Model order reduction for stochastic dynamical systems with continuous symmetries

Abstract

Stochastic dynamical systems with continuous symmetries arise commonly in nature and often give rise to coherent spatio-temporal patterns. However, because of their random locations, these patterns are not well captured by current order reduction techniques and a large number of modes is typically necessary for an accurate solution. In this work, we introduce a new methodology for efficient order reduction of such systems by combining (i) the method of slices, a symmetry reduction tool, with (ii) any standard order reduction technique, resulting in efficient mixed symmetry-dimensionality reduction schemes. In particular, using the Dynamically Orthogonal (DO) equations in the second step, we obtain a novel nonlinear Symmetry-reduced Dynamically Orthogonal (SDO) scheme. We demonstrate the performance of the SDO scheme on stochastic solutions of the 1D Korteweg-de Vries and 2D Navier-Stokes equations.

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References in corpus (3)

• A Geometric Approach to Dynamical Model-Order Reduction
• Reduction of SO(2) symmetry for spatially extended dynamical systems
• Continuous symmetry reduction and return maps for high-dimensional flows

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• Space-time registration-based model reduction of parameterized one-dimensional hyperbolic PDEs
• Learning reduced order models from data for hyperbolic PDEs