3 ms·

Google DeepMind team up to solve the Navier-Stokes million-dollar problem

23 points by bilsbie 1y ago

tocs3 1y ago
Not solved yet.
westurner 1y ago
Notes for such efforts: From https://news.ycombinator.com/item?id=44043518#44053779 https://news.ycombinator.com/item?id=44043518#44053779 re: deep learning poised: > jax-cfd mentions phiflow > PhiFlow: https://github.com/tum-pbs/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 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.html https://docs.sympy.org/latest/modules/utilities/lambdify.htm... dynamicslab/pysindy; https://github.com/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-mathematicians-find-stability-in-chaos-20230615/ https://www.quantamagazine.org/flow-proof-helps-mathematicia... .. https://github.com/dynamicslab/pysindy/issues/383 https://github.com/dynamicslab/pysindy/issues/383 : /? site:github.com anosov https://www.google.com/search?q=site%3Agithub.com+anosov https://www.google.com/search?q=site%3Agithub.com+anosov > GitHub topic: quantum-fluids: https://github.com/topics/quantum-fluids https://github.com/topics/quantum-fluids GitHub topic: Gross-Pitaevskii: https://github.com/topics/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 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 https://naif.jpl.nasa.gov/naif/toolkit.html > SpiceyPy: https://github.com/AndrewAnnex/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/ 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 https://en.wikipedia.org/wiki/Anosov_diffeomorphism Curl: https://en.wikipedia.org/wiki/Curl_(mathematics) https://en.wikipedia.org/wiki/Curl_(mathematics) Vorticity: https://en.wikipedia.org/wiki/Vorticity https://en.wikipedia.org/wiki/Vorticity Bernoulli's principle: https://en.wikipedia.org/wiki/Bernoulli%27s_principle https://en.wikipedia.org/wiki/Bernoulli%27s_principle Gross-Pitaevskii equation: https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equat... Navier-Stokes equations: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equation...
- markstock 1y ago
  Um, no? 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 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.
fasthands9 1y ago
I've long thought that if AI can start solving unsolved math problems we are in for a very weird (or bad) future, since at that point it really can come up with things that no one has thought of before. And perhaps, it would also be able to find new physics or new physical mechanisms very fast. 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.
- eggn00dles 1y ago
  Deepmind team is trying to solve the problem. Not their AI alone. The novel creativity AIs can produce atm are hallucinations. Id wager quantum computers even in their infancy are more capable of generating valid solutions humans are incapable of.
mikhailfranco 1y ago
Terence Tao briefly discusses this problem in the first chapter of his talk with Lex Fridman: Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472 https://www.youtube.com/watch?v=HUkBz-cdB-k https://www.youtube.com/watch?v=HUkBz-cdB-k

23 points by bilsbie 1y ago

Not solved yet.

Notes for such efforts: From https://news.ycombinator.com/item?id=44043518#44053779 https://news.ycombinator.com/item?id=44043518#44053779 re: deep learning poised: > jax-cfd mentions phiflow > PhiFlow: https://github.com/tum-pbs/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 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.html https://docs.sympy.org/latest/modules/utilities/lambdify.htm... dynamicslab/pysindy; https://github.com/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-mathematicians-find-stability-in-chaos-20230615/ https://www.quantamagazine.org/flow-proof-helps-mathematicia... .. https://github.com/dynamicslab/pysindy/issues/383 https://github.com/dynamicslab/pysindy/issues/383 : /? site:github.com anosov https://www.google.com/search?q=site%3Agithub.com+anosov https://www.google.com/search?q=site%3Agithub.com+anosov > GitHub topic: quantum-fluids: https://github.com/topics/quantum-fluids https://github.com/topics/quantum-fluids GitHub topic: Gross-Pitaevskii: https://github.com/topics/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 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 https://naif.jpl.nasa.gov/naif/toolkit.html > SpiceyPy: https://github.com/AndrewAnnex/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/ 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 https://en.wikipedia.org/wiki/Anosov_diffeomorphism Curl: https://en.wikipedia.org/wiki/Curl_(mathematics) https://en.wikipedia.org/wiki/Curl_(mathematics) Vorticity: https://en.wikipedia.org/wiki/Vorticity https://en.wikipedia.org/wiki/Vorticity Bernoulli's principle: https://en.wikipedia.org/wiki/Bernoulli%27s_principle https://en.wikipedia.org/wiki/Bernoulli%27s_principle Gross-Pitaevskii equation: https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equation https://en.wikipedia.org/wiki/Gross%E2%80%93Pitaevskii_equat... Navier-Stokes equations: https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equations https://en.wikipedia.org/wiki/Navier%E2%80%93Stokes_equation...

markstock 1y ago
Um, no? 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 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.

fasthands9 1y ago

I've long thought that if AI can start solving unsolved math problems we are in for a very weird (or bad) future, since at that point it really can come up with things that no one has thought of before. And perhaps, it would also be able to find new physics or new physical mechanisms very fast. 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.

eggn00dles 1y ago
Deepmind team is trying to solve the problem. Not their AI alone. The novel creativity AIs can produce atm are hallucinations. Id wager quantum computers even in their infancy are more capable of generating valid solutions humans are incapable of.

mikhailfranco 1y ago

Terence Tao briefly discusses this problem in the first chapter of his talk with Lex Fridman: Terence Tao: Hardest Problems in Mathematics, Physics & the Future of AI | Lex Fridman Podcast #472 https://www.youtube.com/watch?v=HUkBz-cdB-k https://www.youtube.com/watch?v=HUkBz-cdB-k