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.

Abstract Nickel is a highly important metal, and the detection of Ni2+ using biosensors is a long-stand analytical challenge. DNA has been widely used for metal detection, although no DNA-based sensors were reported for Ni2+. DNAzymes are DNA-based catalysts, and they recruit metal ions for catalysis. In this work, in vitro selection of RNA-cleaving DNAzymes was carried out using a library containing a region of 50 random nucleotides in the presence of Ni2+. To increase Ni2+ binding, a glycyl–histidine-functionalized tertiary amine moiety was inserted at the cleavage junction. A representative DNAzyme named Ni03 showed a high cleavage yield with Ni2+ and it was further studied. After truncation, the optimal sequence of Ni03l could bind one Ni2+ or two Co2+ for catalysis, while other metal ions were inactive. Its cleavage rates for 100 μM Ni2+ reached 0.63 h−1 at pH 8.0. A catalytic beacon biosensor was designed by labeling a fluorophore and a quencher on the Ni03l DNAzyme. Fluorescence enhancement was observed in the presence of Ni2+ with a detection limit of 12.9 μM. The sensor was also tested in spiked Lake Ontario water achieving a similar sensitivity. This is another example of using single-site modified DNAzyme for sensing transition metal ions.