) is a deep active learning framework for simulations and with active learning approaches. For active learning, we propose a novel acquisition function, Latent Information Gain (LIG), calculated in the latent space of NP based models. The results demonstrate STNP outperforms the baselines in the learning setting and LIG achieves the state-of-the-art for active learning.
  arXiv  Detail & Related papers  (2021-06-05T01:31:51Z)

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.