Euler Discretization

Euler discretization is a fundamental numerical method for approximating solutions to differential equations, finding broad application across scientific computing. Current research focuses on improving its accuracy and stability, particularly within complex spaces like Wasserstein space and manifolds of positive semi-definite matrices, often employing variations like Forward-Backward Euler or Riemannian Langevin methods. These advancements are crucial for tackling challenging problems in areas such as optimal transport, physics-informed neural networks, and reservoir computing, leading to more efficient and accurate solutions in diverse scientific and engineering domains.