Integrating statistical inference with mathematical deduction in protein simulation

Abstract

Mathematical deduction and statistical inference are often seen as opposite, competing approaches in order to achieve results, also in protein simulation. Our claim is that, once more, cooperation is, as often, better than competition. A few approaches in this sense are recalled, mainly developed with our pupils over the recent decades, letting us understanding their powerful combination also in protein simulation thanks to a few recalled examples. The mathematical modeling approach is mainly related to piecewise affine identification within the frame of the dynamic-logic hybrid systems, while the statistical inference is within the frame of explainable artificial intelligence with special emphasis on machine learning of rules intelligible to humans.