5 papers
Risk-averse Optimization in Random Materials: Algorithmic Advances and HPC Acceleration
Niklas Baumgarten, Marcel Koch, David Schneiderhan +2
We summarize our advances in the algorithmic development and hardware utilization for risk-averse optimization problems in random materials. This includes risk-averse optimization…
Optimized Multilevel Sampling Methods under Resource Constraints
Niklas Baumgarten
We present recent developments in multilevel sampling methods under resource constraints. Over the past 15 years, multilevel methods have become widely used for uncertainty quantif…
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…
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…
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…