Abstract: A method and system are provided for safe motion planning of an autonomous system using a neural-network-based approximation of a Hamilton-Jacobi (HJ) value function. The method includes computing signed distance fields (SDFs) from occupancy grid maps, deriving temporal differences between SDFs, and using these differences as input to a hypernetwork that generates parameters for a main network. The main network computes a residual of the HJ value function, which is modified using a leaky rectified linear unit and combined with a selected SDF to form an intermediate value function. A state-dependent slack function is added to produce a final HJ value function, which is used as a safety constraint in motion planning. The system enables real-time, adaptive, and robust planning in dynamic and partially observable environments.