3 papers
math.OC2026
Multilevel Stochastic Gradient Descent for Risk-Averse PDE-Constrained Optimization
Niklas Baumgarten, Philipp A. Guth, David Schneiderhan +1
We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The…
math.OC2026
Multilevel Stochastic Gradient Descent for Optimal Control Under Uncertainty
Niklas Baumgarten, David Schneiderhan
We present a multilevel stochastic gradient descent method for the optimal control of systems governed by partial differential equations under uncertain input data. The gradient de…
math.NA2025
A Budgeted Multi-Level Monte Carlo Method for Full Field Estimates of Multi-PDE Problems
Niklas Baumgarten, Robert Kutri, Robert Scheichl
We present a high-performance budgeted multi-level Monte Carlo method for estimates on the entire spatial domain of multi-PDE problems with random input data. The method is designe…