Fixing math...
@@ -65,7 +65,7 @@ The key idea of solving differential equations with ANNs is to reformulate the p
minimize the residual of the differential equations. In a very general sense, a differential equation can be expressed as
$$\mathcal{L}u - f = 0$$
where $\mathcal{L}$ is the differential operator, $u$ is the solution that we wish to find, and $f$ is a known forcing
-function. We denote the output of the neural network as $\hat{u}_{N}$. If $\widehat{u}_{N}$ is a solution to the differential
+function. We denote the output of the neural network as $u_{N}$. If $\widehat{u}_{N}$ is a solution to the differential
equation, then the residual $$\mathcal{R}\left(\widehat{u}_{N}\right) = \mathcal{L}\widehat{u}_{N} - f $$ will be identically zero.
One way to incorporate this into the training process of a neural network is to use the residual as the loss function. In
general, the $L^{2}$ loss of the residual is used. This is the convention that ``NeuroDiffEq`` follows, although we note
