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

2026-04-13

AI Summary

This work addresses the limitations of conventional neural operators in modeling coherent nonlinear wave dynamics, which often neglect the structural information embedded in compact physical descriptors of the initial state, leading to degraded phase coherence and reduced fidelity of key physical quantities. To overcome this, the authors propose a dual-path deep neural operator architecture: a primary path based on DeepONet learns the wavefield evolution, while an auxiliary path injects physical descriptors as residual modulation factors in parallel. The framework incorporates a quantum-mechanics-inspired residual gating mechanism and a multi-head low-rank structure, enabling explicit integration of physical priors and capturing diverse conditional response patterns without substantially increasing model parameters. Experiments demonstrate that the proposed method significantly outperforms feature-augmented baselines on strongly nonlinear conservative waves and dissipative bound-state tasks, achieving enhanced prediction accuracy, phase coherence, and physical fidelity.

Technology Category

• Machine Learning: Quantum Machine Learning
• Search and Optimization: Learning to Search
• Computer Vision: Learning & Optimization for CV

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
• Responsible Web: Machine-in-the-loop, human agency and autonomy

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.

Problem

• coherent nonlinear wave dynamics
• neural operators
• physical descriptors
• input-output mapping
• phase coherence

Innovation

• Multi-Head Residual-Gated DeepONet
• neural operators
• physical descriptors
• residual modulation
• coherent wave dynamics