In the simulation of how water freezes, artificial intelligence breaks the ice

A Princeton University team has accurately simulated the first steps of ice formation by applying artificial intelligence (AI) to solve equations that govern the quantum behavior of individual atoms and molecules.

The resulting simulation describes, with quantum precision, how water molecules transform into solid ice. This level of accuracy, once thought unattainable due to the computing power required, became possible when researchers incorporated deep neural networks, a form of artificial intelligence, into their methods. The study was published in the journal Proceedings of the National Academy of Sciences.

“In a way, this is like a dream come true,” said Roberto Car, Princeton’s Ralph W. *31 Dornte Professor of Chemistry, who co-pioneered the approach to simulating molecular behavior based on the underlying quantum laws more than 35 years ago. “Our hope at the time was that we could eventually study systems like this, but that wasn’t possible without further conceptual development, and that development came via a completely different field, that of artificial intelligence and data science.”

The ability to model the initial steps in water freezing, a process known as ice nucleation, could improve the accuracy of weather and climate modeling, as well as other processing operations such as the flash freezing of food.

The new approach allows researchers to track the activity of hundreds of thousands of atoms over time periods thousands of times longer, albeit still fractions of a second, than early studies.

Car co-invented the approach of using underlying quantum mechanical laws to predict the physical motions of atoms and molecules. Quantum mechanical laws dictate how atoms bind together to form molecules and how molecules bind together to form everyday objects.

Car and Michele Parrinello, a physicist now working at the Istituto Italiano di Tecnologia in Italy, published their approach, known as “ab initio” (Latin for “from the beginning”) to molecular dynamics, in a seminal paper in 1985.

But quantum mechanical calculations are complex and require enormous computing power. In the 1980s, computers could only simulate a hundred atoms over periods of a few trillionths of a second. Subsequent advances in computing technology and the advent of modern supercomputers increased the number of atoms and the time span of the simulation, but the result fell far short of the number of atoms needed to observe complex processes such as ice nucleation.

AI offered an attractive potential solution. Researchers train a neural network, named for its resemblance to how the human brain works, to detect a comparatively small set of selected quantum calculations. Once trained, the neural network can calculate forces between atoms that it has never seen before with quantum-mechanical accuracy. This “machine learning” approach is already being used in everyday applications such as speech recognition and self-driving cars.

In the case of applying AI to molecular modeling, a major contribution came in 2018 when Princeton graduate student Linfeng Zhang, in collaboration with Car and Princeton Professor of Mathematics Weinan E., found a way to extend deep neural networks to the modeling of quantum mechanical interatomic apply forces. Zhang, who received his Ph.D. in 2020 and is now a research fellow at the Beijing Institute of Big Data Research, which calls the approach Deep Potential Molecular Dynamics.

In the current publication, Car and postdoc Pablo Piaggi, along with colleagues, applied these techniques to the challenge of simulating ice nucleation. Using molecular dynamics in the deep potential, they were able to run simulations of up to 300,000 atoms with significantly less computing power and over much longer periods of time than previously possible. They ran the simulations on Summit, one of the world’s fastest supercomputers, located at Oak Ridge National Laboratory.

This work offers one of the best studies of ice nucleation, said Pablo Debenedetti, Princeton’s dean of research and professor of engineering and applied sciences of the Class of 1950 and co-author of the new study.

“Ice nucleation is one of the largest unknowns in weather forecast models,” said Debenedetti. “This is a very significant advance because we see very good agreement with experiments. We were able to simulate very large systems, which was previously unthinkable for quantum calculations.”

Currently, climate models obtain estimates of how quickly ice nuclei form mainly from observations made in laboratory experiments, but these correlations are descriptive, not predictive, and apply to a limited range of experimental conditions. In contrast, molecular simulations of the type performed in this study can generate simulations that predict future situations and can estimate ice formation under extreme temperature and pressure conditions, such as on other planets.

“The deep potential methodology used in our study will help realize the promise of ab initio molecular dynamics to make valuable predictions about complex phenomena such as chemical reactions and the design of new materials,” said Athanassios Panagiotopoulos, Susan Dod Brown -Professor of Chemistry and Bioengineering and co-author of the study.

“The fact that we’re studying very complex phenomena using the fundamental laws of nature is very exciting to me,” said Piaggi, the study’s first author and postdoctoral researcher in chemistry at Princeton. Piaggi earned his Ph.D. Collaborated with Parrinello to develop new techniques to study rare events such as nucleation using computer simulations. Rare events take place over timescales longer than simulation times that even AI can afford, and special techniques are required to speed them up.

Jack Weis, a graduate student in chemical and biological engineering, helped increase the probability of observing nucleation by “seeding” tiny ice crystals into the simulation. “The goal of seeding is to increase the likelihood of water forming ice crystals during the simulation so that we can measure the nucleation rate,” said Weis, who is advised by Debenedetti and Panagiotopoulos.

Water molecules consist of two hydrogen atoms and one oxygen atom. The electrons around each atom determine how atoms can bond together to form molecules.

“We start with the equation that describes how electrons behave,” Piaggi said. “Electrons determine how atoms interact, how they form chemical bonds, and virtually all chemistry.”

The atoms can exist in literally millions of different arrangements, said Car, who is director of the Chemistry in Solution and Interfaces Center, which is funded by the US Department of Energy Office of Science and includes regional universities.

“The wonderful thing is that, based on some physical principles, the machine is able to extrapolate what happens in a relatively small number of configurations of a small collection of atoms to the myriad configurations of a much larger system,” said Car.

Although AI approaches have been available for a number of years, researchers have been cautious about applying them to computations of physical systems, Piaggi said. “When machine learning algorithms became popular, a large part of the scientific community was skeptical because these algorithms are a black box. Machine learning algorithms don’t know anything about physics, so why should we use them?”

In recent years, however, that attitude has changed significantly, Piaggi said, not only because the algorithms work, but also because researchers are using their knowledge of physics to inform the machine learning models.

It is gratifying for Car to see the work begun three decades ago bearing fruit. “The development came about something that was being developed in another field, that of data science and applied mathematics,” said Car. “This kind of mutual interaction between different areas is very important.”

The study “Homogeneous ice nucleation in an ab initio machine learning model of water” by Pablo M. Piaggi, Jack Weis, Athanassios Z. Panagiotopoulos, Pablo G. Debenedetti and Roberto Car was published in the journal Proceedings of the National Academy of Sciences in the week of 08/08/2022.