Bayesian polynomial neural networks and polynomial neural ordinary differential equations
This work addresses the problem of handling noisy data in symbolic regression for science and engineering applications, representing an incremental improvement over existing methods.
The authors tackled the challenge of noisy data in symbolic regression using polynomial neural networks and polynomial neural ODEs by developing Bayesian inference methods, finding the Laplace approximation to be the best approach for this class of problems.
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.