John Crocker had expected to see a flat line – a familiar horizontal track with a few slight peaks and valleys – but the patch of energy in front of him dipped sharply downward.
“It’s a once-in-a-lifetime find,” Crocker says.
“It was as if the simulation had unexpectedly fallen into a deep canyon on an energy surface. This was lucky for two reasons. First, it turned out to be a game-changer for our study of glassy materials. And second, similar canyons have the potential to help others struggling with the same computational hurdles we face in our field, from computer scientists working on machine learning algorithms to bioengineers studying protein folding. significant results because we were curious enough to try a method that shouldn’t have worked. But it did.
The method is metadynamics, a computational approach to exploring energy landscapes. Its counter-intuitive application is the subject of a recent publication in PNAS a group of Penn engineers from the University of Pennsylvania led by Crocker, professor and head of the graduate group in the Department of Chemical and Biological Engineering (CBE), along with Robert Riggleman, associate professor at CBE, and Amruthesh Thirumalaiswamy, Ph.D. student in CBE.
Most solids are glasses (or vitreous). We categorize the rest as crystals. These categorizations are not limited to glass or crystal as one might imagine, but rather indicate how the atoms of any solid are arranged. Crystals have sharp, repeating atomic structures. Glasses, however, are amorphous. Their atoms and molecules take on a large number of disordered configurations.
Glassy configurations lock in while pursuing, like all systems, their most stable and lowest energy states. Given enough time, the glasses will still relax very slowly in energy, but their disordered atoms make this a slow and difficult process.
Stable, low-power glasses, or “ideal glasses,” hold the key to a reservoir of knowledge that researchers want to unlock.
Seeking to understand and possibly replicate the conditions of glassy materials that overcome the obstacles of their own atomic whims, scientists use both experimental and theoretical approaches.
Laboratories have, for example, melted and re-cooled fossilized amber to develop processes to recreate the encouraging effects that millions of years have had on its glassy pursuit of low-energy states. Crocker’s team, affiliated with the interdisciplinary Penn Institute for Computational Science (PICS), explores physical structures with mathematical models.
“We use computer models to simulate the positions and movements of atoms in different glasses,” says Thirumalaiswamy. “In order to keep track of the particles of a material, which are so numerous and dynamic that they are impossible to visualize in three dimensions, we must represent them mathematically in high-dimensional virtual spaces. If we have 300 atoms, for example, we need to represent them in 900 dimensions. We call these energy landscapes. We then study the landscapes, navigating them almost like explorers.
In these computer models, single configuration points, summaries of atomic motion, tell the story of a glass’s energy levels. They show where a glass got stuck and where it could have reached a low energy state.
The problem is that until now, researchers haven’t been able to navigate landscapes efficiently enough to find these rare examples of stability.
“Most studies do random walks around high-dimensional landscapes at huge computational cost. It would take forever to find anything of interest. The landscapes are huge, and these walks are repetitive, wasting a lot fixed amount of time in one state before moving on to the next,” says Riggleman.
And so they took a chance on metadynamics, a method that seemed doomed to failure.
Metadynamics is an algorithmic strategy developed to explore the whole landscape and avoid repetition. It assigns a penalty for returning twice to the same place. However, metadynamics never work in high-dimensional spaces, because the construction of penalties takes too long, negating the strategy’s potential for efficiency.
Yet, as the researchers observed the downward trend in their configuration energy, they realized that it had succeeded.
“We wouldn’t have guessed it, but the landscapes turned out to have these canyons with floors that are only two or three dimensional,” says Crocker. “Our algorithm literally hit the nail on the head. We found low-energy patterns occurring regularly in several different glasses with a method that we believe could be revolutionary for other disciplines as well.”
The potential applications of the Crocker Lab canyons are very varied.
In the two decades since the mapping of the human genome project was completed, scientists have used computer models to turn peptide sequences into proteins. Proteins that fold well in nature have, during evolution, found ways to explore low-energy states analogous to those of ideal glasses.
Theoretical protein studies use energy landscapes to learn about the folding processes that create the functional (or dysfunctional) foundations of biological health. Yet measuring these structures takes time, money, and energy that scientists and the people they aim to serve don’t have to spare. Bogged down by the same computational inefficiencies faced by glassy materials researchers, genomics scientists could find similar success with metadynamics-based approaches, accelerating the pace of medical research.
Machine learning processes have much in common with random walks in high-dimensional space. Training artificial intelligence takes a huge amount of time and computing power and still has a long way to go in terms of predictive accuracy.
A neural network must “see”, for example, thousands or even millions of faces in order to acquire enough skills for facial recognition. With a more strategic computational process, machine learning could become faster, cheaper, and more accessible. The metadynamic algorithm may have the potential to overcome the need for huge and expensive data sets typical of the process.
Not only would this provide solutions for industry efficiency, but it could also democratize AI, allowing people with modest resources to do their own training and development.
“We assume that the landscapes of these different domains have similar geometric structures to ours,” says Crocker. “We suspect that there could be a deep mathematical reason why these canyons exist, and they may be present in these other related systems. That’s our invitation, we look forward to the dialogue he starts.”
Exploring canyons in glassy energetic landscapes using metadynamics, Proceedings of the National Academy of Sciences (2022). DOI: 10.1073/pnas.221053511. www.pnas.org/doi/10.1073/pnas.2210535119
Provided by the University of Pennsylvania
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