Feynman Kac

The Feynman-Kac formula provides a powerful link between stochastic processes and partial differential equations (PDEs), enabling the computation of expectations by solving related PDEs. Current research focuses on improving the efficiency and applicability of this framework, particularly through the use of neural networks (like Physically Informed Neural Networks) and normalizing flows to approximate solutions and reduce variance in estimations, especially in high-dimensional problems. These advancements are impacting diverse fields, including quantum field theory, where they enhance the analysis of complex systems by improving the accuracy and speed of calculations, and machine learning, where they are used to solve challenging symbolic regression problems. The resulting improvements in computational efficiency and accuracy have significant implications for various scientific and engineering applications.