Most of our atomic scale understanding of heterogeneous catalysis stems from experiments performed in under ultra-high vakuum conditions and at low temperatures. In contrast, real life catalysts operate at atmospheric pressures and elevated temperatures. In order to bridge this *pressure gap* a number of experimental setup have been developed, which are able to deliver atomic scale information under realistic operation conditions. At the concomittant higher conversion rates macroscale transport becomes then an important factor, which can mask the targeted correlation between reactivity, reaction conditions and atomic scale information. In order to describe all these aspects, we have developed a multi-scale modeling framework during the last years, which succesively coarse grains electronic structure information up to a stochastic model for the catalysts reactivity. This is then coupled to a continuum mechanical treatment of macroscale mass and heat transport. The mathematical aspects, we investigate in this context, are stochastic simulation, high-dimensional interpolation and the numerical solution of the partial differentail equations governing reactive flow.

Lorenzi, J. M., Stecher, T., Reuter, K., & Matera, S. (2017). Local-metrics error-based Shepard interpolation as surrogate for highly non-linear material models in high dimensions. *The Journal of Chemical Physics*, *147*(16), 164106

Matera, S., Blomberg, S., Hoffmann, M. J., Zetterberg, J., Gustafson, J., Lundgren, E., & Reuter, K. (2015). Evidence for the Active Phase of Heterogeneous Catalysts through In Situ Reaction Product Imaging and Multiscale Modeling. *ACS Catalysis*, *5*(8), 4514-4518.

Matera, S., Maestri, M., Cuoci, A., & Reuter, K. (2014). Predictive-quality surface reaction chemistry in real reactor models: Integrating first-principles kinetic Monte Carlo simulations into computational fluid dynamics. *ACS Catalysis*, *4*(11), 4081-4092.

Matera, S., & Reuter, K. (2012). When atomic-scale resolution is not enough: Spatial effects on in situ model catalyst studies. *Journal of Catalysis*, *295*, 261-268.

Matera, S., & Reuter, K. (2010). Transport limitations and bistability for in situ CO oxidation at RuO 2 (110): First-principles based multiscale modeling. *Physical Review B*, *82*(8), 085446.

Matera, S., & Reuter, K. (2009). First-principles approach to heat and mass transfer effects in model catalyst studies. *Catalysis letters*, *133*(1-2), 156-159.