Bayesian polynomial neural networks and polynomial neural ordinary differential equations

• URL: http://arxiv.org/abs/2308.10892v2
• Date: Fri, 25 Aug 2023 05:05:06 GMT
• Title: Bayesian polynomial neural networks and polynomial neural ordinary differential equations
• Authors: Colby Fronk and Jaewoong Yun and Prashant Singh and Linda Petzold
• Abstract summary: Symbolic regression with neural networks and neural ordinary differential equations (ODEs) are powerful approaches for equation recovery of many science and engineering problems. 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 inference methods: the Laplace approximation, Markov Chain Monte Carlo sampling methods, and Bayesian variational inference.
• Score: 4.550705124365277
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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