TRIE Framework Evaluates Stochastic PDE Surrogates for Scientific Systems.

A new evaluation framework named TRIE has been developed to rigorously assess stochastic Partial Differential Equation (PDE) surrogates, which are crucial for modeling scientific systems with inherent uncertainty. Traditional deterministic neural surrogates often fail to capture the statistical measures and forecast uncertainty essential for such systems, even if they produce plausible short-term predictions. TRIE addresses this by focusing on three key criteria: the ability to reproduce invariant measures, the trustworthiness of predictive uncertainty, and scalability for efficient probabilistic generation. The framework was applied to two stationary chaotic spatially extended SPDEs, stochastic Kuramoto–Sivashinsky and stochastic Kolmogorov flow, across multiple parameter values. The evaluation revealed that standard pointwise-trained neural surrogates, while capable of short, plausible rollouts, consistently fail to match the long-term statistical structure of the systems. Similarly, approximate uncertainty methods like Monte Carlo dropout often produce miscalibrated and overconfident forecasts. In contrast, generative models demonstrated the most consistent performance across all criteria, accurately capturing invariant measure statistics and achieving the lowest CRPS (Continuous Ranked Probability Score) in probabilistic settings. Furthermore, latent generative models with automatic dimension discovery maintained much of this statistical fidelity while significantly reducing inference time, highlighting their potential for efficient and reliable stochastic PDE forecasting.