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utksi committed Jan 15, 2025
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MACE (Message Passing Atomic Cluster Expansion) is an equivariant message passing neural network that uses higher-order messages to enhance the accuracy and efficiency of force fields in computational chemistry.

### **Node Representation**
Each node $\large{i}$ is represented by:
Each node $$\large{i}$$ is represented by:

$$
\large{\sigma_i^{(t)} = (r_i, z_i, h_i^{(t)})}
$$

where $r_i \in \mathbb{R}^3$ is the position, $\large{z_i}$ is the chemical element, and $\large{h_i^{(t)}}$ are the learnable features at layer $\large{t}$.
where $$r_i \in \mathbb{R}^3$$ is the position, $$\large{z_i}$$ is the chemical element, and $$\large{h_i^{(t)}}$$ are the learnable features at layer $$\large{t}$$.

### **Message Construction**
Messages are constructed hierarchically using a body order expansion:
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