A Metaheuristic for Amortized Search in High-Dimensional Parameter
  Spaces
Dominic Boutet Sylvain Baillet
Parameter inference for dynamical models of (bio)physical systems remains a
challenging problem. Intractable gradients, high-dimensional spaces, and
non-linear model functions are typically problematic without large
computational budgets. A recent body of work in that area has focused on
Bayesian inference methods, which consider parameters under their statistical
distributions and therefore, do not derive point estimates of optimal parameter
values. Here we propose a new metaheuristic that drives dimensionality
reductions from feature-informed transformations (DR-FFIT) to address these
bottlenecks. DR-FFIT implements an efficient sampling strategy that facilitates
a gradient-free parameter search in high-dimensional spaces. We use artificial
neural networks to obtain differentiable proxies for the model's features of
interest. The resulting gradients enable the estimation of a local active
subspace of the model within a defined sampling region. This approach enables
efficient dimensionality reductions of highly non-linear search spaces at a low
computational cost. Our test data show that DR-FFIT boosts the performances of
random-search and simulated-annealing against well-established metaheuristics,
and improves the goodness-of-fit of the model, all within contained run-time
costs.