Implements the non-stationary input warping of Xiong, Chen, Apley & Ding (2007, Int. J. Numer. Meth. Engng). The domain \([0,1]\) is split into \(K+1\) intervals by \(K\) interior knots, each carrying a learnable positive slope \(s_k = \exp(r_k)\). The warp is: $$w(x) = \sum_{j<k} s_j (t_{j+1}-t_j) + s_k (x-t_k)$$ for \(x \in [t_k, t_{k+1})\), giving a continuous, monotone piecewise-linear function with \(K+1\) free parameters.
This is the same construction as the knots argument in
DiceKriging.
warp_knots(n_knots = 3, knot_positions = NULL)warp specification string, e.g. "knots(3)" or
"knots(0.25:0.5:0.75)"
number of interior knots \(K \ge 1\) (default 3)
optional numeric vector of \(K\) knot positions
strictly inside \((0,1)\), in increasing order.
When NULL (default), knots are placed uniformly at
\(1/(K+1), 2/(K+1), \ldots, K/(K+1)\).
Xiong, Y., Chen, W., Apley, D. & Ding, X. (2007). A non-stationary covariance-based Kriging method for metamodelling in engineering design. International Journal for Numerical Methods in Engineering, 71(6), 733--756.
WarpKriging