When water freezes, it transitions from a liquid phase to a solid phase, resulting in a drastic change in properties like density and volume. Phase transitions in water are so common most of us probably don’t even think about them, but phase transitions in novel materials or complex physical systems are an important area of study.

To fully understand these systems, scientists must be able to recognize phases and detect the transitions between. But how to quantify phase changes in an unknown system is often unclear, especially when data are scarce.

Researchers from MIT and the University of Basel in Switzerland applied generative artificial intelligence models to this problem, developing a new machine-learning framework that can automatically map out phase diagrams for novel physical systems.

Their physics-informed machine-learning approach is more efficient than laborious, manual techniques which rely on theoretical expertise. Importantly, because their approach leverages generative models, it does not require huge, labeled training datasets used in other machine-learning techniques.

Such a framework could help scientists investigate the thermodynamic properties of novel materials or detect entanglement in quantum systems, for instance. Ultimately, this technique could make it possible for scientists to discover unknown phases of matter autonomously.

“If you have a new system with fully unknown properties, how would you choose which observable quantity to study? The hope, at least with data-driven tools, is that you could scan large new systems in an automated way, and it will point you to important changes in the system. This might be a tool in the pipeline of automated scientific discovery of new, exotic properties of phases,” says Frank Schäfer, a postdoc in the Julia Lab in the Computer Science and Artificial Intelligence Laboratory (CSAIL) and co-author of a paper on this approach.

Joining Schäfer on the paper are first author Julian Arnold, a graduate student at the University of Basel; Alan Edelman, applied mathematics professor in the Department of Mathematics and leader of the Julia Lab; and senior author Christoph Bruder, professor in the Department of Physics at the University of Basel. The research is published today in Physical Review Letters.

Detecting phase transitions using AI

While water transitioning to ice might be among the most obvious examples of a phase change, more exotic phase changes, like when a material transitions from being a normal conductor to a superconductor, are of keen interest to scientists.

These transitions can be detected by identifying an “order parameter,” a quantity that is important and expected to change. For instance, water freezes and transitions to a solid phase (ice) when its temperature drops below 0 degrees Celsius. In this case, an appropriate order parameter could be defined in terms of the proportion of water molecules that are part of the crystalline lattice versus those that remain in a disordered state.

In the past, researchers have relied on physics expertise to build phase diagrams manually, drawing on theoretical understanding to know which order parameters are important. Not only is this tedious for complex systems, and perhaps impossible for unknown systems with new behaviors, but it also introduces human bias into the solution.

More recently, researchers have begun using machine learning to build discriminative classifiers that can solve this task by learning to classify a measurement statistic as coming from a particular phase of the physical system, the same way such models classify an image as a cat or dog.

The MIT researchers demonstrated how generative models can be used to solve this classification task much more efficiently, and in a physics-informed manner.

The Julia Programming Language, a popular language for scientific computing that is also used in MIT’s introductory linear algebra classes, offers many tools that make it invaluable for constructing such generative models, Schäfer adds.

Generative models, like those that underlie ChatGPT and Dall-E, typically work by estimating the probability distribution of some data, which they use to generate new data points that fit the distribution (such as new cat images that are similar to existing cat images).

However, when simulations of a physical system using tried-and-true scientific techniques are available, researchers get a model of its probability distribution for free. This distribution describes the measurement statistics of the physical system.

A more knowledgeable model

The MIT team’s insight is that this probability distribution also defines a generative model upon which a classifier can be constructed. They plug the generative model into standard statistical formulas to directly construct a classifier instead of learning it from samples, as was done with discriminative approaches.

“This is a really nice way of incorporating something you know about your physical system deep inside your machine-learning scheme. It goes far beyond just performing feature engineering on your data samples or simple inductive biases,” Schäfer says.

This generative classifier can determine what phase the system is in given some parameter, like temperature or pressure. And because the researchers directly approximate the probability distributions underlying measurements from the physical system, the classifier has system knowledge.

This enables their method to perform better than other machine-learning techniques. And because it can work automatically without the need for extensive training, their approach significantly enhances the computational efficiency of identifying phase transitions.

At the end of the day, similar to how one might ask ChatGPT to solve a math problem, the researchers can ask the generative classifier questions like “does this sample belong to phase I or phase II?” or “was this sample generated at high temperature or low temperature?”

Scientists could also use this approach to solve different binary classification tasks in physical systems, possibly to detect entanglement in quantum systems (Is the state entangled or not?) or determine whether theory A or B is best suited to solve a particular problem. They could also use this approach to better understand and improve large language models like ChatGPT by identifying how certain parameters should be tuned so the chatbot gives the best outputs.

In the future, the researchers also want to study theoretical guarantees regarding how many measurements they would need to effectively detect phase transitions and estimate the amount of computation that would require.

This work was funded, in part, by the Swiss National Science Foundation, the MIT-Switzerland Lockheed Martin Seed Fund, and MIT International Science and Technology Initiatives.