Differentiable modeling for global water resources under global change

Process-based modeling offers interpretability and physical consistency in many domains of geosciences but struggles to leverage large datasets efficiently. Machine-learning methods, especially deep networks, have strong predictive skills yet are unable to answer specific scientific questions. A recently proposed genre of physics-informed machine learning, called differentiable modeling (DM, https://t.co/qyuAzYPA6Y), trains neural networks (NNs) with process-based equations (priors) together in one stage (so-called end-to-end) to benefit from the best of both NNs and process-based paradigms. The NNs do not need target variables for training but can be indirectly supervised by observations matching the outputs of the combined model, and differentiability critically supports learning from big data. We propose that differentiable models are especially suitable as global hydrologic models because they can harvest information from big earth observations to produce state-of-the-art predictions (https://mhpi.github.io/benchmarks/), enable physical interpretation naturally, extrapolate well (due to physical constraints) in space and time, enforce known physical laws and sensitivities, and leverage progress in modern AI computing architecture and infrastructure. Differentiable models can also synergize with existing global hydrologic models (GHMs) and learn from the lessons of the community. Differentiable GHMs to answer pressing societal questions on water resources availability, climate change impact assessment, water management, and disaster risk mitigation, among others. We demonstrate the power of differentiable modeling using computational examples in rainfall-runoff modeling, river routing, forcing fusion, as well applications in water-related domains such as ecosystem modeling and water quality modeling. We discuss how to address potential challenges such as implementing gradient tracking for implicit numerical schemes and addressing process tradeoffs. Furthermore, we show how differentiable modeling can enable us to ask fundamental questions in hydrologic sciences and get robust answers from big global data.