MS-HyTimeXer: A deep learning model for predicting sap flow in tree trunks

Objective Tree sap flow is an important basis for accurately quantifying tree transpiration and assessing water consumption. Achieving precise prediction of this is crucial for understanding water utilization strategies. Therefore, this study proposes an improved model based on the TimeXer architecture-MS-HyTimeXer(Multi-Scale Hybrid TimeXer). This model can effectively utilize environmental factor information and the temporal characteristics of tree sap flow.

Method Tree trunk fluid flow data are from SAPFLUXNET. The study focuses on white pine(Pinus strobus) in eastern Canada. Data are collected every 30 minutes from January 1,2010 to December 31,2011, totaling 35040 sets of data.The model improves the architecture of TimeXer by introducing three core modules: Multi-Scale Patch Embedding, LSTM Timing Calibration, and Multi-Scale Convolution. The prediction results of DLinear, Informer, PatchTST, iTransformer, TimeXer, and MS-HyTimeXer models for tree trunk fluid flow are evaluated.

Result Under the condition of consistent experimental parameters, the experimental results show that the three improved modules can jointly enhance the prediction accuracy of the MS-HyTimeXer model; the prediction accuracy of the DLinear model is limited(R²=0.75), while the models based on the Transformer architecture(Informer, PatchTST, iTransformer, TimeXer) demonstrate excellent predictive capabilities, with R² ranging from 0.83 to 0.87. The prediction accuracy of the MS-HyTimeXer model is superior to the comparison models, with an MSE of 0.31 cm³/(cm²·h), an MAE of 0.39 cm³/(cm²·h), and an MAPE of 7.65%. It is the lowest among the six deep learning models, and its R² reaches 0.92. When the sliding window length is 512, the medium and long-term prediction results of the MS-HyTimeXer model are the best, with smaller errors.

Conclusion The experiments show that the time series deep learning models can effectively fit the medium and long-term variation trends of sap flow in tree trunks. The MS-HyTimeXer model, by integrating multi-scale features and strengthening temporal dependence, improves the accuracy of medium and long-term predictions, providing a reliable method for estimating tree transpiration in a temperate continental humid climate environment.