DeepM&Mnet: Inferring the electroconvection multiphysics fields based on operator approximation by neural networks

TL;DR

DeepM&Mnet introduces a neural network-based data assimilation framework that rapidly simulates complex multiphysics electroconvection fields by leveraging pre-trained DeepONets, significantly reducing computational time compared to traditional numerical methods.

Contribution

The paper presents a novel DeepM&Mnet framework that combines pre-trained DeepONets with sparse measurements to efficiently infer multiphysics fields, advancing simulation speed and accuracy.

Findings

DeepONets accurately predict individual fields in electroconvection.

DeepM&Mnet achieves fast and accurate 2D electroconvection field inference.

Framework is adaptable to other multiphysics problems with limited data.

Abstract

Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. For small Debye lengths, very steep boundary layers are developed, but standard numerical methods can simulate the different regimes quite accurately. Here, we use electroconvection as a benchmark problem to put forward a new data assimilation framework, the DeepM&Mnet, for simulating multiphysics and multiscale problems at speeds much faster than standard numerical methods using pre-trained neural networks (NNs). We first pre-train DeepONets that can predict independently each field, given general inputs from the rest of the fields of the coupled system. DeepONets can approximate nonlinear operators and are composed of two sub-networks, a branch net for the input fields and a trunk net for the locations of the output field. DeepONets, which are extremely fast, are used as building blocks in the DeepM&Mnet and form constraints for the multiphysics solution along with some sparse available measurements of any of the fields. We demonstrate the new methodology and document the accuracy of each individual DeepONet, and subsequently we present two different DeepM&Mnet architectures that infer accurately and efficiently 2D electroconvection fields for unseen electric potentials. The DeepM&Mnet framework is general and can be applied for building any complex multiphysics and multiscale models based on very few measurements using pre-trained DeepONets in a plug-and-play mode.