Multi-Head Residual-Gated DeepONet for Coherent Nonlinear Wave Dynamics

TL;DR

This paper introduces MH-RG DeepONet, a neural operator that explicitly incorporates physical descriptors via residual gating, improving accuracy and physical fidelity in modeling nonlinear wave dynamics.

Contribution

The paper proposes a novel Multi-Head Residual-Gated DeepONet architecture that effectively integrates physical descriptors through residual modulation, enhancing modeling of nonlinear wave systems.

Findings

MH-RG DeepONet achieves lower error than baselines.

It better preserves phase coherence and dynamical quantities.

The framework performs well on nonlinear and dissipative wave benchmarks.

Abstract

Coherent nonlinear wave dynamics are often strongly shaped by a compact set of physically meaningful descriptors of the initial state. Traditional neural operators typically treat the input-output mapping as a largely black-box high-dimensional regression problem, without explicitly exploiting this structured physical context. Common feature-integration strategies usually rely on direct concatenation or FiLM-style affine modulation in hidden latent spaces. Here we introduce a different paradigm, loosely inspired by the complementary roles of state evolution and physically meaningful observables in quantum mechanics: the wave field is learned through a standard DeepONet state pathway, while compact physical descriptors follow a parallel conditioning pathway and act as residual modulation factors on the state prediction. Based on this idea, we develop a Multi-Head Residual-Gated DeepONet (MH-RG), which combines a pre-branch residual modulator, a branch residual gate, and a trunk residual gate with a low-rank multi-head mechanism to capture multiple complementary conditioned response patterns without prohibitive parameter growth. We evaluate the framework on representative benchmarks including highly nonlinear conservative wave dynamics and dissipative trapped dynamics and further perform detailed mechanistic analyses of the learned multi-head gating behavior. Compared with feature-augmented baselines, MH-RG DeepONet achieves consistently lower error while better preserving phase coherence and the fidelity of physically relevant dynamical quantities.