One-Way Coupling via Patchwise Adaptive Normalization in Transformer Surrogates
Many physical systems exhibit one-way coupling: exogenous fields such as medium density or obstacle geometry influence the dynamics without being affected by them. We investigate how explicitly representing these fields can improve the accuracy and computational efficiency of transformer-based PDE surrogates. Building on spatially adaptive normalization, we introduce Patchwise Adaptive Normalization (PAdaNorm), which partitions exogenous fields into patches aligned with the state tokenization. We evaluate PAdaNorm on datasets from three different domains, using a Walrus-inspired transformer architecture. Across the three PDE families, PAdaNorm is on par with or up to 16% better than param...
| Authors | Emmanuel Gottlob, Hugo Thimonier, Ludovico Buizza et al. |
|---|---|
| Primary category | cs.LG |
| Published | 10 October 2026 |
| Last updated at source | 10 October 2026 |
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