This paper introduces DeepFHT, a survival analysis framework that combines deep neural networks with the time-to-first-arrival (FHT) distribution from stochastic process theory. The event time is represented as the time at which a latent diffusion process reaches an absorbing boundary. The neural network maps input variables to physically meaningful parameters, such as initial conditions, drift, and diffusion, and computes parameters within selected FHT processes, such as Brownian motion with and without drift. This generates closed-form survival and hazard functions that capture time-varying risk without assuming proportional hazards. DeepFHT is compared to the Cox survival model using synthetic and real-world data sets. This method achieves predictive accuracy comparable to state-of-the-art approaches while maintaining a physics-based, interpretable parameterization that clearly describes the relationship between input features and hazard. This combination of stochastic process theory and deep learning provides a principled method for modeling survival phenomena in complex systems.
