Physics-Informed Machine Learning: A New Frontier in Symbolic Regression

Imagine you are given a challenge to find a mathematical formula that describes the orbit of Mars around the Sun. Sounds like a daunting task, right? Well, it is! In fact, it’s NP-hard, which means it’s an exponentially large search space of equations that need to be considered. But don’t worry, we have some tricks up our sleeves to make this problem more manageable.
One approach is to use universal function approximators like multilayer perceptron neural networks. These can handle the vast number of equations in the search space, but they may not provide the most elegant or parsimonious solution. Another option is to use symbolic regression methods, which search for a simple and elegant equation that describes Mars’ orbit. There are three main classes of symbolic regression methods: regression-based, expression tree-based, and physics- or mathematics-inspired.
In this article, we focus on the last category, AI Feynman, a machine learning and physics-inspired algorithm. This approach uses the principles of physics and mathematics to guide the search for an equation that accurately describes Mars’ orbit. By combining these two disciplines, AI Feynman can find a solution that is both simple and elegant.
So how does AI Feynman work? Well, imagine you are trying to find the distance between two points on a sphere (like Mars’ orbit). You could use a straight line to connect them, but that wouldn’t be very accurate since the orbit is curved. Instead, AI Feynman uses the principles of physics and mathematics to find a more accurate representation of the orbit as an ellipse or other curved shape. By combining these two disciplines, AI Feynman can find a solution that is both simple and elegant.
In summary, finding an equation describing Mars’ orbit is a complex challenge, but AI Feynman provides a promising approach by combining the principles of physics and mathematics to guide the search for a simple and elegant solution. By using this approach, we can demystify the complexity of symbolic regression and find a solution that captures the essence of the problem without oversimplifying it.