&Bullet; physics 14, p67

A machine learning technique maps the phase space of water as reliably as the gold standard from the beginning Calculations, but at a much lower computational cost.

Given its familiarity, water is a surprisingly difficult substance to simulate. In addition to its liquid and gaseous phase, water assumes at least 14 different solid configurations depending on temperature and pressure – both in molecular and in ionic form. This complex phase space makes water an ideal test bench for theoretical models that predict material behavior. Now researchers have tested an efficient new model and found that it can predict all phases of water with an accuracy close to that of much more computationally intensive techniques [1] .

The first step in mapping the phase space of a material is to construct its “potential energy surface” (PES) under different conditions. The PES describes the probability of finding a certain configuration at a certain temperature and pressure. The gold standard for this task is to use fromBeginning Calculations that record the quantum mechanical behavior of the electrons in the system. However, the computational burden of this method is so high that it is impractical to simulate more than a narrow range of conditions. So far, most of the phase space of water has been mapped with faster, less reliable approximations.

Linfeng Zhang of Princeton University and colleagues achieve both accuracy and speed through the use of carefully selected ones from the beginning Calculations to train a machine learning algorithm. Starting with a rough phase diagram based on experimental data, the algorithm identifies points on the map at which from the beginning Calculations are most needed. After performing these calculations, the process repeats until the error in the approximation falls below an acceptable threshold.

The researchers plan to use the technology to map parts of the phase space of water that were not recorded experimentally. They also say that future applications could include nuclear quantum effects on the various properties of water.

–Marric Stephens

Marric Stephens is the corresponding editor for physics based in Bristol, UK.


  1. L. Zhang et al., “Phase diagram of a deep potential water model”, Phys. Rev. Lett.126, 236001 (2021).

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