Is it possible to use the capabilities of both physical models and artificial intelligence together, rather than choosing between them? Recent research has demonstrated that the answer to this question could open a new path for the modelling and prediction of complex systems, a path where the laws of physics and machine learning algorithms complement each other instead of competing with each other.

Physical models are built on the basis of the known laws and relationships of nature, and for this reason, it is usually possible to explain why a model has reached a specific result. However, providing an exact description of many complex phenomena using physical equations can be difficult and computationally expensive. On the other hand, machine learning can identify complex patterns and predict the behaviour of a system using data, but its performance is dependent on the quality and volume of the data, and it is not always clear to what extent the model is consistent with the laws governing the actual phenomenon.

This is where the idea of hybrid models is formed: if we incorporate physical knowledge into the machine learning process, and conversely, use the power of machine learning to develop physical models, is it possible to achieve more accurate and efficient models?

A review study has examined existing studies in this field systematically to seek an answer to this question. In this study, various methods of combining physics and machine learning have been investigated and categorised into a single framework based on how the two interact.

The result of this review is the presentation of a triple framework to describe hybrid models. In Physics-Guided Machine Learning (PGML), physical laws and knowledge guide the machine learning model. Simply put, the model does not learn only from data; it also utilises what we know about the physical behaviour of the system. In Machine Learning-Guided Physics (MLGP), the direction of movement is reversed. Machine learning assists physical models and can play a role in their development, solution, or the acceleration of their calculations. In Mutually Guided Physics and Machine Learning models (MGPML), this relationship is two-way; that is, both models use each other’s information to form a hybrid system for solving the problem.

This classification is not merely a theoretical division. By examining numerous examples, the authors have shown that these three approaches have been used in various scientific problems, and each has its own capabilities and challenges.

One of the important advantages of incorporating physical knowledge into machine learning models is the possibility of using limited data more effectively. In some of the studies reviewed, the structure of the neural network was designed based on variables with physical meaning, and in addition to the usual learning error, physical information was also introduced into the model training process. The results of these studies have shown that such an approach can improve the performance of the model compared to conventional methods in conditions where training data is limited.

On the other hand, machine learning can perform some complex physical calculations with greater speed. In one of the examples reviewed, a model based on a neural network was developed to calculate the potential energy surfaces of atomic and molecular systems; a model that, while maintaining some fundamental characteristics of the system, had an accuracy close to quantum mechanics models and a computational cost comparable to empirical potentials.

The significance of this research lies in the fact that it is not limited to a single example or application. By reviewing a collection of different models and applications, the authors have attempted to provide a coherent picture of an emerging interdisciplinary field. This framework can help researchers to better identify the different methods of combining physics and machine learning, understand the differences between them, and choose a more appropriate path for new problems. Furthermore, the review of existing studies reveals some research gaps and areas where the potential for developing hybrid models remains high.

Ultimately, this research shows that the future of scientific modelling does not necessarily lie in choosing between “physics” and “artificial intelligence”; rather, it can be formed at a point where our knowledge of the laws of nature is combined with the machine’s ability to learn from data.

This research, titled “Machine Learning and Physics: A Survey of Integrated Models,” has been conducted by Dr Azra Seyyedi from the Department of Physics, Dr Mahdi Bohlouli from the Department of Computer Science and Information Technology, and Dr Seyed Ehsan Nedaaee Oskoee from the Department of Physics at the Institute for Advanced Studies in Basic Sciences (IASBS). The article was published in the journal ACM Computing Surveys, volume 56, issue 5, article 115, in November 2023.