FlowGEN: A Finite-Horizon Truncation Kernel for Unstable 3D Flow Forecasting Across Meshes

Fast surrogate models for unsteady computational fluid dynamics (CFD) need to maintain representation accuracy under complex spatial discretizations and evolution stability in long-term prediction. However, existing methods still have limited joint modeling of the temporal and spatial dimensions. As a result, they cannot maintain accuracy in both dimensions. We propose FlowGEN, a graph evolution network centered on a Finite-Horizon Truncation Kernel (FHTK). FHTK is a separable temporal support kernel over history lag and forecast offset. Along the history axis, a transient-state mask activates only the latest three states, so an older prediction loses its direct feedback edge after leaving the finite-memory window while its dynamically relevant information remains summarized by the evolved recent states. Along the forecast axis, a normalized finite-support kernel determines which recursively generated states contribute loss and gradient. Its support expands from three to six steps during training, and a nested six-/twelve-step validation kernel balances local transition accuracy with delayed instability beyond the optimized horizon. Every supported state is supervised by standardized data fidelity, kinetic energy (KE) matching, and mixed graph divergence (Div) regularization. Across structured and unstructured unstable flows at four Reynolds numbers, FlowGEN obtains the lowest reported mean in all 48 condition–metric comparisons. Relative to the strongest baseline for each metric, it reduces the error-growth ratio by 32.1%, intermediate-horizon MSE by 8.6%, KE error by 31.5%, and Div error by 3.7%. These results show that explicitly controlling state activation and recursive credit provides a practical mechanism for stable flow forecasting across discretizations.