Noise-balanced multilevel on-the-fly sparse grid surrogates for coupling Monte Carlo models into continuum models with application to heterogeneous catalysis

TL;DR

This paper introduces a noise-balanced sparse grid surrogate modeling approach that efficiently integrates microscopic Monte Carlo models into continuum simulations, addressing sampling noise and high dimensionality in multiscale modeling.

Contribution

The paper presents a novel noise-balanced sparse grid method with a multilevel on-the-fly construction, simplifying surrogate modeling for complex multiscale simulations with minimal hyperparameters.

Findings

Effective control of sampling noise in surrogate models

Reduced computational cost in multiscale simulations

Successful application to heterogeneous catalysis models

Abstract

Multiscale simulations utilizing high-fidelity, microscopic Monte Carlo models to provide the nonlinear response for continuum models can easily become computationally intractable. Surrogate models for the high-fidelity Monte Carlo models can overcome this but come with some challenges. One such challenges arise by the sampling noise in the underlying Monte Carlo data, which leads to uncontrolled errors possibly corrupting the surrogate even though it would be highly accurate in the case of noise-free data. Another challenge arises by the 'curse of dimensionality' when the response depends on many macro-variables. These points are addressed by a novel noise-balanced sparse grids interpolation approach which, in a quasi-optimal fashion, controls the amount of Monte Carlo sampling for each data point. The approach is complemented by a multilevel on-the-fly construction during the multiscale simulation. Besides its efficiency, a particularly appealing feature is the ease of use of the approach with only a single hyperparameter controlling the whole surrogate construction - from the surrogate's accuracy with guaranteed convergence to which data needs to be created with which accuracy. The approach is demonstrated on challenging examples from heterogeneous catalysis, coupling microscopic kinetic Monte Carlo models into macroscopic reactor simulations.