Speaker
Description
We present a high-performance multi-level stochastic gradient descent method to optimally control the state of systems guided by partial differential equations under uncertain input data. The gradient descent method, used to find the optimal control, leverages a parallel budgeted multi-level Monte Carlo method as stochastic sub-gradient estimator. As a result, we get tight control over the sub-gradient’s bias, introduced by numerical discretizations, and the sub-gradient’s variance with respect to the invested computational resources. The method is particularly well-suited for high-dimensional control problems by exploiting the parallelism and the distributed data structure of the budgeted multi-level Monte Carlo method. Lastly, we study the method’s performance at hand of a three-dimensional elliptic problem with log-normal coefficients and Matérn covariance functions.
