Bayesian polynomial neural networks and polynomial neural ordinary differential equations
Year: 2024
Type: article
Abstract: 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.
Source: PLoS Computational Biology
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $2,926
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
Awards: G1110399006, G1141670404, CI-New: Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI), G2232042528, G2760720504, Materials Research Science and Engineering Center at UCSB, G3349485200, G3400352658, Towards Deploying a Science-Driven Regional Interoperable Science DMZ, G401861217, G4281768896, CC* NPEO: Toward the National Research Platform, CCRI: ABR: Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI), Category II: A Prototype National Research Platform, CC*DNI DIBBs: The Pacific Research Platform, StochSS: A Next-Generation Toolkit for Simulation-Driven Biological Discovery, MRI: Acquisition of a High Performance Central Computing Facility at University of California Santa Barbara, CCRI: ENS: Cognitive Hardware and Software Ecosystem Community Infrastructure (CHASE-CI)
OpenAlex ID: W4403295841