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+# $\delta$ parameter learning
+
+## Code Release
+
+- Codes are released at [this zenodo link](https://doi.org/10.5281/zenodo.5227738)
+
+
+## Summary
+
+From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling for routing flows on the river network.
+
+The behaviors and skills of models in many geosciences (e.g., hydrology and ecosystem sciences) strongly depend on spatially-varying parameters that need calibration. 
+A well-calibrated model can reasonably propagate information from observations to unobserved variables via model physics, but traditional calibration is highly inefficient 
+and results in non-unique solutions. Here we propose a novel differentiable parameter learning (dPL) framework that efficiently learns a global mapping between inputs 
+(and optionally responses) and parameters. Crucially, dPL exhibits beneficial scaling curves not previously demonstrated to geoscientists: as training data increases, 
+dPL achieves better performance, more physical coherence, and better generalizability (across space and uncalibrated variables), all with orders-of-magnitude lower 
+computational cost. We demonstrate examples that learned from soil moisture and streamflow, where dPL drastically outperformed existing evolutionary and regionalization
+methods, or required only ~12.5% of the training data to achieve similar performance. The generic scheme promotes the integration of deep learning and process-based models,
+without mandating reimplementation.
+
+## Bibtex Citation
+
+```bibtex
+@article{Tsai_2021,
+   title={From calibration to parameter learning: Harnessing the scaling effects of big data in geoscientific modeling},
+   volume={12},
+   ISSN={2041-1723},
+   url={http://dx.doi.org/10.1038/s41467-021-26107-z},
+   DOI={10.1038/s41467-021-26107-z},
+   number={1},
+   journal={Nature Communications},
+   publisher={Springer Science and Business Media LLC},
+   author={Tsai, Wen-Ping and Feng, Dapeng and Pan, Ming and Beck, Hylke and Lawson, Kathryn and Yang, Yuan and Liu, Jiangtao and Shen, Chaopeng},
+   year={2021},
+   month=oct }
+```