This month's Physics Today features an excellent article by Schneider, Jeevanjee, and Socolow, "Accelerating Progress in Climate Science". In particular, its philosophical orientation with regard to the interacting roles of theory, computation, and machine learning is one of the best articulated I have seen, and more broadly relevant than just for climate science. The emerging role of machine learning in the study of the atmosphere is a topic I've written about previously (here and here).
The authors write, "Researchers have made deductive inferences from fundamental physical laws with some success. But deducing, say, a coarse-grained description of clouds form the underlying fundamental physical laws has remained elusive. Similarly, brute-force computing will not resolve all relevant spatial scales anytime soon. Resolving just the meter-scale turbulence in low clouds globally would require about a factor of 10^11 increase in copmuter performance. Such a performance boost is implausible in the coming decades and would still not suffice to handle droplet and ice-crystal formation."
They continue, "Machine learning (ML) has undeniable potential for harnessing the exponentially growing volume of Earth observations that is available. But purely data-driven approaches cannot fully constrain the vast number of coupled degrees of freedom in climate models. Moreover, the future changed climate we want to predict has no observed analogue, which creates challenges for ML methods because they do not easily generalize beyond the training data."
The authors go on to describe a concept they call parametric sparsity while comparing Newtonian gravity (with a single free parameter) to Ptolemian epicycles and equants, "the deep learning approach of its time." They note that Newtonian gravity theory has a remarkable track record of "out-of-sample predictions, uncertainty estimates, and causal explanations." Ptolemy's theory, like deep learning, is a massively parameterized model of empirical data, overfitted to the training data, but providing little guidance on what to expect outside the training data, the authors seem to argue. The analogy is interesting but imperfect. As I noted previously, deep learning has demonstrated, under some circumstances, an ability to generalize beyond the training data. I wrote then, "We do not know under what circumstances such generalization can reliably
occur, and I believe any such claims about these generalizations must
be validated with independent data sets." Thus, the authors' skepticism about such generalizability is a welcome pragmatic attitude.
The authors write, "Climate science needs to predict a climate that hasn't been observed, on which no model can be trained, and that will only emerge slowly. Generalizability beyond the observed sample is essential for climate predictions, and interpretability is necessary to have trust in models. Additionally, uncertainties need to be quantified for proactive and cost-effective climate adaptation." They advocate for the use of theory to develop coarse-grained models for use in computational simulations. "Where theory reaches its limits, data-driven approaches can harness the detailed Earth observations now available." The authors' advocacy of theory-first, empirical modeling second, might be seen as an answer to Kerry Emanuel's concern about computing too much and thinking too little (discussed here).
I might depart a little from the authors in expressing some skepticism about the quality of uncertainty quantification. Any such quantification is likely to be done in the context of the model itself, and thus fail to account for model uncertainty, which can never be fully quantified. See also my discussion of "Escape from Model-Land" here.
Nonetheless, readers interested in climate science, and more broadly the interacting roles of theory, computation, and machine learning in the scientific endeavor (which truly must be coupled with experiment and observation) should check out the Physics Today article and think about how its ideas might apply to their own work.
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