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 diverse natural and engineered settings, but reliable parameter estimation remains challenging, particularly when observations are sparse, noisy, and restricted to a subset of state variables. Based on physics-informed neural networks (PINNs), a physics-guided Curriculum Learning Identification via PINNs (CLIP) method is introduced in this work, for joint parameter inference and hidden state reconstruction. 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 Min system in bacteria, where only membrane bound species are observed and key kinetic rates span multiple orders of magnitude. Moreover, ablation experiments and loss landscape analyses provide mechanistic evidence that the curriculum stages and anchored transfer enhance trainability and convergence.