CasEm: A Cascade Architecture for Long-Horizon Neural Emulation

Autoregressive neural emulators can drift or diverge over long rollouts despite accurate short-term predictions. We introduce Cascaded Emulation (CasEm), a one-way rollout architecture that augments an existing full-state backbone with an independently evolving model of physically specified aggregates. Its forecasts guide corrections to full-state predictions, without feedback from the backbone to the aggregate model. Effective guidance requires aggregates that cover substantial backbone error, remain accurately predictable, and support useful full-state corrections. We derive a finite-horizon error bound that clarifies these three factors and use empirical diagnostics to guide subsystem selection. Across four ODE/PDE benchmarks, CasEm reduces long-horizon rollout errors across diverse backbones and suppresses the trend toward error divergence in both diffusion tasks using Fourier neural operator backbones. In global climate emulation, CasEm with a regional total-water subsystem reduces 10-year full-state time-mean error by $66.6\%$ and $46.3\%$ for frozen ACE and Spherical DYffusion backbones, respectively, while adding less than $3\%$ to inference time. The implementation can be found at https://anonymous.4open.science/r/CasEm_code-6807.