Arvind, me, and Jonah released a new pre-print on some pen and paper analysis of fundamental failure modes and old school stability analysis for neural PDEs typically used in AI for Science application. https://arxiv.org/abs/2411.15101. 1/n
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Many intrinsic instabilities, errors, failure to generalize in neural PDE/ODE, hybrid models, ML-based parameterization, e.g., in climate models is cast under the blanket of generalization error, sometimes, OOD error, especially in “extrapolation regime”. In this paper, we revisit this.
We show that some of these issues arise from structural difference in numerics, grid resolution, ICs in IVPs, and the errors can be analytically expressed ( via Taylor series expansions), diagnosed a priori with linear stability analysis. We can say a lot about the model behavior and failure mode.
I guess, being careful about the discretization difference between the training data (ERA5), the IC (some other obs product), and numerics in the JAX solver. Some of the instabilities in online models might have nothing do with physics, but simply diff in grid/numerics. Love to chat more.
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