When time is critical, running computationally expensive simulations (e.g. 3D CFD or detailed chemistry analysis) may not be practical. MoDS offers several fast-response surrogates that capture the behaviour of the underlying model, but which can be evaluated in a tiny fraction of the time. The following surrogate forms are available:

  • Polynomial
  • Kriging
  • High Dimensional Model Representation (HDMR)
  • Deep Kernel Learning (with optional auto-tuning of hyperparameters)
  • Thin-plate spline interpolation
  • Inverse distance weighting interpolation


HDMR is a technique well suited to models with many inputs/outputs.

  • Outputs are approximated by combinations of ortho-normal basis functions.
  • Surrogate construction is significantly faster than for a polynomial of the same order.
  • Global sensitivities of each output to each input follow naturally from the expansion coefficients.


Surrogate models can optionally be evaluated via APIs written in the following languages:

  • Java
  • MATLAB/Octave
  • gPROMS