Physics-guided curriculum learning for the identification of reaction-diffusion dynamics from partial observations

Abstract

Reaction-diffusion (RD) systems provide fundamental models for understanding self-organized spatiotemporal patterns across natural and engineered settings, yet reliable parameter estimation remains challenging, particularly when observations are sparse, noisy, and restricted to a subset of state variables. We introduce CLIP (Curriculum Learning Identification via PINNs), a physics-guided framework built on physics-informed neural networks for joint parameter inference and hidden-state reconstruction under partial observability. Leveraging the physical separability of RD systems, the CLIP training progresses from reaction-dominated regimes to full spatiotemporal dynamics using curriculum learning and an anchored widening transfer strategy. Across three canonical reaction-diffusion benchmarks, CLIP achieves more accurate and robust identification than baseline methods. Furthermore, the CLIP framework is successfully applied to infer the dynamics of the Min system in bacteria, where only membrane-bound species are observed and key kinetic rates span multiple orders of magnitude. Ablation experiments and loss-landscape visualizations demonstrate that both the curriculum stages and the anchored transfer are essential for stable convergence.