AI and the World's Hard Problems · Physics · arXiv · 2026-10-23
Learning Cole-Hopf Coordinates for Stochastic Growth Dynamics: the KPZ class
Inferring equations from noisy trajectories of nonlinear stochastic processes is difficult. The method learns a neural change of variables under which the dynamics become linear, and trains it with a short-time moment-matching objective that avoids simulating trajectories. On the one-dimensional KPZ equation, it recovers the Cole-Hopf map and the linear operator from height trajectories alone, and the generated trajectories reproduce KPZ statistics, including the growth law with β=1/3 and the GOE Tracy-Widom height distribution for flat initial conditions.