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

2025-08-30

AI Summary

To address the prohibitively high computational cost of high-dimensional, large-scale coupled multi-physics simulations, this paper proposes a DeepONet–FEM hybrid staggered solver: while retaining conventional finite element methods (FEM) for the mechanical field, it employs an improved physics-informed neural operator (I-FENN) to predict all other coupled fields. I-FENN innovatively integrates a multi-source input expansion architecture with hard boundary condition enforcement, substantially enhancing generalization to unseen load and boundary condition combinations. By decoupling strong inter-field couplings, the framework reduces system degrees of freedom and overall computational complexity. Numerical experiments demonstrate that the method consistently achieves over 95% accuracy in critical regions across all test cases; moreover, computational efficiency improves markedly with increasing problem scale. The approach exhibits robust extrapolation capability and strong practical applicability for engineering-scale multi-physics problems.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Intelligent Robots: Multimodal Perception & Sensor Fusion
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

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.

Problem

• Accelerating coupled multiphysics simulations through hybrid FEM-neural network integration
• Reducing computational cost in thermoelasticity and poroelasticity problems
• Enhancing generalization for unseen boundary conditions and loading scenarios

Innovation

• Integrates DeepONet with Finite Element Method
• Uses hybrid staggered solver for multiphysics problems
• Modified DeepONet handles multiple boundary conditions efficiently