Interpretably reconstruct physical processes with combined machine learning approaches, a case study of evapotranspiration

Machine learning has long been restricted by the mystery of its black box, especially in the fields like geosciences that emphasizes clear expressions of mechanisms. To deal with that issue, we provided a fundamental framework combining two branches, clusters and regressions in machine learning, specifically, spectral clustering in unsupervised clustering methods and artificial neural networks in regression models, to resemble calculations in process-based models. With a case study of evapotranspiration, it was demonstrated that our framework was not only able to discern two processes, aerodynamics and energy, similar to the process-based model, i.e., Penman-Monteith formula, but also provided a third space for potential underrepresented process from canopy or ecosystems. Meanwhile, with only a few hundred of training data in most sites, the simulation of evapotranspiration achieved a higher accuracy (R² of 0.92 and 0.82; RMSE of 12.41W/m² and 8.11 W/m² in training set and test set respectively) than commonly used machine learning approaches, like artificial neural networks in a scale of 100,000 training set (R² of 0.85 and 0.81; RMSE of 42.33W/m² and 46.73 W/m²). In summary, our method provides a new direction of hybridizing machine learning approaches and mechanisms for future work, which is able to tell mechanisms from a little amount of data, and thus could be utilized in validating the known and even exploring the unknown knowledge by providing reference before experiments and mathematical derivations.