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Meshless Methods
=======================
For all computers and based methods we need to find a suitable discrete representation.
For all computer-based methods we need to find a suitable _discrete_ representation.
While this is straight-forward for cases such as data consisting only of integers, it is more challenging
for continuously changing quantities such as the temperature in a room.
While the previous examples have focused on aspects beyond discretization
@@ -52,9 +52,10 @@ amount of additional complexity in an implementation, and the arbitrary
connectivities call for _message-passing_ approaches between the nodes of a graph.
This message passing is usually realized using fully-connected layers, instead of convolutions.
Thus, in the following, we will focus on a particle-based method, which offers
the same flexibility in terms of spatial adaptivity as GNNs, but still
employs a convolution operator for learning the physical relationships.
Thus, in the following, we will focus on a particle-based method {cite}`ummenhofer2019contconv`, which offers
the same flexibility in terms of spatial adaptivity as GNNs. These were previously employed for
a very similar goal {cite}`sanchez2020learning`, however, the method below
enables a real convolution operator for learning the physical relationships.
## Meshless and particle-based methods