GeoHam: Symplectic-Regularized Feature Evolution for Efficient Remote Sensing Change Detection

Abstract

GeoHam is a geometric-regularization framework inspired by Hamiltonian mechanics for remote-sensing change detection (CD). It replaces conventional feature subtraction with multiscale Störmer-Verlet symplectic integration applied to learned feature dynamics. Unlike physics-informed neural networks (PINNs) that enforce PDE residuals from physical laws, GeoHam exploits the mathematical structure of Hamiltonian mechanics as an inductive bias on bitemporal feature trajectories: the symplectic two-form is preserved at every leapfrog step, acting as a geometric regularizer that keeps distinct temporal states distinguishable. Three feature pyramid network (FPN) levels (64×64 , 32×32 , 16×16 ) share a single integrator projected to a common 64-D space

a raw absolute-difference skip at 128×128 preserves boundary detail. Integration steps per scale are selected by Bayesian hyperparameter optimization. GeoHam achieves F1 of 91.20%, 95.89%, and 79.56% on LEVIR-CD, CDD, and CLCD, respectively, with only 7.53M parameters and 4.72GFLOPs, 5.3× fewer GFLOPs than StarCD-Net without any transformer, state-space model, or cross-attention block. © 2016 IEEE.