$$P = f(\mathbf{s}; \theta)$$

Equation 1 · Materials Science

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This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

A structure-property model asserts a functional dependence $P = f(\mathbf{s}; \theta)$. where P is the target property, $\mathbf{s}$ is a structural descriptor vector (lattice parameters, coordination, bonding topology), and $\theta$ are parameters fit to a training set \{($\mathbf{s}_i$, $P_i$)\} . The equation is trivial; the content is entirely in what $\mathbf{s}$ includes and what range of $\mathbf{s}_i$ the training set spans. A model fit only on cubic perovskites extrapolates poorly to a layered structure even if the underlying physics is continuous, because f was never asked to fit that region.

Meanings in this article

• $P$: the target property, $\mathbf{s}$ is a structural descriptor vector (lattice parameters, coordination, bonding topology).
• $\theta$: parameters fit to a training set \{($\mathbf{s}_i$, $P_i$)\}.

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