Fixed space before citation.
@@ -33,8 +33,7 @@ differential equations of practical interest with these techniques[@seefeldt2017
their expressibility is limited by their function representation.
Artificial neural networks (ANN) are a framework of machine learning algorithms that use a collection of connected units to
-learn function mappings. The most basic form of ANNs, multilayer perceptrons, have been proven to be universal function approximators
-[@hornik1989multilayer]. This suggests the possibility of using ANNs to solve differential equations. Previous studies have
+learn function mappings. The most basic form of ANNs, multilayer perceptrons, have been proven to be universal function approximators [@hornik1989multilayer]. This suggests the possibility of using ANNs to solve differential equations. Previous studies have
demonstrated that ANNs have the potential to solve ordinary differential equations (ODEs) and partial
differential equations (PDEs) with certain initial/boundary conditions [@lagaris1998artificial]. These methods show nice
properties including (1) continuous and differentiable solutions, (2) good interpolation properties, (3) less
