M-norm based loss for training data-driven models

A FEM loss is defined as $\parallel z_\Theta \parallel_M=\sqrt{z_\Theta^\top Mz_\Theta}$ where $z$ is a vector, $\Theta$ is a set of model parameters, and $M$ is the mass matrix of a discretized partial differential equation.

• Fast batch calculation using torch.sparse
• Availability of reconstruction loss $L_\Theta=\parallel \tilde v(\Theta)-v \parallel_M=\sqrt{(\tilde v(\Theta)-v)^\top M(\tilde v(\Theta)-v)}$