Publications

CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs

We introduce CALM-PDE, a model based on continuous convolution for discretization-agnostic solving of time-dependent partial differential equations, which achieves strong performance in fluid dynamics simulations.

Jan Hagnberger, Daniel Musekamp, Mathias Niepert

Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent Parametric Partial Differential Equations

We propose a continuous model based on conditional neural fields and linear transformers for solving time-dependent parametric partial differential equations

Jan Hagnberger, Marimuthu Kalimuthu, Daniel Musekamp, Mathias Niepert

Vectorized Conditional Neural Fields: A Framework for Solving Time-dependent PDEs

Utilizing linear transformers, we propose a conditional neural fields based framework for solving time-dependent parametric partial differential equations that is fast and generalizes well to unseen PDE parameters.

Jan Hagnberger, Marimuthu Kalimuthu, Mathias Niepert

Vectorized Conditional Neural Fields for Computational Fluid Dynamics

We introduce a framework named Vectorized Conditional Neural Fields (VCNeF) designed to solve time-dependent parametric partial differential equations, and we showcase its efficacy in fluid dynamics simulations.

Jan Hagnberger, Marimuthu Kalimuthu, Mathias Niepert