We introduce TWIG (Time-Causal Wavelet Operator for Irregular Graphs), a graph-native neural operator for autoregressive surrogate modeling on static irregular graphs. TWIG transforms each node history into causal multiscale temporal features that separate recent variation from progressively slower memory components, then propagates these features through graph-wavelet operator blocks with gated pointwise channel mixing. The architecture is causal by construction and designed for closed-loop forecasting, where predictions are recursively reused as future inputs. We evaluate TWIG on three irregular-domain forecasting problems spanning regional diffusion, three-dimensional subsurface hydrology, and aerodynamic flow, with graphs ranging from 400 to 5,233 nodes and model capacities from approximately 70k to 10M parameters. TWIG achieves the lowest aggregate rollout errors on the subsurface-hydrology and regional-diffusion benchmarks and ranks second on the 10M-parameter aerodynamic-flow benchmark, behind the GPS Transformer. Across all three settings, TWIG consistently outperforms the corresponding non-time-causal Graph WNO baseline. These results demonstrate that TWIG provides an effective and scalable approach to stable autoregressive forecasting of dynamical fields on irregular graphs.

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