When I prefer machine learning models based on test data to physical models

All models are mere approximations of reality whether deterministic or stochastic. Machine learning models need to be validated and used within reasons just like physical models, maybe even more so. It often helps to view the variables of problems as part of a matrix of knowledge as shown below.

Most engineers are fully aware of risks, and that there are unknown parameters in their experiment. Much harder in reality, however, is that their physical models contain some degree of model-form uncertainty as well (this is called epistemic uncertainty by people specialised in surrogate modelling for physical simulations)

Let me give you a quick example.

The figure below shows two probability distributions that show the variability of the location where a flow reattaches after a hill. Both results were calculated using CFD codes. However, it can be seen how the shape and range of the PDFs are quite different. For the high-fidelity and more accurate Direct Numerical Simulation (DNS) on the left-hand side, the mean flow reattaches at about x/h = 4 and the distribution is skewed to the left with a standard deviation of about x/h = 1. For the much cheaper but also significantly less accurate Reynolds Averaged Navier-Stokes (RANS) simulation on the right-hand side, the mean flow reattaches at x/h = 6 and the distribution is highly skewed to the right with a standard deviation of about x/h = 3. This example demonstrates the significant effect of the model-form uncertainty when using models for decision making.

My personal favourite way of solving this has been to build a model based on the best information available, ideally test data and then take it from there. In the below picture you can see eigenfrequencies of a structure predicted using a machine learning model from a FEA simulation (red) and a test stand (blue). Personally, I am rather inclined to take the information from the test stand.