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.

电对流是一个多物理场问题，涉及流场与电场以及阳离子和阴离子浓度场的耦合。在这里，我们以电对流为基准问题，提出了一个新的数据同化框架DeepM＆Mnet，该模型以比使用预训练神经网络的标准数值方法快得多的速度来模拟多物理场和多尺度问题。我们首先对DeepONets进行预训练，使其能够独立预测每个字段，并给出耦合系统其余字段的一般输入。DeepONets可以近似非线性算子，由两个子网，一个用于输入字段的分支网和一个中继网组成。输出字段的位置。DeepONets速度极快，在DeepM＆Mnet中用作构建模块，并构成多物理场解决方案的约束以及对任何领域的一些稀疏可用测量。我们演示了新的方法并记录了每个DeepONet的准确性，随后，我们介绍了两种不同的DeepM＆Mnet体系结构，这些体系结构可以准确有效地推断2D电对流场中看不见的电势。DeepM＆Mnet框架是通用的，可用于以“即插即用”模式使用预训练的DeepONets基于很少的测量来构建任何复杂的多物理场和多尺度模型。