Action Learning for Scientific Simulations

Understanding and controlling how systems evolve is central to science and engineering, where many problems are defined on trajectories rather than individual states. Existing learned methods often predict local dynamics or generate trajectories, while representative path inference, mechanism steering and constrained trajectory optimization require an objective on complete paths. We introduce LEAP (Learned Energy on Action Paths), which treats the stochastic action itself as the learning target and recovers it directly from trajectory samples. LEAP decomposes the unknown action to an evaluable reference process and learns the remaining path space correction from complete trajectories, yielding a differentiable objective on paths. Once learned, the same action can be reused for path ranking, representative path inference, mechanism tilting, constraints and sampling. Across stochastic transition, orbital and molecular systems, LEAP recovers physical drift from terminally selected trajectories, represents a nonadditive action correction induced by a persistent latent regime and reuses a fixed molecular action for completion, basin preferences, angular constraints and temperature transfer. Code is available https://anonymous.4open.science/r/leap-iclr-7E4D/README.mdhere.