GOLA combines attention-based graph message passing with a learnable Fourier encoder and reports lower relative L2 error than GKN on four 2D PDE benchmarks, especially with few training samples.
On long waves and solitons in particle lattices with forces of infinite range
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
We study waves on infinite one-dimensional lattices of particles that each interact with all others through power-law forces $F \sim r^{-\beta}$. The inverse-cube case corresponds to Calogero-Moser systems, which are well known to be completely integrable for any finite number of particles. The formal long-wave limit for unidirectional waves in these lattices is the Korteweg-de Vries equation if $\beta >4$, but with $2<\beta <4$ it is a nonlocal dispersive PDE that reduces to the Benjamin-Ono equation for $\beta=3$. For the infinite Calogero-Moser lattice, we find explicit formulas that describe solitary and periodic traveling waves.
fields
cs.LG 1years
2025 1verdicts
REJECT 1representative citing papers
citing papers explorer
-
Graph-Based Operator Learning from Limited Data on Irregular Domains
GOLA combines attention-based graph message passing with a learnable Fourier encoder and reports lower relative L2 error than GKN on four 2D PDE benchmarks, especially with few training samples.