Defining Formal Validity Criteria for Machine Learning Models

In the context of deterministic scientific simulations, formal validity requirements have typically been defined to help us reason about the relationship between the mathematical model underlying the target system and the computational model used to simulate it. With machine learning simulations entering the picture, we argue that these formal requirements need to be reviewed, as the objects to which they apply have significantly changed. This is due to several reasons: the target system is no longer an available system object of investigation; the probabilistic mathematical model is abstracted from the target system through the mediation of the computational model, which however remains largely opaque to us due to its high complexity. For these reasons, we formulate weaker, probabilistic versions of the traditional relations of Simulation, Bisimulation, and Approximate Simulation. Accordingly, we define three corresponding validity criteria that capture a range of cases, from the strongest to the weakest, depending on the extent to which the machine learning model can be assumed to correctly represent its target system.