Which random is the best random? A study on sampling methods in Fourier surrogate modeling

Shaping and Dilating the Fitness Landscape for Parameter Estimation in Stochastic Biochemical Models

“…In the case of problems modified using a DF or a combination of DF and surF, we exploit the standard version of FST-PSO. All of the analyses were implemented in the Python programming language, exploiting the FST-PSO [14] and surF [13] libraries.…”

“…Another limitation that affects surF regards the algorithm used to generate the surrogate models, which is characterized by a high time and space complexity. As already discussed in [13], surF relies on DFT, which can calculate the multi-dimensional spectra of the fitness landscape from equispaced samples. That is, surF interpolates the samples over a multi-dimensional regular lattice, an operation characterized by exponential complexity.…”

“…Concerning the first settings, in this work, we assume σ = 100, generated using quasi random sampling using Sobol sequences [29], one of the five methods natively supported by surF along with pseudo-random generators, chaotic sequences, quantum random numbers, and entropic point packing [13] . Quasi-random sampling is surF's default because it was shown to be the most effective approach when a few samples can be collected [13].…”

“…Multi-modal, rugged, and noisy fitness landscapes-such as those typically associated with the PE problem of stochastic biochemical models-can be efficiently tackled with a surrogate modeling method called surF [12], which exploits the discrete Fourier transform. While surF is applied here on the landscape induced by a stochastic model, it can clearly be applied to a deterministic landscape, as carried out, for example, in [12,13]. A peculiarity of surF is that the number of low frequency spectral coefficients used for the inverse Fourier transform can be set to adjust the smoothness of the created surrogate model.…”