Energy-Based Deep Learning Initialization Method Achieves Precise Evolution of Soliton Dynamics

Abstract The precise modeling of strong nonlinear transient evolution in nonlinear dynamical systems, including soliton evolution, remains a long-term challenge. Deep learning models with powerful nonlinear fitting capabilities have become efficient tools for physical system modeling. However, existing initialization methods rely on statistical distribution assumptions and lack constraints from physical mechanisms, which easily lead to suboptimal solutions and severely limit model prediction accuracy and generalization. Based on the energy minimization principle of physical systems, this work proposes energy-based initialization (EBI). This method requires only prior structural knowledge of the physical system as input, without experimental data or architecture customization, to guide initial weights to align with the intrinsic dynamical structure of physical systems. The work further derives an upper bound on the distance between EBI initial weights and optimal weights for downstream tasks, and proves that its performance advantage increases monotonically with the expansion of model parameter scale. Validation across four typical physical scenarios shows that EBI outperforms classical initialization schemes across all metrics, while initialization for a model with 4.7 million parameters takes less than 5 minutes. This work fills the gap of specialized initialization methods in AI for physics, provides efficient support for tasks such as transient prediction of optical fiber laser and inverse sensing of laser structures, and is expected to open new directions for interdisciplinary research between artificial intelligence and physics.