From https://news.ycombinator.com/item?id=44043518#44053779 re: deep learning poised:
> jax-cfd mentions phiflow
> PhiFlow: https://github.com/tum-pbs/PhiFlow/
>> A differentiable PDE solving framework for machine learning
SymPy can solve ODEs and some PDEs.
sympy.solvers.pde: https://docs.sympy.org/latest/modules/solvers/pde.html
SymPy's sympy.utilities.lambdify.lambdify() compiles things to faster solvers like CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPy, numexpr, and PyTorch. https://docs.sympy.org/latest/modules/utilities/lambdify.htm...
dynamicslab/pysindy; https://github.com/dynamicslab/pysindy :
> A package for the sparse identification of nonlinear dynamical systems from data
A question about fundamental Anosov flows and CFD in pysindy; due to "Flow Proof Helps Mathematicians Find Stability in Chaos" (2023) https://www.quantamagazine.org/flow-proof-helps-mathematicia... .. https://github.com/dynamicslab/pysindy/issues/383 :
/? site:github.com anosov https://www.google.com/search?q=site%3Agithub.com+anosov
> GitHub topic: quantum-fluids: https://github.com/topics/quantum-fluids
GitHub topic: Gross-Pitaevskii: https://github.com/topics/gross-pitaevskii
OSIRIS-code can simulate laser emissions in plasma, nonlinear optics in plasma,; and supports Checkpointing and thus probably parallelization; https://news.ycombinator.com/context?id=44371059
For simulations of gravity-assisted spacecraft trajectories, in n-body (vortical fluidic) gravity:
> JPL SPICE toolkit: https://naif.jpl.nasa.gov/naif/toolkit.html
> SpiceyPy: https://github.com/AndrewAnnex/SpiceyPy
"Gravity as a fluid dynamic phenomenon in a superfluid quantum space. Fluid quantum gravity and relativity." (2017) https://hal.science/hal-01248015/ :
> [ Bernoulli, Navier-Stokes, Gross-Pitaevskii vortices in a field with curl ]
Shouldn't solving NS also solve for n-body gravity?
Anosov diffeomorphism; hyperbolicity of complex nonlinear dynamic fluid systems, Lyapunov exponents : https://en.wikipedia.org/wiki/Anosov_diffeomorphism
Curl: https://en.wikipedia.org/wiki/Curl_(mathematics)
Vorticity: https://en.wikipedia.org/wiki/Vorticity
Bernoulli's principle: https://en.wikipedia.org/wiki/Bernoulli%27s_principle
Gross-Pitaevskii equation: https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equat...
Navier-Stokes equations: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equation...
This is a fine collection of links - much to learn! - but the connection between flow and gravitation is (in my understanding) limited to both being Green's function solutions of a Poisson problem. https://en.wikipedia.org/wiki/Green%27s_function
There are n-body methods for both (gravitation and Lagrangian vortex particle methods), and I find the similarities and differences of those algorithms quite interesting.
But the Fedi paper misses that key connection: they're simply describing a source/sink in potential flow, not some newly discovered link.
That said, it sounds like teams are guiding the areas of exploration pretty directly. If I was more cynical, I'd say that Google has a lot of financial incentive to claim it was integral to any breakthroughs the team comes up with.
Id wager quantum computers even in their infancy are more capable of generating valid solutions humans are incapable of.
Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472
tocs3•7mo ago