NATURE REVIEWS | PHYSICS

0123456789();: Modelling and forecasting the dynamics of multiphysics and multiscale systems remains an open scientific prob-lem. Take for instance the Earth system, a uniquely com-plex system whose dynamics are intricately governed by the interaction of physical, chemical and biological pro-cesses taking place on spatiotemporal scales that span 17 orders of magnitude1. In the past 50 years, there has been tremendous progress in understanding multiscale PHYSICS in diverse applications, from geophysics to biophysics, by numerically solving partial differential equations (PDEs) using finite differences, finite elements, spectral and even meshless methods. Despite relentless progress, model-ling and predicting the evolution of nonlinear multiscale systems with inhomogeneous cascades- of- scales by using classical analytical or computational tools inevi-tably faces severe challenges and introduces prohibitive cost and multiple sources of uncertainty. Moreover, solv-ing inverse problems (for inferring material properties in functional materials or discovering missing PHYSICS in reactive transport, for example) is often prohibitively expensive and requires complex formulations, new algorithms and elaborate computer codes.

the performance of a learning algorithm. A recent exam-ple reflecting this new learning philosophy is the family of ‘physics-informed neural networks’ (PINNs) 7. This is a class of deep learning algorithms that can seam-lessly integrate data and abstract mathematical opera-tors, including PDEs with or without missing physics (Boxes 2,3 ...

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