Thema der Dissertation:
On-the-fly multilevel sparse grids for multiscale models of heterogeneous catalysis Thema der Disputation:
Reduced Order Modeling for fluid dynamics PDEs with nonlinear boundary conditions and applications to heterogeneous catalysis
On-the-fly multilevel sparse grids for multiscale models of heterogeneous catalysis Thema der Disputation:
Reduced Order Modeling for fluid dynamics PDEs with nonlinear boundary conditions and applications to heterogeneous catalysis
Abstract: Many practical problems are described by partial differential equations (PDEs) with nonlinear, parameter-dependent boundary conditions — a prominent example being reactive flow in heterogeneous catalysis.The numerical simulation of such PDEs remains computationally demanding, particularly in many-query contexts such as parameter studies and optimization. Reduced Order Models (ROMs) address this challenge by constructing computationally tractable low-dimensional approximations of high-fidelity discretizations, enabling rapid parametric evaluations at a fraction of the computational cost. However, standard projection-based techniques face significant numerical difficulties when highly nonlinear boundary conditions are present. Therefore, specialized techniques that exploit the fact that the problematic nonlinearities are localized on the boundary are essential. In this talk, I present recent reduced order modeling strategies for such problems, motivated by heterogeneous catalysis. In these systems, chemical reactions occur at the fluid–solid interface, where the nonlinearities enter as nonlinear reaction kinetics on the catalytic surface. I discuss the efficiency and limitations of these methods and compare them with standard reduced bases obtained via Proper Orthogonal Decomposition. I further demonstrate the application of these techniques to realistic problems from heterogeneous catalysis, including reactive flow in complex reaction chamber geometries coupled with challenging chemical kinetics.
This thesis presents a multilevel 'on-the-fly' sparse grid surrogate approach (ML-OTF-SG) for replacing high-fidelity Monte Carlo–type models with cheap-to-evaluate surrogates in multiscale simulations. Two main contributions are introduced. First, an on-thefly local refinement strategy is presented that constructs sparse grids only in regions relevant to the queries of a nonlinear continuum solver. This approach ensures self-consistency — producing identical surrogate responses for fixed inputs — and maintains all sparse grid properties locally. It is complemented by a multilevel scheme that further increases efficiency. Second, an extension to (kinetic) Monte Carlo models is introduced, for which a balancing mechanism is developed that controls the Monte Carlo sampling effort in a quasi-optimal manner. Convergence of this approach is guaranteed. The methodology is demonstrated on high-fidelity Monte Carlo models from the literature coupled to a macroscale reactor model. Besides computational efficiency, the ML-OTF-SG approach offers practical simplicity, with a single hyperparameter controlling the entire scheme in both noise-free and stochastic settings.
This thesis presents a multilevel 'on-the-fly' sparse grid surrogate approach (ML-OTF-SG) for replacing high-fidelity Monte Carlo–type models with cheap-to-evaluate surrogates in multiscale simulations. Two main contributions are introduced. First, an on-thefly local refinement strategy is presented that constructs sparse grids only in regions relevant to the queries of a nonlinear continuum solver. This approach ensures self-consistency — producing identical surrogate responses for fixed inputs — and maintains all sparse grid properties locally. It is complemented by a multilevel scheme that further increases efficiency. Second, an extension to (kinetic) Monte Carlo models is introduced, for which a balancing mechanism is developed that controls the Monte Carlo sampling effort in a quasi-optimal manner. Convergence of this approach is guaranteed. The methodology is demonstrated on high-fidelity Monte Carlo models from the literature coupled to a macroscale reactor model. Besides computational efficiency, the ML-OTF-SG approach offers practical simplicity, with a single hyperparameter controlling the entire scheme in both noise-free and stochastic settings.
Zeit & Ort
09.10.2026 | 16:10
Seminarraum 032
(Fachbereich Mathematik und Informatik, Arnimallee 6, 14195 Berlin)
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