Kastor Accelerates PDE Simulations with Generative AI Emulation

Machine learning offers a powerful way to speed up physical simulations by replacing traditional, computationally intensive Partial Differential Equation (PDE) solvers with faster, differentiable surrogate models. However, standard auto-regressive ML emulators often struggle with accumulating errors over long simulation horizons and fail to accurately capture the inherent stochasticity of complex physical systems. This paper introduces Kastor, a comprehensive methodology designed to adapt deterministic physics foundation models into highly efficient and accurate generative surrogates. Kastor employs a two-stage inference scheme that pairs a large-stride causal auto-regressive model with a non-causal temporal super-resolution network. This combination effectively minimizes error accumulation while keeping computational costs low. Furthermore, Kastor incorporates Mean Prediction Regularization (MPR), a novel training objective that ensures the generative model accurately predicts the deterministic distribution mean under null noise conditions, significantly enhancing stability and performance for both Functional Generative Networks (FGN) and diffusion-based emulators. The methodology also integrates spatial gradient matching to boost simulation accuracy and physical fidelity, as evidenced by power spectrum density. Extensive evaluations on diverse simulation datasets show Kastor outperforms competing methods in forecasting accuracy, spectral consistency, and computational efficiency, achieving a 42.9% average reduction in forecasting error compared to a reference Walrus finetuning approach.