Uncertainty Prediction Neural Network (UpNet): Embedding Artificial Neural Network in Bayesian Inversion Framework to Quantify the Uncertainty of Remote Sensing Retrieval
This work addresses the need for efficient uncertainty quantification in remote sensing for applications like data assimilation and ecosystem modeling, representing a novel integration rather than an incremental improvement.
The study tackled the problem of quantifying uncertainty in remote sensing retrieval of vegetation biophysical parameters using artificial neural networks (ANNs), proving that ANNs trained with squared loss output the posterior mean and developing the UpNet algorithm, which achieved over a million-fold acceleration compared to standard Bayesian methods while maintaining consistency in results.
For the retrieval of large-scale vegetation biophysical parameters, the inversion of radiative transfer models (RTMs) is the most commonly used approach. In recent years, Artificial Neural Network (ANN)-based methods have become the mainstream for inverting RTMs due to their high accuracy and computational efficiency. It has been widely used in the retrieval of biophysical variables (BV). However, due to the lack of the Bayesian inversion theory interpretation, it faces challenges in quantifying the retrieval uncertainty, a crucial metric for product quality validation and downstream applications such as data assimilation or ecosystem carbon cycling modeling. This study proved that the ANN trained with squared loss outputs the posterior mean, providing a rigorous foundation for its uncertainty quantification, regularization, and incorporation of prior information. A Bayesian theoretical framework was subsequently proposed for ANN-based methods. Using this framework, we derived a new algorithm called Uncertainty Prediction Neural Network (UpNet), which enables the simultaneous training of two ANNs to retrieve BV and provide retrieval uncertainty. To validate our method, we compared UpNet with the standard Bayesian inference method, i.e., Markov Chain Monte Carlo (MCMC), in the inversion of a widely used RTM called ProSAIL for retrieving BVs and estimating uncertainty. The results demonstrated that the BVs retrieved and the uncertainties estimated by UpNet were highly consistent with those from MCMC, achieving over a million-fold acceleration. These results indicated that UpNet has significant potential for fast retrieval and uncertainty quantification of BVs or other parameters with medium and high-resolution remote sensing data. Our Python implementation is available at: https://github.com/Dash-RSer/UpNet.