Tingwei Meng
UCLA
Title
AI-Driven Methods for Scientific Computing: Bridging Optimal Control and Modern AI Techniques
Abstract
The convergence of artificial intelligence (AI) and applied mathematics offers transformative potential for addressing challenges in scientific computing and control. In this talk, I will highlight my research at the intersection of optimal control and modern AI methods, focusing on the development of scalable, robust, and efficient algorithms to tackle high-dimensional systems with uncertainty. I will introduce two key frameworks: the HJ-sampler and the In-Context Operator Network (ICON). The HJ-sampler is a novel method for Bayesian inference, designed to infer the history of stochastic processes by bridging stochastic optimal control and generative modeling techniques. ICON, inspired by large language models, serves as a general framework for solving diverse mathematical problems. Moreover, ICON can act as a surrogate model for the environment in optimal control settings and has potential applications in computing optimal order execution strategies in financial mathematics. Looking ahead, my research aims to leverage modern AI methods to improve the efficiency and adaptability of scientific computing while using mathematical insights to enhance the interpretability and robustness of AI models. These hybrid approaches hold promise for applications in areas such as financial mathematics, uncertainty quantification, and weather forecasting, where high-dimensional complexity and dynamical systems play a critical role.
