New method helps AI models learn equations from messy, real-world data
Researchers have developed a Bayesian framework that allows neural networks to recover scientific equations while handling noisy experimental data—a longstanding limitation. The advance could accelerate discovery in physics, chemistry, and engineering by automating the extraction of clean mathematical rules from imperfect measurements.
Originaltitel: Bayesian polynomial neural networks and polynomial neural ordinary differential equations
<p>Symbolic regression with polynomial neural networks and polynomial neural ordinary differential equations (ODEs) are two recent and powerful approaches for equation recovery of many science and engineering problems. However, these methods provide point estimates for the model parameters and are currently unable to accommodate noisy data. We address this challenge by developing and validating the following Bayesian inference methods: the Laplace approximation, Markov Chain Monte Carlo (MCMC) sampling methods, and variational inference. We have found the Laplace approximation to be the best method for this class of problems. Our work can be easily extended to the broader class of symbolic neural networks to which the polynomial neural network belongs.</p>