Process-based modelling 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. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. Differentiable modelling is an approach that flexibly integrates the learning capability of machine learning with the interpretability of process-based models. This Perspective highlights the potential of differentiable modelling to improve the representation of processes, parameter estimation, and predictive accuracy in the geosciences.

Process-based modelling 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. In this Perspective, we explore differentiable modelling as a pathway to dissolve the perceived barrier between process-based modelling and machine learning in the geosciences and demonstrate its potential with examples from hydrological modelling. ‘Differentiable’ refers to accurately and efficiently calculating gradients with respect to model variables or parameters, enabling the discovery of high-dimensional unknown relationships. Differentiable modelling involves connecting (flexible amounts of) prior physical knowledge to neural networks, pushing the boundary of physics-informed machine learning. It offers better interpretability, generalizability, and extrapolation capabilities than purely data-driven machine learning, achieving a similar level of accuracy while requiring less training data. Additionally, the performance and efficiency of differentiable models scale well with increasing data volumes. Under data-scarce scenarios, differentiable models have outperformed machine-learning models in producing short-term dynamics and decadal-scale trends owing to the imposed physical constraints. Differentiable modelling approaches are primed to enable geoscientists to ask questions, test hypotheses, and discover unrecognized physical relationships. Future work should address computational challenges, reduce uncertainty, and verify the physical significance of outputs. Differentiable modelling is an approach that flexibly integrates the learning capability of machine learning with the interpretability of process-based models. This Perspective highlights the potential of differentiable modelling to improve the representation of processes, parameter estimation, and predictive accuracy in the geosciences.

A vector‐river network explicitly uses realistic geometries of river reaches and catchments for spatial discretization in a river model. This enables improving the accuracy of the physical properties of the modeled river system, compared to a gridded river network that has been used in Earth System Models. With a finer‐scale river network, resolving smaller‐scale river reaches, there is a need for efficient methods to route streamflow and its constituents throughout the river network. The purpose of this study is twofold: (1) develop a new method to decompose river networks into hydrologically independent tributary domains, where routing computations can be performed in parallel; and (2) perform global river routing simulations with two global river networks, with different scales, to examine the computational efficiency and the differences in discharge simulations at various temporal scales. The new parallelization method uses a hierarchical decomposition strategy, where each decomposed tributary is further decomposed into many sub‐tributary domains, enabling hybrid parallel computing. This parallelization scheme has excellent computational scaling for the global domain where it is straightforward to distribute computations across many independent river basins. However, parallel computing for a single large basin remains challenging. The global routing experiments show that the scale of the vector‐river network has less impact on the discharge simulations than the runoff input that is generated by the combination of land surface model and meteorological forcing. The scale of vector‐river networks needs to consider the scale of local hydrologic features such as lakes that are to be resolved in the network.

A vector‐river network explicitly uses realistic geometries of river reaches and catchments for spatial discretization in a river model. This enables improving the accuracy of the physical properties of the modeled river system, compared to a gridded river network that has been used in Earth System Models. With a finer‐scale river network, resolving smaller‐scale river reaches, there is a need for efficient methods to route streamflow and its constituents throughout the river network. The purpose of this study is twofold: (1) develop a new method to decompose river networks into hydrologically independent tributary domains, where routing computations can be performed in parallel; and (2) perform global river routing simulations with two global river networks, with different scales, to examine the computational efficiency and the differences in discharge simulations at various temporal scales. The new parallelization method uses a hierarchical decomposition strategy, where each decomposed tributary is further decomposed into many sub‐tributary domains, enabling hybrid parallel computing. This parallelization scheme has excellent computational scaling for the global domain where it is straightforward to distribute computations across many independent river basins. However, parallel computing for a single large basin remains challenging. The global routing experiments show that the scale of the vector‐river network has less impact on the discharge simulations than the runoff input that is generated by the combination of land surface model and meteorological forcing. The scale of vector‐river networks needs to consider the scale of local hydrologic features such as lakes that are to be resolved in the network.