Many common AI methods are based on the principle of supervised machine learning: a model – for instance a neural network – is specifically trained to predict a particular target quantity directly. One example that illustrates this approach is image recognition, where the AI system is shown numerous images in which it is known whether or not a cat is depicted. On this basis, the system learns to identify cats in new, previously unseen images. “However, such a direct approach is difficult in the case of the chemical potential, because determining it usually requires computationally expensive algorithms,” says Prof. Dr. Matthias Schmidt, Chair of Theoretical Physics II at the University of Bayreuth. He and his research associate Dr. Florian Sammüller address this challenge with their newly developed AI method. It is based on a neural network that incorporates the theoretical structure of liquids – and more generally, of soft matter – allowing it to predict their properties with great accuracy.
“What is special about our method is that the AI does not learn the chemical potential at all,” Schmidt explains. Instead, the AI learns the universal density functional, which captures the fundamental physical relationships within a liquid and remains the same across many different systems. “This can be illustrated by comparing different surfaces coated with the same liquid. Even though the surfaces may differ in structure or material, the liquid still follows the same underlying physical laws. These ‘intrinsic’ properties of the liquid correspond to the universal density functional that is captured via machine learning,” says Schmidt.
Between the learned density functional and observable properties of a system – such as the particle density profile and the external potential – a remaining difference persists. This gap is not closed by the AI model but by physical principles: from general considerations of thermodynamic stability, it follows that this remaining difference uniquely corresponds to the chemical potential.
“Our method combines data-driven learning with fundamental insights from theoretical physics: the AI-derived density functional provides a universal framework, while the chemical potential itself is derived from established physical conditions. This approach makes it possible to determine the chemical potential indirectly, but consistently, without having to train it explicitly,” notes Sammüller. He adds: “In terms of image recognition, it would be almost as if an AI could recognise cats without ever having seen one during training.”
