Learning hierarchies of reduced-dimension and context-aware low-fidelity models for multi-fidelity Monte Carlo sampling

Ionut-Gabriel Farcas (U of Texas, Austin)

May 04. 2022, 16:15 — 16:45

In traditional model reduction, low-cost low-fidelity models are explicitly constructed to replace computationally expensive high-fidelity models for speeding up computations. In contrast, in multi-fidelity methods, low-
and high-fidelity models are used together, therefore the primary purpose of low-fidelity models is supporting
computations with the high-fidelity models rather than approximating and replacing them.
In the first part of this talk, we introduce a Data-driven Multi-fidelity Monte Carlo approach in which a
hierarchy of low-fidelity models are constructed using both the full set of uncertain inputs and subsets comprising
only selected, important parameters. We illustrate the power of this method by applying it to a realistic plasma
turbulence problem with 14 stochastic parameters, demonstrating that it is about two orders of magnitude
more efficient than standard Monte Carlo methods measured in single-core performance, which translates into
a runtime reduction from around eight days to one hour on 240 cores on parallel machines.
In the second part, we present our Context-aware Multi-fidelity Monte Carlo sampling
algorithm, in which context-aware low-fidelity models are explicitly constructed for being used together with
high-fidelity models. This is realized by quasi-optimally trading off adapting the low-fidelity models–to improve
their deterministic approximation quality–with sampling the models–to reduce the statistical error. Our analysis
shows that the quasi-optimal computational effort to spend on improving the low-fidelity models is bounded,
meaning that low-fidelity models can become too accurate for multi-fidelity methods, which is in stark contrast
to traditional model reduction. We illustrate our context-aware algorithm in a realistic plasma turbulence simulations with $12$ uncertain parameters, in which, for example, only $263$ high-fidelity samples are necessary to train a fully-connected feed-forward deep neuronal network model.

Further Information
ESI Boltzmann Lecture Hall
Associated Event:
Computational Uncertainty Quantification: Mathematical Foundations, Methodology & Data (Thematic Programme)
Clemens Heitzinger (TU Vienna)
Fabio Nobile (EPFL, Lausanne)
Robert Scheichl (U Heidelberg)
Christoph Schwab (ETH Zürich)
Sara van de Geer (ETH Zürich)
Karen Willcox (U of Texas, Austin)