Keywords: automatic train operation, multi-objective optimization, neural network controller, physics-informed neural network, differentiable physics simulation, real-time control, optimal control.

The transition towards autonomous trains necessitates intelligent automatic train operation systems capable of real-time, multi-objective trajectory optimization for highly efficient operations. While traditional open-loop optimal control methods are computationally demanding for online adaptation, data-driven approaches such as behavioral cloning inherently suffer from compounding errors, and standard reinforcement learning struggles to satisfy safety constraints in sparse-reward settings. To bridge this gap, this paper presents a novel learning framework for robust, closed-loop train control. We propose a two-step methodology: first, a neural policy is warm-started through pre-training on a dataset of constraint-satisfying open-loop trajectories generated via numerical optimization. Subsequently, the policy is fine-tuned in closed-loop via direct policy search within a continuous neural ordinary differential equation architecture. By backpropagating gradients directly through the system dynamics, a curriculum learning strategy is used to optimize multi-objective costs such as energy consumption, wear and punctuality. Simulation results demonstrate that this physics-informed approach effectively eliminates the compounding errors, adheres to nonlinear speed boundaries, and achieves real-time operational robustness. The resulting controller evaluates in milliseconds and synthesizes energy-efficient driving profiles under varying operational disturbances. This framework enables automated trains to adapt their driving style on the tracks, reducing energy consumption and ensuring a more comfortable, on-time journey.

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