In an article recently published in Physical Review Research, we show how deep learning can help solve the fundamental equations of quantum mechanics for real-world systems. Not only is this an important fundamental scientific question, but it also could lead to practical uses in the future, allowing researchers to prototype new materials and chemical syntheses in silico before trying to make them in the lab. Today we are also releasing the code from this study so that the computational physics and chemistry communities can build on our work and apply it to a wide range of problems. We’ve developed a new neural network architecture, the Fermionic Neural Network or FermiNet, which is well-suited to modeling the quantum state of large collections of electrons, the fundamental building blocks of chemical bonds. The FermiNet was the first demonstration of deep learning for computing the energy of atoms and molecules from first principles that was accurate enough to be useful, and it remains the most accurate neural network method to date. We hope the tools and ideas developed in our AI research at DeepMind can help solve fundamental problems in the natural sciences, and the FermiNet joins our work on protein folding, glassy dynamics, lattice quantum chromodynamics and many other projects in bringing that vision to life.
A Brief History of Quantum Mechanics
Mention “quantum mechanics” and you are more likely to inspire confusion than anything else. The phrase conjures up images of Schrödinger’s cat, which can paradoxically be both alive and dead, and fundamental particles that are also, somehow, waves. In quantum systems, a particle such as an electron doesn’t have an exact location, as it would in a classical description. Instead, its position is described by a probability cloud - it’s smeared out in all places it’s allowed to be. This counterintuitive state of affairs led Richard Feynman to declare: “If you think you understand quantum mechanics, you don’t understand quantum mechanics.” Despite this spooky weirdness, the meat of the theory can be reduced down to just a few straightforward equations. The most famous of these, the Schrödinger equation, describes the behavior of particles at the quantum scale in the same way that Newton’s laws describe the behavior of objects at our more familiar human scale. While the interpretation of this equation can cause endless head-scratching, the math is much easier to work with, leading to the common exhortation from professors to “shut up and calculate” when pressed with thorny philosophical questions from students.
These equations are sufficient to describe the behavior of all the familiar matter we see around us at the level of atoms and nuclei. Their counterintuitive nature leads to all sorts of exotic phenomena: superconductors, superfluids, lasers and semiconductors are only possible because of quantum effects. But even the humble covalent bond - the basic building block of chemistry - is a consequence of the quantum interactions of electrons. Once these rules were worked out in the 1920s, scientists realised that, for the first time, they had a detailed theory of how chemistry works. In principle, they could just set up these equations for different molecules, solve for the energy of the system, and figure out which molecules were stable and which reactions would happen spontaneously. But when they sat down to actually calculate the solutions to these equations, they found that they could do it exactly for the simplest atom (hydrogen) and virtually nothing else. Everything else was too complicated.
The heady optimism of those days was nicely summed up by Paul Dirac:
“The underlying physical laws necessary for the mathematical theory of a large part of physics and the whole of chemistry are thus completely known, and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble. It therefore becomes desirable that approximate practical methods of applying quantum mechanics should be developed”
-Paul Dirac, 1929
Many took up Dirac’s charge, and soon physicists built mathematical techniques that could approximate the qualitative behavior of molecular bonds and other chemical phenomena. These methods started from an approximate description of how electrons behave that may be familiar from introductory chemistry. In this description, each electron is assigned to a particular orbital, which gives the probability of a single electron being found at any point near an atomic nucleus. The shape of each orbital then depends on the average shape of all other orbitals. As this “mean field” description treats each electron as being assigned to just one orbital, it is a very incomplete picture of how electrons actually behave. Nevertheless, it is enough to estimate the total energy of a molecule with only about 0.5% error.
