Model Reduction with Memory and the Machine Learning of Dynamical Systems

DOI10.4208/cicp.OA-2018-0269zbMath1473.35450arXiv1808.04258OpenAlexW2963721506WikidataQ128468120 ScholiaQ128468120MaRDI QIDQ5161393

Chao Ma, Jianchun Wang, E. Weinan

Publication date: 29 October 2021

Published in: Communications in Computational Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1808.04258

zbMATH Keywords

model reductionrecurrent neural networksMori-Zwanzig

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Numerical problems in dynamical systems (65P99)

Related Items

Machine learning for prediction with missing dynamics, Analytic continuation of noisy data using Adams Bashforth residual neural network, Dynamically learning the parameters of a chaotic system using partial observations, The deep learning Galerkin method for the general Stokes equations, Simultaneous neural network approximation for smooth functions, A framework for machine learning of model error in dynamical systems, Regression-Based Projection for Learning Mori–Zwanzig Operators, NySALT: Nyström-type inference-based schemes adaptive to large time-stepping, Learning Theory for Dynamical Systems, PDE-Net 2.0: learning PDEs from data with a numeric-symbolic hybrid deep network, Unnamed Item, Better Approximations of High Dimensional Smooth Functions by Deep Neural Networks with Rectified Power Units, Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks, Error bounds of the invariant statistics in machine learning of ergodic Itô diffusions, Kernel-based prediction of non-Markovian time series, Recurrent neural network closure of parametric POD-Galerkin reduced-order models based on the Mori-Zwanzig formalism, Using machine learning to predict extreme events in complex systems

Uses Software

• Adam

Cites Work

• A thermodynamic study of the two-dimensional pressure-driven channel flow
• Quantifying and reducing model-form uncertainties in Reynolds-averaged Navier-Stokes simulations: a data-driven, physics-informed Bayesian approach
• Efficient implementation of essentially nonoscillatory shock-capturing schemes
• Optimal prediction with memory
• A dynamic subgrid scale model for large eddy simulations based on the Mori-Zwanzig formalism
• Transport, Collective Motion, and Brownian Motion
• Reynolds averaged turbulence modelling using deep neural networks with embedded invariance