Finite Expression Method

The Finite Expression Method (FEX) is a novel numerical technique designed to solve high-dimensional partial differential and integro-differential equations, overcoming the computational limitations of traditional methods like finite element and finite difference approaches. Current research focuses on applying FEX to challenging problems such as committor calculations in transition path theory and discovering governing equations from data, often employing reinforcement learning to optimize the method's parameters and achieve high accuracy. FEX's ability to produce interpretable, explicit solutions with reduced computational cost offers significant advantages for various scientific and engineering applications requiring the solution of complex, high-dimensional systems.