Message Passing Module

[dario-coscia]

Is your feature request related to a problem? Please describe.
Message-passing networks are everywhere now in SciML, from PDE modelling to molecule generation, and more. These models can be efficiently implemented using graph structures, specifically the PyG library. Nevertheless, PyG does not provide a complete list of message-passing networks (only the base ones), and it would be amazing to introduce these types of blocks/models in PINA.

Why Message Passing NNs?
Message Passing NNs excel at modelling relational data, capturing complex dependencies between nodes in graphs (e.g., social networks, molecules). They aggregate and propagate information between nodes, enabling learning from the graph's structure.

Why Equivariant Message Passing NNs?
Equivariant GNNs respect symmetries (e.g., rotations, translations) in the data, ensuring consistent predictions regardless of the graph's orientation or node arrangement. This boosts efficiency, accuracy, and generalization, particularly in applications like physics simulations and molecular modelling (more here).

Describe the solution you'd like
Implement message-passing algorithms starting from blocks and extending to models. In particular, we can implement:

• Standard Message-Passing Layers
  1. Interaction Networks (Battaglia et al. 2016)
  2. Deep Tensor Neural Networks (Schütt et al. 2017)
  3. Graph Convolutional Network (Kipf and Welling 2016) / Graph Attention Network (Petar Veličković et al. 2018) but these two are already in PyG
  4. ...
• Equivariant Message-Passing Layers
  1. E(n) Equivariant Graph Neural Networks (Satorras et. al 2022) E(n)-Equivariant
  2. Radial Fields (Köhler et al. 2019) E(n)-Equivariant
  3. SchNet (Schütt et al. 2017) E(n)-Equivariant

Above SE(n), E(n) indicate the Euclidean group in n-dimensions. Using stacks of multiple layers we can then easily implement models.

Additional context
Consider these papers to have further insights:
Relational inductive biases, deep learning, and graph networks
Neural Message Passing for Quantum Chemistry
E(n) Equivariant Graph Neural Networks