When Network Architecture Meets Physics: Deep Operator Learning for Coupled Multiphysics

TL;DR

This paper investigates how neural network architecture should reflect physical coupling strength in multiphysics problems, demonstrating that architecture-aware DeepONets excel in strongly coupled systems and enable rapid, accurate surrogate modeling.

Contribution

It provides the first systematic evaluation of DeepONet variants across different physical coupling regimes, highlighting the importance of architecture alignment with physical interactions.

Findings

Single-branch DeepONets outperform multi-branch in strongly coupled systems.

Multi-branch architectures are advantageous for decoupled problems.

Surrogate models run up to 18,000 times faster than finite-element solvers.

Abstract

Scientific applications increasingly demand real-time surrogate models that can capture the behavior of strongly coupled multiphysics systems driven by multiple input functions, such as in thermo-mechanical and electro-thermal processes. While neural operator frameworks, such as Deep Operator Networks (DeepONets), have shown considerable success in single-physics settings, their extension to multiphysics problems remains poorly understood. In particular, the challenge of learning nonlinear interactions between tightly coupled physical fields has received little systematic attention. This study addresses a foundational question: should the architectural design of a neural operator reflect the strength of physical coupling it aims to model? To answer this, we present the first comprehensive, architecture-aware evaluation of DeepONet variants across three regimes: single-physics, weakly coupled, and strongly coupled multiphysics systems. We consider a reaction-diffusion equation with dual spatial inputs, a nonlinear thermo-electrical problem with bidirectional coupling through temperature-dependent conductivity, and a viscoplastic thermo-mechanical model of steel solidification governed by transient phase-driven interactions. Two operator-learning frameworks, the classical DeepONet and its sequential GRU-based extension, S-DeepONet, are benchmarked using both single-branch and multi-branch (MIONet-style) architectures. Our results demonstrate that architectural alignment with physical coupling is crucial: single-branch networks significantly outperform multi-branch counterparts in strongly coupled settings, whereas multi-branch encodings offer advantages for decoupled or single-physics problems. Once trained, these surrogates achieve full-field predictions up to 1.8e4 times faster than high-fidelity finite-element solvers, without compromising solution accuracy.