| Abstract: |
| Scientific machine learning is transforming the field of data assimilation by providing accurate and cheap-to-evaluate surrogate models for many dynamical systems. In the first part of this talk, I will show that Fourier Neural Operators (FNOs) enjoy polynomial sample complexity for estimating the solution map of a wide class of evolution PDEs. Our theory leverages that these PDEs can be accurately approximated via spectral methods, and that these numerical schemes can in turn be efficiently learned using FNOs. In the second part of this talk, I will show that ensemble Kalman filters with machine-learned surrogate models achieve long-time filter accuracy under standard observability assumptions on the true dynamics and observation models. |
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