Thermodynamics of learning physical phenomena

In a 2009 compilation of essays, the fourth paradigm of science was first described [1]. After centuries of science based on observation--the empirical period of the first paradigm--came a period based on the establishment of scientific laws--the second paradigm, think of Newton--and much more recently a period in which simulation took an important role--the third paradigm. Very recently, the authors of this essay argue that we have entered a period in which data plays a prominent role in scientific discovery and where theory and experiments, symbiotically, help data to achieve higher goals. Scientific Machine Learning is precisely a new field in which data coming from scientific experiments is used massively to unveil new, still unknown scientific laws. Some authors have begun to think about an even more recent fifth paradigm of science, in which data is obtained not from experiments, but from simulations [2].