From: A method for efficient Bayesian optimization of self-assembly systems from scattering data
1. Matern 3/2 (ARD): \(\sigma ^{2}(1+\sqrt {3}\sqrt {r}) * exp[-\sqrt {3}\sqrt {r}]\) |
2. Matern 5/2 (ARD): \(\sigma ^{2}(1+\sqrt {5}\sqrt {r}+(5r)/3) * exp[-\sqrt {5}\sqrt {r}]\) |
3. Rational Quadratic (ARD): σ2(1+r/(2α)−α |
4. Rational Quadratic (ISO): σ2(1+s/(2α)−α |
5. Gabor (ARD): \(h(x_{1} \!\,-\, x_{2}); h(t) \,=\, exp[\,-\,\sum \!((t.^{2})./(diag(P.^{2})]*cos[\!2\pi \!\sum \!(t./p)]\) |
6. Neural Network: \(\sigma ^{2} \arcsin {\left [x_{1}^{T}P x_{2} / \sqrt {\left (1 + x_{1}^{T}P x_{2}\right)*\left (1 + x_{1}^{T}P x_{2} \right) }\right ]} \) |
7. Square Exponential (ARD): σ2exp[−r/2] |
r=(x1−x2)T∗P−1∗(x1−x2);s=(x1−x2)T∗(ℓ∗I)−1∗(x1−x2) |
P is the diagonal matrix of ARD lengthscale hyperparameters. |
â„“ is a scalar lengthscale hyperparameter; I is the unit matrix. |
α is a shape hyperparameter for the rational quadratic kernel. |
p is a vector of period hyperparameters. |