We outline a perspective of an entirely new research branch in Earth and climate sciences, where deep neural networks and Earth system models are dismantled as individual methodological approaches and reassembled as learning, self-validating, and interpretable Earth system model-network hybrids. Following this path, we coin the term "Neural Earth System Modelling" (NESYM) and highlight the necessity of a transdisciplinary discussion platform, bringing together Earth and climate scientists, big data analysts, and AI experts. We examine the concurrent potential and pitfalls of Neural Earth System Modelling and discuss the open question whether artificial intelligence will not only infuse Earth system modelling, but ultimately render them obsolete.
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