Before revision:  The resulting WSINDy _PDE algorithm uses separable test functions implemented efficiently via convolutions for discovery of PDE models with computational complexity O(NM)from data points with M = N ^{D+1(N^{D+1}\log(N)) for datasets with N points } in each of D+1 dimensions . We demonstrate on several notoriously challenging PDEsthe speed and accuracy with which WSINDy_PDE recovers the correct models from datasets with surprisingly large levels noise (often with levels of noise much greater than 10\%)(\log(N)) operations per datapoint).
After revision:  The resulting WSINDy _PDE algorithm uses separable test functions implemented efficiently via convolutions for discovery of PDE models with computational complexity O(NM)from data points with M = N ^{D+1(N^{D+1}\log(N)) for datasets with N points } in each of D+1 dimensions (i.e. \mathcal{O(\log(N)) operations per datapoint).