Non-asymptotic bounds for modified tamed unadjusted Langevin algorithm in non-convex setting by Ng, Matthew Cheng En

“…We consider the problem of sampling from a target distribution $\pi_\beta$ on $\mathbb{R}^d$ with density proportional to $\theta\mapsto e^{-\beta U(\theta)}$ using explicit numerical schemes based on discretising the Langevin stochastic differential equation (SDE). In recent literature, taming has been proposed and studied as a method for ensuring stability of Langevin-based numerical schemes in the case of super-linearly growing drift coefficients for the Langevin SDE. …”
Get full text

Deep learning-based numerical methods for partial differential equations by Dou, Yao

“…The objective of this Final Year Project is to study deep learning-based numerical methods, with a focus on the Deep BSDE Solver, that can be applied on stochastic control problems, backward stochastic differential equations (BSDE) and partial differential equations (PDE) in high-dimensional space. …”
Get full text