no code implementations • 28 May 2021 • Mark Ainsworth, Justin Dong
We present a new approach to using neural networks to approximate the solutions of variational equations, based on the adaptive construction of a sequence of finite-dimensional subspaces whose basis functions are realizations of a sequence of neural networks.
no code implementations • 14 Jul 2020 • Mark Ainsworth, Yeonjong Shin
No assumptions are made on the number of neurons relative to the number of training data, and our results hold for both the lazy and adaptive regimes.
