Standard Model is extremely well tested, but e.g. is incompatible with general relativity, is rather for effective perturbative approximations, also uses this gigantic Lagrangian found in epicycle-style: by guess&fit terms.

So maybe, like in Copernican Revolution, we should search for compact deeper nonperturbative Lagrangian (e.g. Skyrme-like), effectively described close to Standard Model + gravity?

Nonperturbative Lagrangians look simple, but have extremely complex consequences - maybe AI could search through them, automatically performing simulations testing various agreements?

This kind of approaches have already started, e.g.: "Towards AI-assisted neutrino flavor theory design": https://www.nature.com/articles/s42005-026-02627-2 , "Agentic Exploration of Physics Models" https://journals.aps.org/prx/abstract/10.1103/xnqc-q6nt , or https://github.com/openwave-labs/openwave/blob/main/MODELS.md actually testing such deeper Lagrangian candidates - currently winning is liquid-crystal-like: just assumption that field has preferred anisotropy.

What do you think about such approaches? Where to search for such deeper Lagrangians?

Would be great if Wolfram had independent model benchmarking environment like OpenWave ...