Interesting case of Schrodinger equation & deep learning (and possible application in Commutative Hodge Conjecture)

If my readers remember my old blog (written under the pseudoname of DataHulk 😏), I used to talk about Physics Informed Neural Networks, Physics formed deep learning & Data, Machine learning & Deep learning to solve math conjectures 12 years back... much before The Ramanujan Machine (AI to Solve Math Conjectures) was born. 

And Yes, I saw review on my 2013 book - Healthcare Social Media Management and Analytics, so I know some of my readers have missed me 🙌🙌🙌





1. Here is a curious case which was written few months back - Data-driven vector soliton solutions of coupled nonlinear Schrödinger equation using a deep learning algorithm - https://www.researchgate.net/publication/355789067_Data-driven_vector_soliton_solutions_of_coupled_nonlinear_Schrodinger_equation_using_a_deep_learning_algorithm In this paper, there is pre-fixed multi-stage training algorithm by combining the error measurement & multi-stage training. This algorithm is much better suited for different dynamical behaviors of solitons with faster convergence rate.


2. Recently, G. Tabuada from MIT proposed a series of noncommutative counterparts all conjectures including Grothendieck standard conjecture, Voevodsky nilpotence conjecture, Tate conjecture, Weil conjecture etc. XUN LIN has also proposed NON-COMMUTATIVE HODGE CONJECTURE.


Similar physics informed neural nets or GANs can be used for commutative Hodge Conjecture. More to come soon on this topic.


On a different topic, Please do listen to András Juhász & Marc Lackenby (similar to University of Sydney mathematician Geordie Williamson's work with DeepMind on representation theory) - https://www.youtube.com/watch?v=hIUiPi-jAjM