A Metaheuristic for Amortized Search in High-Dimensional Parameter Spaces

TL;DR

This paper introduces DR-FFIT, a gradient-free metaheuristic that uses feature-informed transformations and neural network proxies to efficiently perform parameter inference in high-dimensional, non-linear models, outperforming traditional methods.

Contribution

The paper presents a novel metaheuristic, DR-FFIT, that enables efficient high-dimensional parameter search through feature-informed transformations and neural network-based gradients.

Findings

DR-FFIT improves performance of random search and simulated annealing.

It enhances model fit quality.

It maintains low computational costs.

Abstract

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.