The behaviors and skills of models in many geosciences, e.g., hydrology and ecosystem sciences, strongly depend on spatially varying parameters that need calibration. Here we propose a novel differentiable parameter learning (dPL) framework that solves a pattern recognition problem and learns a more robust, universal mapping. Crucially, dPL exhibits virtuous scaling curves not previously demonstrated to geoscientists: as training data collectively increases, dPL achieves better performance, more physical coherence, and better generalization, all with orders-of-magnitude lower computational cost. We demonstrate examples of calibrating models to soil moisture and streamflow, where dPL drastically outperformed state-of-the-art evolutionary and regionalization methods, or requires ~12.5% the training data to achieve the similar performance. The generic scheme promotes the integration of deep learning and process-based models, without mandating reimplementation.
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