Deep learning (DL) models, despite their wide and successful applications, are prone to overfitting for small training datasets, produce a poor predictive performance for uncertain data, and provide point estimations without any indication of accuracy and credibility. These limitations of the deterministic DL models hinder their effective application in ecological science where the labelled data are sparse and noisy and where the predictive uncertainty quantification is needed for scientific understanding. Integration of Bayesian inference into DL models adds an estimate of uncertainty and regularization in the predictions. However, traditional Bayesian methods are computationally unaffordable and inflexible for high-dimensional problems, which limits their application to DL systems that typically have millions of model parameters. In this effort, we propose a data-efficient Bayesian machine learning method to advance ecological forecasting and uncertainty quantification.
Results/Conclusions
In a demonstration, we integrate the proposed Bayesian algorithm with a feedforward neural network (NN) to build a fast-to-evaluate surrogate of the complex Energy Exascale Earth System Land Model (ELM) for efficient modeling. The formulated Bayesian NN, using a small number of training data (i.e., a few computationally expensive ELM simulations), produces an accurate prediction with high credibility, whereas with the same small training size, the traditional deterministic NN cannot yield a reasonable estimation and does not provide confidence information. The proposed Bayesian machine learning method is computationally efficient and flexible, which can be used for sensitivity analysis, data assimilation and uncertainty quantification so as to advance ecological forecasting.