Path Integral

Path integral methods offer a powerful framework for solving problems involving probability distributions and stochastic processes, primarily by representing probabilities as sums over all possible paths a system can take. Current research focuses on developing efficient sampling algorithms, often leveraging stochastic optimal control and neural networks, to address challenges in areas like generative modeling and optimal control. These techniques are finding applications in diverse fields, including finance (pricing models), robotics (trajectory optimization), and machine learning (sampling from complex distributions), improving the accuracy and efficiency of existing methods. The ability to analytically control and efficiently sample from complex probability distributions makes path integral approaches increasingly significant across scientific disciplines.