Is deep learning inevitably synonymous with “black boxes”? These methods are often criticized for their lack of transparency, resulting in unintelligible models. This issue is particularly relevant in physics, where the goal is to model the laws governing our universe as comprehensible equations, rather than opaque neural networks composed of millions of numbers.
Wassim Tenachi, Rodrigo Ibata, two astrophysicists based in France and Foivos Diakogiannis, a researcher at Australia’s national science agency, CSIRO tackled this problem by creating an artificial intelligence algorithm that produces analytical physical models from raw scientific data. Their work was published in the American journal, The Astrophysical Journal, on December 11.
Manipulating even elementary mathematical symbols like addition or division can be a complex challenge for neural networks. However, thanks to advances in artificial intelligence techniques related to natural language processing and drawing from methods used in symbolic computation, it is now possible to create neural networks that generate equations.
Nevertheless, the quest for the ideal equation that perfectly models a dataset while having the freedom to combine a plethora of mathematical symbols can quickly become a combinatorial nightmare. As you may have been told many times in school, in physics, you can’t “add potatoes and carrots together”, for example, you can’t add a length and a velocity because it doesn’t make physical sense. These rules, known as dimensional analysis, prohibit certain combinations of mathematical symbols when writing a physical equation, greatly reducing the combinatorial space.
Illustration of the combinatorial space reduction provided by dimensional analysis.
The artificial intelligence method, known as “PhySO” (Physical Symbolic Optimization), designed by these researchers French and Australian scientists formulates thousands of equations per second and autonomously learns to formulate increasingly high-quality equations through trial and error while capitalizing on these dimensional analysis rules.
PhySO, the artificial intelligence developed by the Franco-Australian collaboration, rediscovering the equation of the textbook harmonic oscillator from a dataset.
This study made a lot of noise on Twitter, quickly becoming the most-discussed scientific article of the week on the social network. It was even shared by Professor Yann Lecun, the scientist often considered the father of modern artificial intelligence and the head of the artificial intelligence department at Meta (formerly Facebook).
This kind of approach raises many questions about the role of humans in the scientific process. “The goal is not to replace the physicist but simply to equip us with a powerful tool to explore the space of equations that empirically meet experimental or observational constraints,” emphasize the authors.
In this first study, the Franco-Australian collaboration focused on the automated formulation of empirical equations, aligning more with observational and experimental needs than the theoretical aspects of physics.
It is worth noting the impartiality of this type of unsupervised method regarding the precise configuration of the equations sought. Could this intrinsic impartiality one day lead to a more agnostic scientific research?
Scientific contacts :
- Wassim Tenachi (PhD Student) wassim.tenachi@astro.unistra.fr
- Rodrigo Ibata (DR CNRS) rodrigo.ibata@astro.unistra.fr
Article: Wassim Tenachi, Rodrigo Ibata, Foivos Diakogiannis, Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws, ApJ (DOI: 10.3847/1538-4357/ad014c)