Clifford Neural Layers for PDE Modeling

Understand

Partial differential equations (PDEs) see widespread use in sciences and engineering to describe simulation of physical processes as scalar and vector fields interacting and coevolving over time.

• Due to the computationally expensive nature of their standard solution methods, neural PDE surrogates have become an active research topic to accelerate these simulations.
• However, current methods do not explicitly take into account the relationship between different fields and their internal components, which are often correlated.
• Viewing the time evolution of such correlated fields through the lens of multivector fields allows us to overcome these limitations.