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From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs
Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale...
arXiv cs.LG··Paper: ~15 min
2-Minute Brief
According to arXiv cs.LG: Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural operators have emerged as powerful data-driven alternatives, they conventionally treat all discretized spatial points as uniform, independent tokens. This monolithic approach ignores the intrinsic scale separation of physical fields, applying computationally pro
From Complex Dynamics to DynFormer: Rethinking Transformers for PDEs
TLDR
Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale...
According to arXiv cs.LG: Partial differential equations (PDEs) are fundamental for modeling complex physical systems, yet classical numerical solvers face prohibitive computational costs in high-dimensional and multi-scale regimes. While Transformer-based neural operators have emerged as powerful data-driven alternatives, they conventionally treat all discretized spatial points as uniform, independent tokens. This monolithic approach ignores the intrinsic scale separation of physical fields, applying computationally pro