4 papers
Merging Memory and Space: A State Space Neural Operator
Nodens Koren, Samuel Lanthaler
We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulatio…
A Probabilistic Framework for Solving High-Frequency Helmholtz Equations via Diffusion Models
Yicheng Zou, Samuel Lanthaler, Hossein Salahshoor
Deterministic neural operators perform well on many PDEs but can struggle with the approximation of high-frequency wave phenomena, where strong input-to-output sensitivity makes op…
Scale-Consistent Learning for Partial Differential Equations
Zongyi Li, Samuel Lanthaler, Catherine Deng +4
Machine learning (ML) models have emerged as a promising approach for solving partial differential equations (PDEs) in science and engineering. Previous ML models typically cannot…
Global existence of weak solutions to a two-phase diffuse interface model of ferrofluids dynamics
Samuel Lanthaler, Franziska Weber
Ferrofluids are a class of materials that exhibit both fluid and magnetic properties. We consider a two-phase diffuse interface model for the dynamics of ferrofluids on a bounded d…