When water freezes, it changes from a liquid phase to a solid phase, which causes 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 recent materials or complicated physical systems are an significant area of research.
To fully understand these systems, scientists must be able to recognize the phases and detect transitions between them. However, how to quantify phase changes in an unknown system is often unclear, especially when little data is available.
Researchers from MIT and the University of Basel in Switzerland have applied generative artificial intelligence models to this problem, developing a recent machine learning platform that can automatically map phase diagrams for novel physical systems.
Their physics-based machine learning approach is more effective than labor-intensive, manual techniques that rely on theoretical knowledge. Importantly, because their approach uses generative models, it does not require the huge, labeled training datasets used in other machine learning techniques.
Such a framework could lend a hand scientists, for example, study the thermodynamic properties of recent materials or detect entanglement in quantum systems. Ultimately, this technique could enable scientists to discover unknown phases of matter on their own.
“If you had a new system with completely unknown properties, how would you choose the observable quantity to study? The hope, at least with data-driven tools, is that you can scan large new systems in an automated way and it will point you to important changes in the system. This could be a tool in the making for the automated discovery of new, exotic phase properties,” says Frank Schäfer, a postdoc at the Julia Lab at the Computer Science and Artificial Intelligence Laboratory (CSAIL) and co-author of a paper on this approach.
Schäfer was joined in writing this work by first author Julian Arnold, a graduate of the University of Basel; Alan Edelman, professor of applied mathematics in the Department of Mathematics and director of the Julia Lab; and senior author Christoph Bruder, professor at the Department of Physics at the University of Basel. The research is there published today IN
Phase transition detection using artificial intelligence
While turning water into ice may be one of the most obvious examples of a phase change, scientists enjoy more exotic phase changes, such as a material going from a regular conductor to a superconductor.
These transitions can be detected by identifying the “order parameter”, i.e. the quantity that is significant and expected to change. For example, water freezes and turns into a solid phase (ice) when its temperature drops below 0 degrees Celsius. In this case, the appropriate order parameter can be defined in terms of the proportion of water molecules that are part of the crystal lattice relative to those that remain in a disordered state.
In the past, researchers relied on physical knowledge to manually create phase diagrams, relying on theoretical knowledge to know which order parameters were significant. Not only is this burdensome for complicated systems and perhaps impossible for unfamiliar systems with novel behaviors, but it also introduces human biases into the solution.
Recently, researchers have begun to utilize machine learning to create discriminative classifiers that can solve this task by learning to classify a measurement statistic as coming from a specific phase of a physical system, in the same way that such models classify an image as a cat or a dog.
MIT researchers have shown how generative models can be used to solve this classification task much more effectively in a physics-based way.
The Julia programming languagethe popular scientific computing language, which is also used in introductory linear algebra classes at MIT, offers many tools that make it invaluable for constructing such generative models, Schäfer adds.
Generative models, such as those underlying ChatGPT and Dall-E, typically work by estimating the probability distribution of some data, which they utilize to generate recent data points that fit the distribution (such as recent cat photos similar to existing cat images). .
However, if simulations of a physical system using proven scientific techniques are available, researchers receive a model of its probability distribution for free. This distribution describes the measurement statistics of a physical system.
A more competent model
The MIT team noted that this probability distribution also defines a generative model from which a classifier can be built. They plug the generative model into standard statistical formulas to directly construct a classifier, rather than learning it from trials as was the case with discriminative approaches.
“It’s a really cool way to incorporate knowledge about a physical system deep into the machine learning framework. This goes far beyond simply performing feature engineering on data samples or simple inductive biases,” says Schäfer.
This generative classifier can determine what phase a system is in by taking into account some parameter such as temperature or pressure. And because researchers directly approximate the probability distributions underlying measurements from a physical system, the classifier has systemic knowledge.
This makes their method perform better than other machine learning techniques. And because it can work automatically without the need for extensive training, their approach significantly increases the computational efficiency of identifying phase transitions.
Finally, just as you might ask ChatGPT to solve a math problem, researchers can ask the generative classifier questions such as “is this sample Phase I or Phase II?” or “was this sample generated at high or low temperature?”
Scientists could also utilize this approach to solve various binary classification tasks in physical systems, for example to detect entanglement in quantum systems (is a state entangled or not?) or to determine whether theory A or B is best suited to solve a particular problem. They could also utilize this approach to better understand and improve enormous language models like ChatGPT by identifying how certain parameters should be tuned for the chatbot to deliver the best results.
In the future, researchers also want to explore theoretical guarantees on the number of measurements needed to successfully detect phase transitions and estimate the amount of computation required.
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.