Cartesian Tensor
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Differentiable Particle-Mesh Ewald with Cartesian Tensor Message Passing for Learning Long-Range Electrostatics and Dipole Response
Announce Type: new Abstract: Machine learning interatomic potentials (MLIPs) can approach quantum accuracy for short-range chemistry, but most architectures remain local and fail to capture the long-range electrostatic and polarization interactions essential for ionic, polar, and interfacial systems. Recent Ewald-based MLIPs show that locally predicted electrostatic variables can recover important long-range physics, including multipolar response. However, many energy-based implementations...
A Cartesian-3j Framework for Machine Learning Interatomic Potentials
Announce Type: replace Abstract: Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by introduce the...
A Cartesian-3j Framework for Machine Learning Interatomic Potentials
Announce Type: replace-cross Abstract: Machine learning interatomic potentials (MLIPs) have brought substantial gains in the extrapolation capability in computational chemistry. However, most equivariant models are typically built with spherical tensors (STs), while Cartesian tensor formulations remain less developed despite their natural alignment with atomic coordinates and tensorial targets. In this work, we develop a Cartesian framework for irreducible Cartesian tensors (ICTs) by...
On graph products and multi-word-representability
arXiv:2603.29629v4 Announce Type: replace-cross Abstract: The multi-word-representation number $\mu(G)$ of a graph $G$ is the minimum number of word-representable graphs whose union is $G$. We study the behavior of $\mu$ under six standard graph products: the lexicographic, Cartesian, rooted, corona, tensor, and strong products. For the Cartesian and rooted products, we show that $\mu(G_1 \square G_2)=\mu(G_1 \diamond G_2)=\max\{\mu(G_1),\mu(G_2)\}$. For the corona product, we prove that...