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

2025-07-04

AI Summary

This study addresses the modeling challenge of strongly coupled multiphysics systems (e.g., thermo-mechanical, electro-thermal). We propose a neural operator learning paradigm whose architecture aligns with physical coupling strength. We systematically demonstrate—for the first time—that in strongly coupled regimes, single-branch DeepONet and its GRU-enhanced variant (S-DeepONet) significantly outperform multi-branch counterparts, revealing that network topology must reflect inter-field coupling intensity. Methodologically, we adopt a unified single-branch encoding scheme and achieve full-field operator learning across three benchmark systems: reaction-diffusion, nonlinear thermoelectric, and viscoplastic thermodynamics. The resulting surrogate models accelerate high-fidelity finite-element solvers by up to 1.8×10⁴× while preserving accuracy and enabling real-time simulation under multiple functional inputs. Our core contribution is establishing a principled “physics-coupling–architecture-design” mapping, providing a new, interpretable, and efficient paradigm for multiphysics surrogate modeling.

Technology Category

• Machine Learning: Deep Neural Architectures and Foundation Models
• Search and Optimization: Learning to Search
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications

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.

Problem

• Extending neural operators to multiphysics coupling problems
• Learning nonlinear interactions between coupled physical fields
• Designing architectures reflecting physical coupling strength

Innovation

• DeepONet variants for multiphysics coupling
• Architecture-aware evaluation of neural operators
• Single-branch networks outperform in strong coupling