Roman Belousov

Eager to read about recent advances in symbolic machine learning unlocked by SymTorch, I nevertheless stumbled over the authors’ premise: “In physics, interpretability means using concise equations that reliably explain phenomena.” The quote reminded me of a joke: any series expansion can be called a special function, even if it is special only to your particular physical problem. If a concise equation describes the data well, does it necessarily have an obvious physical interpretation—or any at all?

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Mathematically, there is nothing wrong with Newtonian physics. So why do we need relativity and quantum mechanics? Why is the geocentric model of the solar system wrong? Because such are the laws of the material world: but how do the physicists find out which models are right, and why others are wrong?

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Can a mathematically rigorous model still be physically irrelevant? Absolutely. That observation may lie at the heart of physics. Here is an example for my colleagues from biology: You can classify a dragon, model its fire-breathing mathematically, and still fail to conjure biology...

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