Bayesian polynomial neural networks and polynomial neural ordinary differential equations
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.
Authors
- Linda Petzold (ORCID: https://orcid.org/0000-0001-6251-6078)
- Prashant Singh (ORCID: https://orcid.org/0000-0002-3123-3478)
- Colby Fronk (ORCID: https://orcid.org/0000-0002-5943-1257)
- Jae-Woong Yun
Institutions
- Uppsala University (SE)
- University of California, Santa Barbara (US)
- Science for Life Laboratory (SE)
Publication Details
- Journal
- PLoS Computational Biology
- Published
- 2024-10-10
- DOI
- https://doi.org/10.1371/journal.pcbi.1012414
- Citations
- 8
- Primary Topic
- Model Reduction and Neural Networks
- Type
- article
- Field-Weighted Citation Impact
- 2.25
Funders
- National Science Foundation
- Universiteit van Amsterdam
- Aalto-Yliopisto
- University of Toronto
- China Scholarship Council
- Rheinische Friedrich-Wilhelms-Universität Bonn
- University of California, Santa Barbara
- University of California, San Diego
- Materials Research Science and Engineering Center, Harvard University
- Office of the President, University of California
- National Institute of Biomedical Imaging and Bioengineering
- Division of Materials Research
- California NanoSystems Institute