AI RESEARCH
HS-FNO: History-Space Fourier Neural Operator for Non-Markovian Partial Differential Equations
arXiv CS.LG
•
ArXi:2605.09523v1 Announce Type: new Neural operators provide fast surrogate models for time-dependent partial differential equations, but their standard autoregressive use usually assumes that the instantaneous field $u(t,\cdot)$ is a complete state. This assumption fails for delay equations, distributed-memory systems, and other non-Markovian dynamics: two trajectories may agree at time $t$ and. nevertheless. have different futures because their histories differ. We