The time required to calculate the quantum behavior of 100 electrons using brute force exceeds the age of the universe.
A single drug molecule can have thousands of electrons; battery materials have even more. Simulating them is a fundamental requirement for developing drugs, batteries, and chips.
On August 24, the team led by Anima Anandkumar at Caltech published a paper that reduced the complexity of such computations from cubic to nearly linear using an AI model.
https://x.com/AnimaAnandkumar/status/2092031815448248594
The results are truly impressive: a metal defect simulation involving 82,500 electrons was completed on a single GPU, whereas similar calculations in 2019 required approximately 7,800 GPUs.
A bottleneck that has persisted for 60 years
The most commonly used computational method in quantum chemistry is density functional theory (DFT), a Nobel Prize-winning theory essential for drug screening, catalyst design, and battery material development.
The problem is that it's too slow: as the system grows larger, the computational load increases cubically—when the number of electrons increases tenfold, the computational load increases by a factor of 1,000.
For 60 years, physicists have been searching for ways to speed it up, but have made no substantial breakthroughs.
The AI has tried two approaches.
One approach is to have the model directly predict the final result in a single step.
Performs well within the training distribution but has very poor extrapolation ability: once the numerator exceeds anything seen in the training set, the error spirals out of control.
Experimental results show that when extrapolating from small molecules to drug-like molecules, the error of direct prediction models increases from less than 1% to approximately 10%, reaching up to 41%.
Another approach follows the traditional path of physicists, having AI learn an inverse mapping.
This approach is mathematically unstable; in the paper's control experiments, all calculations diverged after just a few iterations, resulting in complete failure.
Iterate like a chain of thought rather than guessing the answer in one step.
This paper has taken a different direction.
The DFT calculation process is an iterative procedure: in each cycle, given a set of input conditions, the electron density is computed and then used to update the input conditions, repeating until the results converge.
Traditional methods get stuck because each iteration requires a computationally intensive step that is cubic in complexity.
The Anandkumar team’s approach is to replace this step with AI.
Train a Fourier Neural Operator (FNO) to learn the forward mapping from input conditions to the corresponding electron density, reducing computational complexity from O(N³) to O(N log N).
Then reinsert the model into the original iterative loop and proceed with the remaining steps as usual.
https://x.com/AnimaAnandkumar/status/2090125110309204371
You can think of it this way: a direct prediction model is like asking an LLM to give the final answer to a difficult problem in one step—it works fine for simple questions, but tends to make mistakes on harder ones.
The Kohn-Sham FNO is like giving the model a chain of thought during inference, enabling step-by-step reasoning where each step can self-correct; if an error occurs, subsequent iterations will bring it back on track.
This design also has an advantage that direct prediction models lack: a safety valve.
If the model is pushed beyond its capabilities, the iterations will diverge, and researchers immediately know the results are unreliable.
The first attempt at the magnesium dislocation experiment in the paper confirmed this: using a general-purpose pretrained model directly caused all computations to immediately diverge—divergence itself was an alert.
The direct prediction model provides an answer, but you cannot determine whether it is right or wrong.
The training data used only 8,504 structures, with a single model handling both molecules and solid materials, covering the first five rows of the periodic table.
This is made possible by a domain-invariant FNO variant designed by the team: a single set of learned filters is shared across systems of different sizes, allowing the same model to handle both small molecules and bulk crystals.
When extrapolating to drug-sized molecules not seen in the training set, the density error of Kohn-Sham FNO is 2.23%, compared to 9.97% for the direct prediction model.
The larger the molecule, the more pronounced the difference: at 45 heavy atoms, the direct prediction error spikes to 41%, while Kohn-Sham FNO remains at just 4%.
1 GPU, 80,000 electrons
The team conducted large-scale validation on the dislocation structure of magnesium.
In 2019, a study nominated for the ACM Gordon Bell Award performed full DFT calculations on 6,164 magnesium atoms, utilizing approximately 7,800 NVIDIA V100 GPUs on the Summit supercomputer.
The latest Kohn-Sham FNO achieved full convergence for a system of 8,250 atoms and 82,500 valence electrons on a single NVIDIA B300 GPU.
The measured scaling exponent is 1.03 (close to perfect linearity), compared to 3.37 for traditional methods (cubic).
One B300 is not a direct hardware equivalent to 7,800 V100s, but the scaling exponent remains unaffected by hardware: one scales nearly linearly, the other cubically—the larger the system, the more irreversible the gap becomes.
On the same day the paper was published, Anandkumar announced the founding of the AI physical simulation company Accelerated Understanding, which was subsequently reported by Reuters.
https://www.reuters.com/business/ai-founders-who-walked-away-bezos-backed-prometheus-model-universe-2026-08-25/
According to her post on X, the company’s AI models simulate physical phenomena in 4D space with a context length exceeding 5 trillion.
https://x.com/AnimaAnandkumar/status/2092236528898675014
Currently, the Kohn-Sham FNO has only learned one step in the computational process; a further post-processing step is required to complete the energy calculation.
But the path is clear: AI does not replace physics, but rather the most costly step in physical computation—the repetitive calculations.
The team's next step is to complete the remaining components, at which point post-processing will also be eliminated. The future looks promising.
Photo of the founding team
Reference: https://tensorlab.cms.caltech.edu/users/anima/ks_fno.html
This article is from the WeChat public account "New Intelligence Yuan," author: ASI Revelation; editor: Marco