Speaker
Description
Most simulations of continuum models require the repetitive evaluation of some non-linear functions. If these functions are only implicitly given by the outcome of some expensive high-fidelity model, these evaluations can easily become the computational bottleneck of this coupled simulation. A surrogate model for the high-fidelity part is therefore needed. However, if the input dimension of the high-fidelity model is high, the training of the surrogate often requires infeasible numbers of simulations, the so-called curse of dimensionality. During the last years, we have developed a multilevel on-the-fly sparse grid approach to address this problem [1]. This approach exploits the good convergence behavior of sparse grids also in higher dimensional settings and, additionally, that only a small low-dimensional subset of the high-dimensional input space is visited during a continuum simulation. We present the extension of this approach to cases when the evaluation of the high-fidelity model requires statistical sampling. Each evaluation therefore carries some finite noise error, which variance depends inversely on the invested CPU time. We present ideas for balancing these errors with the sparse grid approximation error to ensure convergence and, at the same time, to avoid unnecessarily accurate and expensive sampling. We showcase the approach on realistic problems from heterogeneous catalysis, where continuum reactor models are coupled with kinetic Monte Carlo simulations for the surface reactions. We find that the proposed approach requires only modest computational resources for these problems, where a direct coupling would be infeasible. Finally, we discuss for these kinds of models how an automatic termination can be realized.
[1] T. Hülser, B. Kreitz, C.F. Goldsmith, S. Matera, Computers and Chemical Engineering (2024), https://doi.org/10.1016/j.compchemeng.2024.108922
