I-FENN with DeepONets: accelerating simulations in coupled multiphysics problems

Coupled multiphysics simulations for high-dimensional, large-scale problems can be prohibitively expensive due to their computational demands. This article presents a novel framework integrating a deep operator network (DeepONet) with the Finite Element Method (FEM) to address coupled thermoelasticity and poroelasticity problems. This integration occurs within the context of I-FENN, a framework where neural networks are directly employed as PDE solvers within FEM, resulting in a hybrid staggered solver. In this setup, the mechanical field is computed using FEM, while the other coupled field is predicted using a neural network (NN). By decoupling multiphysics interactions, the hybrid framework reduces computational cost by simplifying calculations and reducing the FEM unknowns, while maintaining flexibility across unseen scenarios. The proposed work introduces a new I-FENN architecture with extended generalizability due to the DeepONets ability to efficiently address several combinations of natural boundary conditions and body loads. A modified DeepONet architecture is introduced to accommodate multiple inputs, along with a streamlined strategy for enforcing boundary conditions on distinct boundaries. We showcase the applicability and merits of the proposed work through numerical examples covering thermoelasticity and poroelasticity problems, demonstrating computational efficiency, accuracy, and generalization capabilities. In all examples, the test cases involve unseen loading conditions. The computational savings scale with the model complexity while preserving an accuracy of more than 95\% in the non-trivial regions of the domain.