A Competitive Learning Approach for Specialized Models: A Solution for Complex Physical Systems with Distinct Functional Regimes

TL;DR

This paper introduces a competitive learning method that trains multiple models simultaneously with dynamic loss functions to identify distinct regimes in complex physical systems, improving accuracy over traditional global models.

Contribution

It presents a novel competitive learning framework with dynamic loss functions for regime detection and model discovery in complex systems, enhancing data-driven modeling capabilities.

Findings

Successfully identifies functional regimes in complex systems

Discovers true governing equations from data

Reduces test errors compared to traditional methods

Abstract

Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately represent the system. In response to this challenge, we propose a novel competitive learning approach for obtaining data-driven models of physical systems. The primary idea behind the proposed approach is to employ dynamic loss functions for a set of models that are trained concurrently on the data. Each model competes for each observation during training, allowing for the identification of distinct functional regimes within the dataset. To demonstrate the effectiveness of the learning approach, we coupled it with various regression methods that employ gradient-based optimizers for training. The proposed approach was tested on various problems involving model discovery and function approximation, demonstrating its ability to successfully identify functional regimes, discover true governing equations, and reduce test errors.