Reliable and resource preserving emulation for Bayesian model inference

<!--HTML-->As a result of the observed discrepancies within the $\Lambda \mathrm{CDM}$ model, a lot of work is being done to reconcile the observations from the early and late universe with new cosmological models. The resulting model testing is often based on inference algorithms that depend on a large number of computationally intensive simulations that conclude in large computational efforts. In our work we show that it is possible to substantially reduce the number of computations by emulating the simulation and interpolating between individual simulations. We demonstrate this by emulating the widely used linearized Boltzmann Einstein solver $\mathrm{CLASS}$ utilizing cosmology inspired neural networks. This intuition of the underlying physical effects allows us to keep the network sizes shallow and lightweight which results in fast evaluation and training. Additionally we use dynamic switching between the emulator and the full simulation to keep the used parameter range of the emulator as narrow as possible, still remaining accurate in the most relevant parameter region. This results in small training sets and ,thus, a faster adoption and training of this emulator for new models of interest. The code with example scripts on usage is publicly available under the name $\mathrm{CLASSNET}$.