SKM 2023 – wissenschaftliches Programm

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DY: Fachverband Dynamik und Statistische Physik

DY 17: Machine Learning in Dynamics and Statistical Physics I

DY 17.1: Vortrag

Dienstag, 28. März 2023, 10:00–10:15, ZEU 160

On-the-fly adaptive sparse grids for coupling high-fidelity and coarse-grained models — •Tobias Hülser, Sina Dortaj, and Sebastian Matera — Fritz-Haber-Institut der MPG, Berlin, Germany

Most simulations of continuum models require the repetitive evaluation of some non-linear functions. If the latter are only given by the outcome of some high-fidelity simulation, these evaluations can easily become the computational bottleneck of the coupled simulation. To overcome this limitation, computationally efficient machine-learning models have become popular as surrogates of the high-fidelity model in the continuum scale simulation. However, if the input dimension of these models is high, the training of the surrogate often requires infeasible numbers of simulations, the so-called curse of dimensionality. We present an on-the-fly adaptive sparse grids approach, which lifts these limitations. This exploits that, on the one hand, sparse grids are only mildly affected by the curse of dimensionality and allow for an adaptive, local error based training set design. On the other hand, we utilize that, during a continuum simulation, only a small low-dimensional subset of the high-dimensional input space of the high-fidelity model is visited. We therefore construct the surrogate on the fly during the continuum simulation, only generating the high-fidelity data which is needed to interpolate this subset.

We demonstrate the approach on exemplary physical-chemical models from the field of heterogeneous catalysis. We find that our approach can significantly reduce the number of high-fidelity evaluations compared to the direct coupling.