Department of Chemical Engineering, University of California, Santa Barbara, California; United States of America.
Department of Statistics and Applied Probability, University of California, Santa Barbara, California; United States of America.
PLoS Comput Biol. 2024 Oct 10;20(10):e1012414. doi: 10.1371/journal.pcbi.1012414. eCollection 2024 Oct.
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.
基于多项式神经网络和多项式神经网络常微分方程（ODE）的符号回归是最近出现的两种强大的方法，可用于恢复许多科学和工程问题的方程。然而，这些方法提供模型参数的点估计，并且目前无法适应噪声数据。我们通过开发和验证以下贝叶斯推理方法来解决此挑战：拉普拉斯近似，马尔可夫链蒙特卡罗（MCMC）采样方法和变分推理。我们发现拉普拉斯近似是此类问题的最佳方法。我们的工作可以轻松扩展到更广泛的符号神经网络类别，其中包括多项式神经网络。
