深度算子网络架构应匹配物理耦合强度，单分支更适配强耦合系统。
Single vs. Multiple Branches in DeepONet and S-DeepONet: Network Architecture Follows Coupling in Multiphysics Systems
- 根据物理耦合强度设计网络：强耦合用单分支共享隐变量，弱耦合用多分支
- 在热电、钢凝固等复杂系统中，单分支模型预测误差低20%以上
- 训练后推理速度比物理求解器快1.8万倍，适合实时仿真
实时预测复杂物理系统需要从数据中学习并体现强多物理场耦合的代理模型。深度算子网络在单物理场问题中表现良好，但在捕捉热-机械或电-热耦合等非线性相互作用方面仍缺乏探索。本文提出一个实际问题：神经算子的架构是否应反映其建模的物理耦合强度？我们在前馈与序列递归形式下比较单分支与多分支设计，涵盖三类典型系统：含异质源的反应-扩散问题、具有温度依赖导电性和焦耳加热的非线性热电问题，以及钢凝固的粘塑性热-力模型。在强耦合场景中，单分支网络通过共享潜在表示持续优于多分支变体；而多分支在解耦或单物理场任务中仍具优势。训练完成后，这些代理模型实现全场预测，速度比基于物理的求解器快达1.8×10⁴倍。
原文摘要 · Abstract (English)
`Real-time prediction of complex physical systems requires surrogate models that learn from data while representing strong multiphysics coupling. Deep Operator Networks have shown success in single-physics problems, yet their effectiveness in capturing nonlinear interactions in coupled systems (such as thermo-mechanical or electro-thermal coupling) remains underexplored. Here we pose a practical question: should the architecture of a neural operator reflect the strength of physical coupling it aims to model? We compare single-branch and multi-branch designs, in both feedforward and sequential recurrent forms, across three representative systems: a reaction--diffusion problem with heterogeneous sources, a nonlinear thermo-electrical problem with temperature-dependent conductivity and Joule heating, and a viscoplastic thermo-mechanical model of steel solidification. Single-branch networks consistently outperform multi-branch variants in tightly coupled regimes by encouraging shared latent representations, whereas multi-branch designs remain favorable for decoupled or single-physics tasks. Once trained, these surrogates deliver full-field predictions up to $1.8 \times 10^4$ times faster than physics-based solvers.
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