The research reflects a broader shift in modern physics toward combining artificial intelligence with first-principles science to tackle problems that were previously too computationally difficult to solve.

Researchers at Temple University have uncovered new insight into one of science’s most puzzling questions: why water behaves differently from almost every other liquid on Earth.

Using a combination of artificial intelligence and advanced quantum mechanical simulations, the research team developed a highly accurate model that explains why water reaches its maximum density at about 4 degrees Celsius before expanding again as it freezes.

The findings are detailed in the paper, “Understanding the density maximum of water with machine-learned potentials,” published in the journal Science Advances.

Water’s unusual property is essential to life on Earth. Because water expands as it freezes, ice floats instead of sinks. Lakes and rivers freeze from the top down, insulating the water below and allowing aquatic ecosystems to survive winter temperatures.

“Water seems simple because we interact with it every day, but at the microscopic level it is an extraordinarily complex liquid,” said Xifan Wu, professor of physics at Temple and a member of the research team. “Its molecules are constantly reorganizing through hydrogen bonds, and many of its unusual properties emerge from that collective behavior.”

Scientists have struggled to fully explain water’s strange density behavior because doing so requires understanding interactions occurring simultaneously across vastly different scales. Quantum mechanical calculations can accurately describe individual molecules and electrons, but those calculations become computationally overwhelming when applied to the thousands of interacting molecules needed to simulate real liquid water.

The Temple team overcame that challenge by combining machine learning with first-principles quantum mechanics—essentially the fundamental laws of physics governing electrons and atoms without relying heavily on experimental assumptions. The researchers trained an AI-based model on highly accurate quantum calculations, allowing them to simulate water at much larger scales while preserving quantum-level precision.

“Our work demonstrates how artificial intelligence can help bridge the gap between microscopic quantum mechanics and large-scale physical behavior,” Wu said. “This combination allowed us to study water at experimentally relevant scales in a way that was previously not feasible.”

The simulations revealed that water’s density anomaly arises from a delicate balance inside its hydrogen-bond network. At small scales, water molecules naturally organize into local tetrahedral structures, arrangements in which each molecule bonds with roughly four neighbors in a geometry similar to the structure of ice. But at slightly larger scales, surrounding layers of molecules partially collapse inward as temperatures change, allowing the liquid to pack more efficiently near 4 °C.

The result is a new microscopic explanation for one of the defining properties of water. Rather than being caused by a simple structural transition, the researchers found that water’s behavior emerges from competition between order and disorder occurring at different length scales simultaneously.

“A simple way to think about it is that water molecules prefer to form open, ice-like structures, while heat pushes them toward more compact arrangements,” Wu said. “Near 4 degrees Celsius, those competing effects reach an optimal balance, producing water’s highest density.”

Housed at Temple’s Institute for Computational Molecular Science, the project involved an interdisciplinary collaboration spanning computational physics, chemistry and high-performance computing. Yizhi Song, a Temple postdoctoral researcher in physics, served as first author and led much of the computational work. Renowned computational chemist Michael L. Klein, Carnell Professor of Science at Temple, was a member of the research team. Visiting graduate student Renxi Liu and Princeton University graduate student Yifan Li also contributed to the project.

Researchers say the next phase of the work will apply the same AI-driven methods to even more complex systems, including salt water, supercooled water, confined water and water under extreme pressures. The approach could help scientists study a wide range of materials whose properties emerge from large-scale collective molecular behavior.

“This work opens new opportunities for combining machine learning with first-principles physics to study difficult problems across chemistry, materials science and energy research,” Wu said.