Physics-Informed ML for Climate

Problem

Climate science faces a fundamental compute-accuracy tradeoff that standard deep learning cannot resolve. High-fidelity numerical models like general circulation models, ocean solvers, are prohibitively expensive to run at the spatial and temporal resolutions needed for regional impact assessment. Pure ML surrogates are fast but physically unreliable: they can produce predictions that look statistically plausible while violating conservation of mass, energy, or momentum. The bottleneck is the absence of a principled framework for combining the speed of learned models with the physical fidelity of numerical methods. The objective of this research was to survey the state of Physics-Informed Neural Networks applied to climate problems, synthesize the key design decisions and benchmark results across sub-fields, and produce a reference that helps practitioners navigate the space.

Approach

Conducted an independent systematic review of PINN architectures across climate science domains: atmospheric dynamics, ocean circulation, hydrology, and extreme event prediction. The review analyzes how physical laws are embedded into models, whether as hard architectural constraints, soft PDE-residual penalties in the loss function, or structural priors via Neural ODEs and universal differential equations, and evaluates the tradeoffs of each approach. Key findings include the persistent tension between tight constraint satisfaction and training stability, the strong empirical performance of hybrid architectures that combine PINNs with data assimilation, and the significant gap between benchmark accuracy and real-world deployment readiness. The paper synthesizes results across 60+ publications and proposes a taxonomy for categorizing physics-ML integration strategies by the mechanism, depth, and fidelity of physical supervision. A preprint is in preparation.

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