Automative model selection and model certification for reaction-diffusion equations

Abstract

This paper discusses the problem of automative model selection for low-fidelity models learned from data generated by a high-fidelity model. The models describe the time and space dependent interaction of virus and T cells in liver infections. While the high-fidelity model uses more a-priori knowledge and therefore a non-local reaction term, the low-fidelity models only consists of local interaction terms. We discuss the results from a model-theoretic perspective and compare three approaches with different complexity levels. The results include some surprising parameter choices even in the physics-based approach and a discussion of the model choice out of an insufficient model family.