Dissertation defense for Mathematics PhD student Miao Yang titled "Deep-Learning Approach to Reflected Backward Stochastic Differential Equations".

High-dimensional parabolic PDEs and their BSDE representations are difficult to solve with classical grid-based methods. This dissertation develops deep-learning-based solvers for standard BSDEs and reflected BSDEs (rBSDEs), emphasizing robust path-dependent representations and practical constraint handling. For standard BSDEs, I introduce an attention-based formulation that learns the control process from the entire simulated path using a shared sequence model, leading to improved stability and a unified error decomposition separating discretization, approximation, and optimization effects. For reflected problems, I study and compare two complementary formulations: (i) a multi-loss approach that learns reflection increments directly, and (ii) a penalty/projection approach that enforces obstacles via penalization and projection with stop-gradient. Both methods are evaluated under a unified experimental protocol across single- and double-obstacle benchmarks. Overall, the dissertation connects solver design, theoretical consistency, and numerical evaluation for deep-learning-based approximation of BSDE-type problems.

Advisor: Dr. Song Yao