Duda Jarek

Tests from OpenWave by Fable - which ones should be checked for candidates of deeper model?

Just wanted to stimulate discussion on the topic in title, e.g. by gathering my thoughts on it in this talk. Here is a mainstream lecture "Physics-Informed Machine Learning – Lecture 1 | Why Physics + AI? ": https://www.youtube.com/watch?v=BVkGy4oz3Lg

(How and why) could AI (help to) find deeper physics? - talk: https://www.youtube.com/watch?v=RSqIUWnnvqA Current physics works on particles as abstract perfect points - what is only effective perturbative approximation. Deeper there are complex field configurations, mainstream doesn't understand - e.g. angular momentum of electron. Many candidates for deeper Lagrangians were proposed, but understanding their consequences need extremely difficult simulations - now top LLM models can automatically write, run, analyze - what is already leading to rigorous tests, improvements, maybe search by AI - to finally get one level deeper in our physics understanding, what will have huge consequences.

ps. or fresh Fable simulations of muon/taon decay into electron (hedgehog of one of 3 axes in 3D), releasing energy difference into neutrinos as topological vortex loops: https://github.com/openwave-labs/openwave/blob/main/openwave/xperiments/m5_liquid_crystal/research/findings/m5_21_6_note.md

I was also skeptical, but recently work with Fable: multiple agents writing&performing simulations, asking questions, planning new tasks, discussing ... only sometimes asking human for suggestions, but it is becoming less and less frequent :/ What more can human do? E.g. yesterday report: https://github.com/openwave-labs/openwave/blob/main/openwave/xperiments/m5_liquid_crystal/research/findings/m5_20_3_method_note.md

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 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 Lagrangian?

Standard Model Lagrangian is for perturbative approximations (particles as perfect points from creation operators, with probability distributions), incompatible with gravity, and gigantic found epicycle-style: by guess&fit new terms when previous disagreed. Previous Copernican Revolution was compressing epicycles into compact form - we need a new one: deeper nonperturbative Lagrangian (e.g. Skyrme-like), effectively described close to Standard Model + gravity.

My basic approach is to represent entire shape as Gaussian times polynomial, then find rotation invariants of this polynomial - as features for chemoinformatics, or vector to compare for shape similarity metric. Interesting mathematics to speedup MRI: https://en.wikipedia.org/wiki/Compressed_sensing

Update: working on proof of such similarity test for general matrices, it is convening to use Schur decomposition rotating A and B to upper-diagonal (can be complex), can be chosen with same diagonals thanks to tested Tr(A^k)=Tr(B^k). Then seems we should use induction d\to d+1 from d x d matrix A, vector v, scalar a: From their equality for A and B, and right hand side using powers lower by 1, we should conclude Tr(A^k (A^T)^l) = Tr(B^k (B^T)^l)$ and equality of vectors ...

This one is quite far future work, but maybe will move forward with interns from https://www.qaif.org/events/aintern/aintern-2026

Yes, one direction here is considering more sophisticated primitives than in gaussian splitting, e.g. multiplied by polynomial. But direct question is about better rotation invariants than e.g. spherical harmonics - offering only rough description modulo rotation, while here should be complete.

There is this basic similarity test Tr(A^k) = Tr(B^k) for k=1..d for symmetric matrices allowing to conclude existence of orthogonal O such that AO = OB. Practical question is how (if possible?) to generalize it (finally to tensors, but at least) to non-symmetric matrices e.g. including transpositions. Checking Jacobian criterion for Tr(A^k (A^T)^l) = Tr(B^k (B^T)^l) for k=1..d, l=0..k-1 at least for up to d=5 has sufficient number of independent invariants (d(d+1)/2) - is it sufficient condition in general dimension? If not, how to extend it? Used Mathematica code using Jacobian criterion to find the number of independent invariants, assuming upper-diagonal as in Schur decomposition, getting d(d+1)/2 as required up to d=5: d = 5; M = Table[If[i > j, 0, Subscript[a, Row[{i, j}]]], {i, d}, {j, d}]; inv = Table[Tr[MatrixPower[M, k].MatrixPower[Transpose[M], l] , {k, d}, {l, 0, k - 1}]; MatrixRank[jac = Table[D[Catenate[inv], v], {v, Variables[inv]}]]Motivations ( https://arxiv.org/pdf/2601.03326 ), especially if reaching also for tensors, is complete shape description up to rotation e.g. for chemoinformatics, medical imaging:

So how do you interpret these huge negative regions in radio flux maps from https://iopscience.iop.org/article/10.3847/1538-4357/ac0e93/pdf ? Don't radiotelescopes measure energy balance: positive if absorbed, negative if emitted? Doesn't S-matrix <psi_f |U| psi_i> say photon exchange depend on both emitter in psi_f, but also absorber in psi_i?

Positive signal means telescope absorbs energy from source, so seems negative means telescope emits energy? Like for wave behind marine propeller: carrying energy, momentum, and angular momentum - could excite resonator, but reversing rotation it could cause its deexcitation: There is also mechanical analog - coupled oscillators periodically exchange energy like Rabi cycles, what would be stopped without one acting as absorber. In astronomy such absorber might be e.g. black hole, emitter in telescope. Anyway, they clearly see negative signals e.g. in this Fig. 1 from https://iopscience.iop.org/article/10.3847/1538-4357/ac0e93/pdf , usually saying this is just noise ... but these are huge regions of similar luminosity but reversed sign - maybe hypothesis of actually being positive could be verified? Or if negativity would remain, we should try to finally understand it ...

Radiation pressure is p=<ExB>/c vector: there is focus on positive, but can be also negative: https://scholar.google.pl/scholar?q=negative+radiation+pressure , https://scholar.google.pl/scholar?q=optical+pulling If positive radiation pressure gives positive signal in radiotelescopes, shouldn't negative give negative? They clearly see also large regions of negative signal in radio flux maps, e.g. below from https://arxiv.org/pdf/2107.02695 What objects could generate negative radiation pressure? E.g. if white hole would generate positive, shouldn't black holes generate negative?