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DY: Fachverband Dynamik und Statistische Physik

DY 6: Machine Learning in Dynamics and Statistical Physics I

DY 6.9: Vortrag

Montag, 9. März 2026, 11:45–12:00, HÜL/S186

Noise-Balanced Sparse Grid Surrogates for Multiscale Coupling of Monte Carlo and Continuum Models — •Tobias Hülser and Sebastian Matera — Fritz-Haber-Institut der MPG, Berlin

Incorporating a high-fidelity microscopic Monte Carlo model into multiscale simulations can easily become intractable, implying the necessity of surrogate models in many practical applications. Unfortunately, if the microscopic model depends on many macro-variables this can become quite challenging due to the ’curse of dimensionality’. Furthermore, the sampling noise in the underlying Monte Carlo data can lead to uncontrolled errors corrupting the surrogate even though it would be highly accurate in the case of noise-free data. To address these points, we have developed a novel sparse grids interpolation approach which balances interpolation and noise induced errors complemented by a multilevel on-the-fly construction during the multi-scale simulation. Besides its efficiency, an appealing feature is the ease of use of the approach with a single hyperparameter controlling the whole surrogate construction - from which data needs to be created (and how accurately) to the surrogate’s accuracy with guaranteed convergence. We demonstrate the approach on examples from heterogenous catalysis, incorporating microscopic kinetic Monte Carlo models into convection-diffusion type reactor scale simulations.

Keywords: Surrogate models; Monte Carlo; Convection diffusion; Multiscale physics