When water freezes, it changes from a liquid phase to a solid phase, causing a drastic change in properties such as density and volume. Phase transitions in water are so common that most of us probably don't even think about them, but phase transitions in new 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 transitions between them. But how to quantify phase changes in an unknown system often remains 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 capable of automatically drawing phase diagrams for new physical systems.
Their physics-based machine learning approach is more effective than laborious manual techniques that rely on theoretical expertise. Importantly, because their approach relies on generative models, it does not require huge labeled training datasets used in other machine learning techniques.
Such a framework could help scientists study the thermodynamic properties of new materials or detect entanglement in quantum systems, for example. Ultimately, this technique could allow scientists to independently discover unknown phases of matter.
“If you had a new system with completely unknown properties, how would you choose which observable quantity to study? The hope, at least with data-driven tools, is that you can analyze large new systems in an automated way, which will tell you important changes in the system. This could be a tool in the process of automated scientific discovery of new exotic phase properties,” says Frank Schäfer, postdoctoral fellow in the Julia Lab of the Computer Science and Artificial Intelligence Laboratory (CSAIL) and co-author of a paper on this approach.
Schäfer is joined by first author Julian Arnold, a graduate student at the University of Basel; Alan Edelman, professor of applied mathematics in the Department of Mathematics and head of the Julia Lab; and lead author Christoph Bruder, professor in the Department of Physics at the University of Basel. The research is published today In Physical examination letters.
Detecting phase transitions using AI
Although the transition from water to ice may be one of the most obvious examples of a phase change, more exotic phase changes, such as when a material goes from being a normal conductor to becoming a superconductor, are of interest. urge the scientists.
These transitions can be detected by identifying a “control parameter,” a quantity that is large and likely to change. For example, 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 crystal lattice versus those remaining in a disordered state.
In the past, researchers relied on physics expertise to manually construct phase diagrams, relying on theoretical understanding to know which order parameters were important. Not only is this tedious for complex systems, and perhaps impossible for unknown systems with new behaviors, but it also introduces human biases into the solution.
More recently, researchers have begun to use machine learning to create discriminative classifiers that can solve this problem by learning to classify a measurement statistic as coming from a particular phase of the physical system, similar to how such models do. classify an image as a cat or a dog.
MIT researchers have demonstrated how generative models can be used to solve this classification task in a much more efficient and physics-based manner.
THE Julia programming languagea popular language for scientific computing that is also used in MIT's introductory linear algebra courses, offers many tools that make it invaluable for building such generative models, Schäfer adds.
Generative models, like those underlying ChatGPT and Dall-E, typically work by estimating the probability distribution of some data, which they use to generate new data points that match the distribution (like new images of cats similar to existing cat images). .
However, when simulations of a physical system using proven scientific techniques are available, researchers obtain a model of its probability distribution for free. This distribution describes the measurement statistics of the physical system.
A more informed model
The MIT team believes that this probability distribution also defines a generative model on which a classifier can be built. They integrate the generative model with standard statistical formulas to directly construct a classifier instead of learning it from samples, as was done with discriminative approaches.
“It's a really good way to incorporate something you know about your physical system deep into your machine learning program. This goes way beyond simple feature engineering on your data samples or simple inductive biases,” explains Schäfer.
This generative classifier can determine which phase the system is in based on a given parameter, such as temperature or pressure. And because researchers directly approximate the probability distributions underlying measurements of the physical system, the classifier has knowledge of the system.
This allows their method to work better than other machine learning techniques. And because it can operate automatically without requiring extensive training, their approach significantly improves the computational efficiency of identifying phase transitions.
Ultimately, in the same way that one might ask ChatGPT to solve a math problem, researchers can ask the generative classifier questions such as “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 to determine whether A or B theory 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 adjusted so that the chatbot gives the best results.
In the future, the researchers also want to explore theoretical guarantees regarding the number of measurements they would need to effectively detect phase transitions and estimate the amount of calculations needed.
This work was funded in part by the Swiss National Science Foundation, the MIT-Switzerland Lockheed Martin Seed Fund, and the MIT International Science and Technology Initiatives.