Before revision:  This construction makes it extremely robust to noise and applicable to small data sets  and, contrary to other deep learning methods, does not require a training set and is impervious to overfitting. We illustrate this approach on several physical problems , such as the Burgers', Korteweg-de Vries , advection-diffusion and Keller-Segel equations, and find that it requires as few as O (10^2) samples and works at noise levels up to 75 \%.
After revision:  This construction makes it extremely robust to noise and applicable to small data sets and, contrary to other deep learning methods, does not require a training set . We benchmark our approach on several physical problems , such as the Burgers', Korteweg-de Vries , advection-diffusion and Keller-Segel equations, and find that it requires as few as O (10^2) samples and works at noise levels up to 75 \%.