<p>Under-actuated autonomous marine vehicles are frequently used for complex underwater tasks like mine detection and naval patrol in stochastic dynamic ocean flows. Efficient path planning algorithms, optimal in time, energy, or data, significantly improve performance and cost efficiency. We present a novel method that uses a physics-based dynamically orthogonal stochastic ocean flow prediction model with a deep transformer neural network for path planning. Our Physics-Guided Path Planning Transformer (PGPPT) is a sequence-to-sequence model with a flow-encoder-path-decoder architecture, trained in a physics-guided approach. The PGPPT uses the agent’s flow knowledge as the source sequence and the desired optimal actions as the target sequence. Physics-based simulations are used to obtain training data. Ocean flow fields are represented through dynamically orthogonal (DO) partial differential equations (PDEs) and are provided to the agent as DO embedding vectors. The target optimal path sequences for specific flows are obtained by solving the optimal control problem using dynamic programming within a Markov Decision Process framework or the Hamilton-Jacobi level set path planning PDEs. PGPPT predicts the optimal path from a flow sequence provided during inference. We conduct experiments in idealized flow scenarios (wind-driven double gyre flow and flow past a circular island) simulated by Quasi Geostrophic ocean flow equations (2D in space and 1D in time). We demonstrate that the trained transformer efficiently computes near-optimal paths for new flow scenarios and obstacle arrangements, outperforming the DP or HJLS-PDE solvers in speed. Our new planner performs better than the behavior-cloning-based imitation learning baseline. In addition, we examine and visualize the attention scores on the predicted paths, providing insight into the physics-guided training.</p>