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

Highlights: • DeepONets can learn the electroconvection operator using a small number of data. • DeepONets achieve high accuracy at 1000X speed for the unseen testing data. • DeepM&Mnet is proposed as a new data assimilation framework. • DeepM&Mnet enables the combination of data measurements and pre-trained DeepONets. • A comparison between two DeepM&Mnet architectures is performed. Electroconvection is a multiphysics problem involving coupling of the flow field with the electric field as well as the cation and anion concentration fields. 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. 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.