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Multilevel Stochastic Gradient Descent for Risk-Averse PDE-Constrained Optimization

arXiv CS Tuesday 09 June 2026, 04:00 UTC By Niklas Baumgarten, Philipp A. Guth, David Schneiderhan, Tommaso Vanzan 1 min read
Key Points

Announce Type: cross Abstract: We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The algorithm uses adaptive multilevel Monte Carlo gradient estimates, provides parallel scalability as well as improved convergence rates and computational complexity compared to standard batched stochastic gradient descent methods. We study the method in computationally demanding...

arXiv:2606.09291v1 Announce Type: cross Abstract: We present recent advances in applying and analyzing multilevel stochastic gradient descent algorithms to risk-averse, three-dimensional PDE-constrained optimization problems. The algorithm uses adaptive multilevel Monte Carlo gradient estimates, provides parallel scalability as well as improved convergence rates and computational complexity compared to standard batched stochastic gradient descent methods. We study the method in computationally demanding settings using three-dimensional elliptic diffusion problems and large risk-aversion parameters.
Originally published by arXiv CS Read original →

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