Complexity reduction of physical models: an equation-free approach by means of scaling

TL;DR

This paper introduces a scale-dependent, equation-free method for reducing the complexity of physical models by identifying parameters and terms that can be discarded without losing essential predictive capabilities.

Contribution

It presents a general, model-independent approach that quantifies conditions for asymptotic model reduction based on scale and dimension interplay.

Findings

Provides explicit thresholds for parameter reduction

Applicable to various physical models including projectile dynamics

Helps mitigate over-parameterization and improve calibration

Abstract

The description of complex physical phenomena often involves sophisticated models that rely on a large number of parameters, with many dimensions and scales. One practical way to simplify that kind of models is to discard some of the parameters, or terms of underlying equations, thus giving rise to reduced models. Here, we propose a general approach to obtaining such reduced models. The method is independent of the model in use, i.e., equation-free, depends only on the interplay between the scales and dimensions involved in the description of the phenomena, and controls over-parametrization. It also quantifies conditions for asymptotic models by providing explicitly computable thresholds on values of parameters that allow for reducing complexity of a model, while preserving essential predictive properties. Although our focus is on complexity reduction, this approach may also help with calibration by mitigating the risks of over-parameterization and instability in parameter estimation. The benefits of this approach are discussed in the context of the classical projectile model.