HighDimPDE.jl: A Julia package for solving high-dimensional PDEs

High-dimensional PDEs cannot be solved with standard numerical methods, as their computational cost increases exponentially in the number of dimensions. This problem, known as the curse of dimensionality, vanishes with HighDimPDE.jl. The package implements novel solvers that can solve non-local nonlinear PDEs in potentially up to 1000 dimensions.

High-dimensional partial differential equations (PDEs) arise in a variety of scientific domains including physics, engineering, finance and biology. High-dimensional PDEs cannot be solved with standard numerical methods, as their computational cost increases exponentially in the number of dimensions, a problem known as the curse of dimensionality. HighDimPDE.jl is a Julia package that breaks down the curse of dimensionality in solving PDEs. Building upon the SciML ecosystem, the package implements novel solvers that can solve non-local nonlinear PDEs in potentially up to thousands of dimensions. Already proposing two solvers with different pros and cons, it aims at hosting more.

In this talk, we firstly introduce the package, briefly present the two currently implemented solvers, and showcase their advantages with concrete examples.