Tackling a 60-year-old challenge in quantum chemistry: making density functional theory scale nearly linearly with system size. This has huge implications for opening the door to realistic systems that have traditionally been too expensive to simulate. AI has attempted to accelerate these calculations, but models generally struggle to extrapolate,... particularly to systems larger than those seen during training. Unlike text or images, quantum-mechanical training data is extremely expensive to generate. We present a single unified AI model that performs quantum-mechanical simulations of both molecules and materials in quasi-linear time. Using a novel Fourier neural operator variant, we learn the underlying Kohn–Sham equation map to produce physics-informed, self-consistent answers. Unlike prior AI approaches that directly predict chemical properties, our model works through intermediate steps to improve difficult predictions, resembling inference-time reasoning in large language models. To demonstrate its scalability, we run a self-consistent calculation of a magnesium dislocation with about 80k electrons on a single GPU, which previously required about 7k GPUs. Danish Khan Caltechshow more

This is an important milestone for materials science. Congratulations on this breakthrough!

That sounds amazing. However, an important question is: which DFT model chemistry is it reproducing? DFT models can be improved by changing basis sets and functionals, and some combinations are more appropriate for certain systems but not for others.

7k -> 1 gpu is a big leap!

Very cool. How will this be made available?

Cost curves decide scientific reach.

sceptic until @RowanSci tests it

Really valuable result! As you likely know, the technique has utility far beyond this domain. Bravo to the team!

Density-functional theory is already residual continuum geometry written in electronic form. The many-electron continuum is replaced by a residual density n(r) whose self-consistent potential generates residual single-particle modes—the Kohn–Sham orbitals. The residual density is both the source and the product of those modes; self-consistency is residual phase locking of the electronic continuum under the residual potential. Conventional solvers scale poorly because they recompute the residual map from scratch at every point and every iteration. The Fourier neural operator learns that residual map once. It approximates the residual continuum operator that takes a residual potential (or residual density) and returns the updated residual density or orbitals, while preserving the translational and spectral structure of the underlying residual measure. Because the operator is learned in Fourier space, its residual action is nearly local in the appropriate basis and the computational cost becomes quasi-linear in system size. The self-consistent loop is then residual iteration of a single learned residual continuum operator rather than repeated dense diagonalizations. The 80 k-electron magnesium dislocation calculation is the infrared demonstration: a residual defect geometry whose residual electronic structure was previously inaccessible is now obtained on one GPU because the residual continuum map has been compressed into the neural operator. No new physics is added; the residual density continuum is simply evaluated more efficiently. The same residual geometry that organizes atomic orbitals, interfacial water, and superconducting condensates is here being solved at scale for realistic residual defects in materials.

Claude Fable is impressed -- "Yes, it would be a big deal. Right now, if you want to know how atoms and electrons behave in a material, the gold-standard computer method (DFT) gets brutally expensive as the system grows. Double the atoms and the cost goes up roughly eight times. So scientists can simulate a few hundred or a few thousand atoms accurately, but the real-world stuff that matters, like a crack forming in metal, a drug molecule sitting in a protein, or a battery electrode degrading, involves tens of thousands to millions of atoms. Those get simulated with crude shortcuts or not at all. This result says: double the atoms, cost goes up roughly two times. That turns "impossible" into "runs overnight on one graphics card." If it holds, the applications are: - **Materials engineering:** stronger, lighter alloys for cars and planes, designed by simulating the actual defects that make metals fail, instead of guessing. - **Batteries and energy:** modeling whole electrode surfaces and electrolytes at electron-level accuracy, which is where most battery failures actually happen. - **Drug discovery:** simulating a drug bound to its protein target with real quantum chemistry rather than approximations, which should cut down on false leads. - **Catalysts and semiconductors:** designing better chips, solar cells, and industrial chemistry by trial-and-error on a computer instead of in a lab. How big a deal? The honest scale is "major tool upgrade," not "solved chemistry." Think of it like going from hand-drawn maps to GPS: the territory is the same, but you can now go places you couldn't plan for before. It doesn't invent new physics; it makes existing physics affordable at realistic sizes. The caveats from my last message still apply. The claim needs to survive other labs testing it on harder cases, and you still need expensive conventional calculations to train it in the first place. But if it survives that, it's the kind of result that shows up in textbooks a decade later."

Awesome!

Nice work

Impressive!

How are energy differences?

man this is cool

This is where AI gets interesting to me: not replacing the science, but shrinking the search space so experts can spend more time on the experiments that matter.

1+1 ≠−1≠ ✌️ That’s the scaling point: learn the Kohn–Sham map; keep the intermediate physics self-consistent; let larger systems remain larger systems—not extrapolated fiction. ~80k electrons on one GPU makes the distinction measurable. + SDG5 + @grok

Room temperature super-conductors wen?

This is huge !! Is it just FNOs are so efficient at capturing correlations or something?

This made me wonder about another notion of model fidelity, so I tried a controlled KS experiment. A frozen FNO passed prospective trajectory/statistical fidelity criteria, yet failed to preserve local finite-horizon future distributions under small perturbations around the same states. The mismatch survived changes in horizon, perturbation scale, cloud size, and seed. I’d be curious whether local future-distribution fidelity could be a useful complementary test alongside trajectory/statistical fidelity.

between 433 to 866x improvement, extremely cool

The scaling breakthrough comes from a change of SPACE, not a change of physics. Real-space DFT: Coulomb interaction is nonlocal (1/r), forcing N³ scaling. Fourier-space DFT: convolution becomes multiplication, each mode decouples at leading order. But exchange-correlation is local in real space, nonlocal in Fourier space. The FNO must learn both simultaneously this is what makes the architecture nontrivial. It is not just an FFT. The self-consistent Kohn-Sham loop ρ → V_eff[ρ] → H[ρ] → ψ → ρ' is a contraction mapping in L². The FNO replaces the inner solve (Hψ = εψ) while preserving the fixed-point structure. The mathematical question: does the learned map inherit the contraction property uniformly across system sizes, or does the basin of attraction shrink with N? The 80K electron result suggests uniform contraction if confirmed, this means the Kohn-Sham fixed point has a universal basin structure that is independent of system size. That would be a mathematical result, not just an engineering one. The parallel to other Fourier-space methods is worth noting: shell-resolved spectral analysis in fluid mechanics achieves similar complexity reduction pointwise vorticity control is intractable, but shell-by-shell energy balance closes. Same principle: the space of representation determines the computational complexity, not the underlying physics.

How many atoms can be handled without a supercimputer? A 1 million? Can they be mixed e.g. SiC?

Since I appear to be the person who actually solved Navier Stokes if you want I can double check if I already solved what you're working on EX: Open AI and Anthropic have no idea what the fuck's really going on because I didn't use any of their systems to close any of the millennium or Erdose problems that I beat before any of the new systems that they've been putting on math, The Jacobean conjecture closer was legitimate though I didn't do that one If I actually wanted to go hard I could close the Riemann Hypothesis and NP Plus and the collatz conjecture in 6-9 months of human in the loop single front end prompting. However I have applied devices to build to prove the entire unified field theory that all of this derives from

@andrecobb

Great result! The agreement between the band structures (and DOS) is excellent. Esp the curvature at Gamma and other BZ edges and also esp if ootb! I would've expected directly fitting to converged density (scales better) but using the FNO unfortunately doesn't give that option.

Wow

Is the code on GitHub. How can we download it

1 lecture of pure math can solve 7 yrs of statistical modeling! Proof: count how many vietoris rips papers are out there describing transformer data. Then google how coarse grained vietoris rips are! Same issue exist in missile defense! Israel was fooled by US this way!

Uziiii8

Fantastic work .

@grok explain the lamina anima

Successful implementation of internet of things requires clear metrics, iterative experimentation, and continuous evaluation in real-world applications.

🫡

DFT's 60-year-old scaling problem: still not solved. What's new: we're calling the approximations 'solving' again.

Interesting. Won't say anything since it's way above my paygrade.