DeepParticle: Learning Invariant Measure by Deep Neural Network Minimizing Wasserstein Distance

Explore an innovative approach to solving high-dimensional partial differential equations in this one-hour webinar from Inside Livermore Lab. Delve into the DeepParticle method, which integrates deep learning, optimal transport, and interacting particle techniques to tackle challenges in computational physics. Learn how this mesh-free approach overcomes limitations of traditional methods, particularly for solutions with large gradients or concentrations at unknown locations. Examine a case study on Fisher-Kolmogorov-Petrovsky-Piskunov front speeds in incompressible flows, and discover how stochastic representation and the Feynman-Kac formula enable a genetic interacting particle algorithm. Understand the process of learning invariant measures parameterized by physical parameters using neural networks, and see how this methodology extends to learning stochastic particle dynamics in various contexts, including Keller-Segel chemotaxis systems. Gain insights from Dr. Z. Zhang, an expert in scientific computation, as he shares his research on uncertainty quantification, numerical methods for stochastic differential equations, and applications in quantum chemistry, wave propagation, and fluid dynamics.