> For instance, we solve nontrivial nonlinear PDEs (one HJB equation and one Black-Scholes equation) in 100,000 dimensions in 6 hours on a single GPU using SDGD with PINNs<p>100,000 dimensions? I thought there were like... 11 tops? <a href="https://imagine.gsfc.nasa.gov/science/questions/superstring.html#:~:text=The%20only%20consistent%20framework%20to%20describe%20those%20strings%20implies%20a%2010%2D%20or%20even%20conceivably%20an%2011%2Ddimension%20world" rel="nofollow noreferrer">https://imagine.gsfc.nasa.gov/science/questions/superstring....</a><p>(edit: oops, I misunderstood the context of dimensions here. my bad. thanks)
Iiii do not think you should be able to solve the Schrodinger equation with thousands of dimensions in general on a non-quantum computer, what with that being a quantum-mechanical equation some of whose solutions would reflect quantum-hard problems?