Bayesian polynomial neural networks and polynomial neural ordinary differential equations.

Fronk C, Yun J, Singh P, Petzold L

PLoS Comput Biol 20 (10) e1012414 [2024-10-00; online 2024-10-10]

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.

Prashant Singh

SciLifeLab Fellow

PubMed 39388392

DOI 10.1371/journal.pcbi.1012414

Crossref 10.1371/journal.pcbi.1012414

pmc: PMC11476690
pii: PCOMPBIOL-D-23-02023

Pre-print publication available
DOI: 10.48550/arXiv.2308.10892 
Bayesian polynomial neural networks and polynomial neural ordinary differential equations