Unification of a general relativity and quantum electrodynamics framework using neural networks and classical computers

Practical quantum computing is an elusive goal. On the other hand, to a limited extent, Einstein’s dream to unify electrodynamics and general relativity appears to be within reach at the mesoscopic scale, because of combining modern computational science with neural networks. I want to discuss this in context of low rank neural modeling of partial differential equations [1], [2]. I will relate this to general relativity via parametrization of the PDEs that allows a pseudo-mass structure to be defined n context of a multidimensional manifold. I will also try to show that a neural network, suitably adapted, can be thought of as a thermalized and renormalized system derived from an underlying quasi-quantum electrodynamics structure. Because these two very disparate structures, one scaling down from a large-scale system, and one scaling up from a small, converge within a neural network framework, we can think of modern computing technology as having brought Einstein’s goal of unification within reach at the mesoscopic scale.



References

[1] Peherstorfer, B. 2022. Breaking the Kolmogorov barrier with nonlinear model reduction. Notices of the American Mathematicl Society. DOI: https//:doi.org/10.1090/noti2475.

[2] Berman, J. Peherstorfer, B. 2024. CoLoRA: Continuous low-rank adaptation for reduced implicit neural modeling of parameterized partial differential equations. Proceedings of the 41^st International Conference on Machine Learning, Vienna, Autria. PMLR 235.