Roman Belousov

Modeling complex systems appears to me in striking contrast with the image of physics that emerges from famous stories and anecdotes about scientific struggle: poor Galileo pacing up and down the Tower of Pisa, Newton’s revelation “beaten” into his head by an apple, desperate or uncanny hypotheses introduced by Planck, Bohr, and Einstein just to make progress. These examples give the impression, that the hardest part of the problem is to find even a single model describing the experimental observations. Today, when it comes to complex systems, suddenly there is a multitude of mathematical models for the same problem... Does it matter which one we choose?

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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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