Artificial Intelligence Solves Schrödinger’s Equation, a Fundamental Problem in Quantum Chemistry

Quantum Physics Concept

Scientists at Freie Universität Berlin develop a deep learning method to solve a fundamental problem in quantum chemistry.

A team of scientists at Freie Universität Berlin has developed an artificial intelligence (AI) method for calculating the ground state of the Schrödinger equation in quantum chemistry. The goal of quantum chemistry is to predict chemical and physical properties of molecules based solely on the arrangement of their atoms in space, avoiding the need for resource-intensive and time-consuming laboratory experiments. In principle, this can be achieved by solving the Schrödinger equation, but in practice this is extremely difficult.

Up to now, it has been impossible to find an exact solution for arbitrary molecules that can be efficiently computed. But the team at Freie Universität has developed a deep learning method that can achieve an unprecedented combination of accuracy and computational efficiency. AI has transformed many technological and scientific areas, from computer vision to materials science. “We believe that our approach may significantly impact the future of quantum chemistry,” says Professor Frank Noé, who led the team effort. The results were published in the reputed journal Nature Chemistry.

Central to both quantum chemistry and the Schrödinger equation is the wave function – a mathematical object that completely specifies the behavior of the electrons in a molecule. The wave function is a high-dimensional entity, and it is therefore extremely difficult to capture all the nuances that encode how the individual electrons affect each other. Many methods of quantum chemistry in fact give up on expressing the wave function altogether, instead attempting only to determine the energy of a given molecule. This however requires approximations to be made, limiting the prediction quality of such methods.

Other methods represent the wave function with the use of an immense number of simple mathematical building blocks, but such methods are so complex that they are impossible to put into practice for more than a mere handful of atoms. “Escaping the usual trade-off between accuracy and computational cost is the highest achievement in quantum chemistry,” explains Dr. Jan Hermann of Freie Universität Berlin, who designed the key features of the method in the study. “As yet, the most popular such outlier is the extremely cost-effective density functional theory. We believe that deep “Quantum Monte Carlo,” the approach we are proposing, could be equally, if not more successful. It offers unprecedented accuracy at a still acceptable computational cost.”

The deep neural network designed by Professor Noé’s team is a new way of representing the wave functions of electrons. “Instead of the standard approach of composing the wave function from relatively simple mathematical components, we designed an artificial neural network capable of learning the complex patterns of how electrons are located around the nuclei,” Noé explains. “One peculiar feature of electronic wave functions is their antisymmetry. When two electrons are exchanged, the wave function must change its sign. We had to build this property into the neural network architecture for the approach to work,” adds Hermann. This feature, known as “Pauli’s exclusion principle,” is why the authors called their method “PauliNet.” 

Besides the Pauli exclusion principle, electronic wave functions also have other fundamental physical properties, and much of the innovative success of PauliNet is that it integrates these properties into the deep neural network, rather than letting deep learning figure them out by just observing the data. “Building the fundamental physics into the AI is essential for its ability to make meaningful predictions in the field,” says Noé. “This is really where scientists can make a substantial contribution to AI, and exactly what my group is focused on.”

There are still many challenges to overcome before Hermann and Noé’s method is ready for industrial application. “This is still fundamental research,” the authors agree, “but it is a fresh approach to an age-old problem in the molecular and material sciences, and we are excited about the possibilities it opens up.”

Reference: “Deep-neural-network solution of the electronic Schrödinger equation” by Jan Hermann, Zeno Schätzle and Frank Noé, 23 September 2020, Nature Chemistry.
DOI: 10.1038/s41557-020-0544-y

47 Comments on "Artificial Intelligence Solves Schrödinger’s Equation, a Fundamental Problem in Quantum Chemistry"

  1. Daniel W Bright | January 2, 2021 at 10:22 pm | Reply

    This should get the Nobel prize

  2. How do you reward the AI unit for a job well done? Some good high-frequency super-modulated electicity? Working on the wave equation. Existence defined over time. Wave Mechanics …. its more difficult than your basic algebra. I wonder if one day, we will be able to have 1 on 1 talks with an AI unit? I wonder what they would say about space aliens?

  3. george avraamid | January 3, 2021 at 2:51 am | Reply

    Quite a good abstract und summary of the authentic paper published

  4. Robert Jungquist | January 3, 2021 at 5:51 am | Reply

    So is the cat dead or alive?

    • Torbjörn Larsson | January 3, 2021 at 7:31 am | Reply

      Yes. (It is a theoretical superposition of both – in practice a cat is too large and actively chasing balls or climbing into boxes.)

    • It depends on the observer and the cat?

      • In a shell nut.

      • Torbjörn Larsson | January 4, 2021 at 2:36 am | Reply

        This is the general relativistic case already – same laws, different observations – but superpositions adds fragility. A “practical” cat is either or, but when we get to the core of it the size and lifetime of superpositions is a dynamic thing.

        The interest is usually that a “Wiegner’s friend” will see things differently, and people trying to make transfer of properties (such as knowledge) mysterious. But I don’t think they get any further than in the classical case. Quantum physics has more interesting outcomes (e.g. wavefunction collapse, nonlocality, no hidden variables).

    • There is no cat. What, did you think the cat was just going to wait around forever in that damned box? Goedel thinks it may be his cat now….but hes uncertain. Heisenberg claimed it was his cat, but when I asked him to show me proof, he could only show me the cats position, or its velocity. Bohr told everyone we could settle ownership with some dice rolls, but einstein refused.
      …matter of fact, I think the only person with a constant claim was plank, but fermi told him itxd be a miracle if the cat stuck around. Plank grew irate at that, and asked him what that meant. Fermi replied it was less than twenty percent.
      Bohr laughed at everyone, told everyone it could be everyone’s cat, depending on how you looked at it. But that pissed off von Newman so bad he infinitely regressed.

      *shrug* particle physicists. Always arguing over the smallest of things.

  5. Atlantis illusion autor book Imanuel Alex Nowicki

  6. Now you just need AI to invent some more advanced math so we can get off this planet for good. The infintile math we use now just isn’t getting the job done.

  7. The cat is alive in death and dead in life

  8. Where do artificial lemons grow

  9. Wow. Phenomenal. Great work to all of you who worked on the project. God bless you.

  10. Jegarakshagan Gokul | January 3, 2021 at 8:05 am | Reply

    Amazing application of AI in the field of quantum mechanics

  11. It is eerie… seeing “Doctor No” talk about Quantum Monte Carlo and PauliNet. Shades of James Bond!

    • Torbjörn Larsson | January 4, 2021 at 2:53 am | Reply

      Usually film descriptions of science is garbage or at least incomplete (as in popular science series that need to terse). To the point I had never seen a correct description and got shocked yesterday watching Spiderman “Far From Home” and they delivered that.

      I.e. the Marvel world context was bull and the specific technology used was vastly extrapolated or impossible. But the plot MacGuffin prompted a short exchange on how a putative cosmic singularity is problematized by inflation. Which is a current question!

      [By the way, I didn’t appreciate all of the movie’s topics, but it was well scripted and acted.]

      • Ah, he’s really referring to the fact the s ientist in question is doctor noe, not the fact that there is any likeness to a movie trope.

  12. Quinn Laidler | January 3, 2021 at 9:49 am | Reply

    Yay! Brain stuff!

  13. Schridinger.kocka | January 3, 2021 at 10:14 am | Reply

    A v jiném vesmíru je tomu právě naopak.

  14. Title is a bit misleading given the content of the article. We have made a step in the right direction to solving this problem and the results may be promising, but accuracy is still not an exact, analytic solution, so AI has not in fact “solved” the Schrödinger equation.

    • Torbjörn Larsson | January 4, 2021 at 2:28 am | Reply

      As in many equation cases it is impossible to make analytic solutions – the space of those is much smaller than the space of physically meaningful equations (c.f. gravitational problems) – so developing new methods is sometimes the best we can do.

      That said, clickbait title.

      • I concur the way to go and grow is developing a sort of meta- AI system that can resolve the issues of the lower level AI system. Such a super-system would make mince meat of the Boolean Pythagorean triples problem, but give countless PhDs nightmares as to whether their dissertation subject has become passe.

      • … I have some topology issues, and you just look like a person who will be helpful, …

  15. Joseph Liskowsky | January 3, 2021 at 11:04 am | Reply

    This really needs a better edit. You don’t solve the SE the way you prove Fermat’s Last Theorem; the title is misleading. Also, you don’t have a ground state of the SE, you have a ground state of a system, the time evolution of which the SE models. Also, the mentioned neural network isn’t a representation of the electron wave function, it is a program that creates a model of the quantum mechanical behavior of an electron, which represents the wave function. The language here is sloppy and needs a decent edit.

  16. …”Então passa lá em casa, to fazendo vários nada”…

  17. Good job.

  18. Interesting…..

  19. CLICK BAIT BYE | January 3, 2021 at 4:24 pm | Reply

    Click bait.

  20. Village Blacksmith | January 3, 2021 at 6:45 pm | Reply

    If it’s Deep Learning, why did I understand it?

  21. richie vamatta | January 3, 2021 at 6:53 pm | Reply

    please get ai to solve hair loss next

  22. What is the meaning of life?

  23. Cindy sellari | January 4, 2021 at 1:05 am | Reply

    42 🥰

  24. Cindy sellari | January 4, 2021 at 1:07 am | Reply


  25. thats amazing.gonna use this for my college seminar

  26. The probability that an AI will destroy the fabric of the universe before the singularity happens just went up exponentially.

  27. … now I am looking for a example that will solve three pawns of white and black color on 3*3 board with 24 boxes and four colors balls…
    bp bp bp
    * * *
    wp wp wp
    I would draw the table, but it won’t work… or it would

    black pawn
    black pawn
    black pawn

    empty field
    empty field
    empty field

    white field
    white field
    white field

  28. it breaks the line… and white field needs to be exchanged with white pawn…

  29. Next step: a Monte Carlo AI quantum computer simulator! Problem solved.
    Who needs near 0K temperatures when you can just simulate it? 😛
    For AI, higher temperatures just add extra complexity.

  30. argyn kuketayev | January 4, 2021 at 11:09 am | Reply

    I got to figure how to suppress the garbage that is coming from this web site into my news feed. This article is the straw that broke my camel’s back.

  31. Arabinda Pradhan | January 4, 2021 at 10:14 pm | Reply

    Not only quantam chemistry, or quantam physics, or schorodinger equation, all in this Cosmos get to by birth, or as being, is solely for wave functions. Ocean, must have originated from ‘one’ wave, but functions (wave-jumps) are many. This oneness of wave possessed the universe also. Its function means wave-jump, not that wave-collapse. I mean collapse is hypothetical big crunch. Quantam physics is sailing journey easier with particles, but there is extremely difficult to capture wave jumps. Spin or angular momentum of particles, likely electron and other -ve charged particles is therefore represents as wave jumps. In fact, physicists give up on experimenting the wave function altogether. Instead, they should have attempting to determine the energy factor of this wave, the one wave. But how? I have an hypothetical view in this regard, not by light but by sound. Because only sound can explain wave. Any electromagnetic phenomenon without sound is impossible. In the form of 4-dimensional (a+i+u)m that is OM or AIUM is represented as energy. And energy always depends upon functional waves. But why a-i-u? Surprisingly, One cannot pronounce any word or consonant without these vowels.

  32. wow….i understand nothing

  33. Edward Thorndile | January 10, 2021 at 1:53 pm | Reply

    this article is truly amazing. by reading and discussing it, I can keep my grade up.

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