Extremely Fast Surrogates for Large-Scale Models
Developed as part of a data assimilation system, we have implemented fast surrogates, that mimic the dynamics of a large-scale river-estuary-ocean simulations. The surrogates are trained on a database of simulations and used for fast prediction of the system state (water elevation, local salinity, temperature and velocity) given tidal, river flux, and atmospheric (wind fields, pressure, temperature, solar flux) forcings.
The data assimilation system developed by my group (Lu et al., Frolov et al. 2007, Frolov et al. 2008) uses sigma point Kalman filter techniques (developed at OHSU) for Bayesian estimation of the state (including all physical variables modeled by the circulation codes, and their history going back 30 hrs, corresponding to the longest tidal period).
The CORIE model grids typically carry 10^7 degrees of freedom. This prohibits data assimilation with a Kalman Filter based on the full circulation models. The solution lies in developing extreme acceleration for the model, in the form of fast surrogates that mimic the dynamics of the full circulation model in a very small fraction of the time required for the full model --- typically 1-12 thousand times faster. Our surrogates use recurrent neural networks executing on a reduced-dimensionality state space (van der Merwe et al. 2007). The animations linked below (xvid codec) show the salinity fields predicted by the full simulation (SELFE or ELCIRC codes), those salinity fields as rendered by the dimension-reduced (n=30-100) state approximation from principle component analysis (PCA) implemented by SVD, and the fields reconstructed from the neural network surrogate predictions.
This animation shows a transect through the estuary with the ocean boundary to the left of the left edge of the frame, and the river (Bonneville dam) boundary beyond the right edge of the frame. The vertical scale is greatly exaggerated. The bottom frame shows the prediction from the ELCIRC circulation code, the center frame shows that field reconstructed from the PCA subspace, the top frame shoes the fast surrogate prediction. Salinity is encoded by color; deep red is salt water, deep blue is fresh water. The tidal cycles of water elevation change and the salt wedge intrusion and expulsion from the estuary is evident, as is the fresh-water plume at the surface of the ocean region to the far left. The animation shows the operation of the surrogate for one week of data not in the training set. The surrogate predicts the behavior of the full model extremely accurately.
This animation shows the dynamics of the fresh-water plume in the near ocean region. The dynamics of the plume are sensitive to wind fields and up-welling and down-welling events, and the plume shape responds to Coriolis force. The SELFE circulation models in the left frame shows development of complex shapes in the plume and the strong differences in the plum from one tidal cycle to the next. The reconstruction of the salinity field from the low-dimensional PCA state estimate SELF model (labeled EOF in the middle frame) captures much of the dynamics of the plume, but shows some deviation as well. The prediction of the fast surrogate in the right frame shows some deviation from the PCA reconstruction of the field as well. Nonstationarities in the forcing conditions are responsible for much of the deviations and point to the need for more sophisticated dimensionality reduction and surrogate technology to more precisely capture plume dynamics. Nonetheless our current technology, coupled with Kalman filter state estimation apparatus, is capable of improving the raw model predictions in the plume (Frolov, 2007). As in the first video, the animation shows the predictions from the surrogate over a time period (10 days) not represented in the training set.