FORMA: Feedback-Conditioned Spatial Memory for Field Forecasting

Long-horizon geophysical forecasting requires a predictive state that can remember persistent seasonal structure while rapidly adapting to moving fronts, changing spatial interactions, and unreliable observations. Existing forecasting architectures provide powerful temporal or spatial modeling mechanisms, but coupling long-term memory with observation-dependent spatial adaptation remains difficult. We introduce FORMA, a forecasting architecture centered on Field Memory, a field-valued predictive state whose evolution is regulated by feedback from the observed geophysical field. Seasonal phase, observation reliability, and interface dynamics determine what information is retained, what new evidence is written, and how memory propagates across space. FORMA implements this idea with an RWKV-style temporal recurrence together with efficient global and local spatial interaction, preserving spatial tokens throughout the historical scan while maintaining linear complexity in history length and grid size. On 90-day sea-surface-temperature forecasting, FORMA reduces area RMSE by 19.1% over a matched RWKV recurrence and by 7.9% over the strongest baseline in our comparison, with consistent gains in interface and basin-scale accuracy. The same architecture also transfers to Arctic sea-ice concentration forecasting, reducing concentration RMSE by 4.3% and sea-ice-extent error by 25.4%. These results demonstrate that explicitly modeling a feedback-regulated spatial predictive state is a promising alternative for long-horizon forecasting of evolving geophysical fields.