A Multifidelity deep operator network approach to closure for multiscale systems

Abstract

Projection-based reduced order models (PROMs) have shown promise in representing the behavior of multiscale systems using a small set of generalized (or latent) variables. Despite their success, PROMs can be susceptible to inaccuracies, even instabilities, due to the improper accounting of the interaction between the resolved and unresolved scales of the multiscale system (known as the closure problem). In the current work, we interpret closure as a multifidelity problem and use a multifidelity deep operator network (DeepONet) framework to address it. In addition, to enhance the stability and accuracy of the multifidelity-based closure, we employ the recently developed "in-the-loop" training approach from the literature on coupling physics and machine learning models. The resulting approach is tested on shock advection for the one-dimensional viscous Burgers equation and vortex merging using the two-dimensional Navier-Stokes equations. The numerical experiments show significant improvement of the predictive ability of the closure-corrected PROM over the un-corrected one both in the interpolative and the extrapolative regimes.

arXiv comment24 pages, 21 figures

References in corpus (22)

• DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators
• Fourier Neural Operator for Parametric Partial Differential Equations
• The GNAT method for nonlinear model reduction: effective implementation and application to computational fluid dynamics and turbulent flows
• A Novel Model Order Reduction Approach for Navier-Stokes Equations at High Reynolds Number
• A deep learning enabler for non-intrusive reduced order modeling of fluid flows
• On closures for reduced order models $-$ A spectrum of first-principle to machine-learned avenues
• Solver-in-the-Loop: Learning from Differentiable Physics to Interact with Iterative PDE-Solvers
• On the stability of projection-based model order reduction for convection-dominated laminar and turbulent flows
• Stable a posteriori LES of 2D turbulence using convolutional neural networks: Backscattering analysis and generalization to higher Re via transfer learning
• Comparison of POD reduced order strategies for the nonlinear 2D Shallow Water Equations
• Minimal subspace rotation on the Stiefel manifold for stabilization and enhancement of projection-based reduced order models for the compressible Navier-Stokes equations
• Data-Driven Variational Multiscale Reduced Order Models
• Data-driven Discovery of Closure Models
• Stabilized Neural Ordinary Differential Equations for Long-Time Forecasting of Dynamical Systems
• Learned Turbulence Modelling with Differentiable Fluid Solvers: Physics-based Loss-functions and Optimisation Horizons
• Interpreting and Stabilizing Machine-learning Parametrizations of Convection
• Learning physics-constrained subgrid-scale closures in the small-data regime for stable and accurate LES
• A priori analysis on deep learning of subgrid-scale parameterizations for Kraichnan turbulence
• On-the-fly Reduced Order Modeling of Passive and Reactive Species via Time-Dependent Manifolds
• Predictive Reduced Order Modeling of Chaotic Multi-scale Problems Using Adaptively Sampled Projections
• Real-Time Reduced-Order Modeling of Stochastic Partial Differential Equations via Time-Dependent Subspaces
• Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

Cited by in corpus (4)

• Deep Learning in Deterministic Computational Mechanics
• Review of multi-fidelity models
• Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems
• A multifidelity approach to continual learning for physical systems