Mathematical explanation is not required in many areas.

Perhaps you can’t perfectly explain it but you can at least understand it statistically.

For example is not currently possible to mathematically explain people’s behaviour, but there is statistical evidence and also accountability on an individual. Eg a doctor making a decision about a scan result.

I raise another example, to question, you can statistically solve the famous diffusion problem.

It's even simpler than that. You don't need any particular level of understanding, you just can't lie about what your level of understanding is.

The following would seem to be OK: "This model performs well in a set of tests we devised, your mileage may vary."

Non-linear models often perform better. You’re never going to approach anything like GPT with a linear model.

Theoretically you could use a polynomial model which, while not linear, is pretty high on the explainability scale.

I don't think mentioning non-linearality means you can bypass the singularities you may cause typically CUSP, buckling etc and omit the analysis intentionally or negeliccantly.