Fundamental science historically relies on a reductionist paradigm called "constructionism": the ability to start from the fundamental laws and reconstruct the universe. For complex systems, this paradigm breaks down due to an intractable tangle of nonlinear interactions. Computational methods and numerical approximations are thus indispensable for studying complex systems. However, modern computational models have become so sophisticated that the complexity of their outputs are often on par with the natural systems they simulate. Harnessing the data deluge from model outputs and observational measurements, machine learning offers a new nonlinear toolset to help parse this complexity. I will elaborate on how these ideas intersect with weather and climate applications. First, I will discuss the breakdown of constructionism for understanding extreme weather events and how unsupervised discovery can help fill the gap. Next, I will address the "black box" nature of data-driven models and show that optimal predictive models learn the underlying physics of the system, albeit they do so implicitly. A key construction that emerges in this work is the probability distribution over possible futures conditioned on past observations. These predictive distributions are central to the recent trend in stochastic data-driven models, including ensemble weather forecasting. Finally, I will discuss how data-driven causal discovery can help untangle the web of nonlinear interactions in complex systems.
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