Abstract
Many complex physical systems exhibit a rich variety of discrete behavioural modes. Often, the system complexity limits the applicability of standard modelling tools. Hence, understanding the underlying physics of different behaviours and distinguishing between them is challenging. Although traditional machine learning techniques could predict and classify behaviour well, typically they do not provide any meaningful insight into the underlying physics of the system. In this paper we present a novel method for extracting physically meaningful clusters of discrete behaviour from limited experimental observations. This method obtains a set of physically plausible functions that both facilitate behavioural clustering and aid in system understanding. We demonstrate the approach on the V-shaped falling paper system, a new falling paper type system that exhibits four distinct behavioural modes depending on a few morphological parameters. Using just 49 experimental observations, the method discovered a set of candidate functions that distinguish behaviours with an error of 2.04%, while also aiding insight into the physical phenomena driving each behaviour.
Highlights
Complex physical phenomena are often governed by highly non-linear, multidimensional dynamics
In this paper we present Physics Driven Behavioural Clustering (PDBC), a novel method that automates the process of discovering functions that enable behavioural clustering and physical understanding of systems with discrete behavioural modes
We address the challenging problem of clustering and understanding the falling behaviours in the V-Shaped Falling Paper (VSFP) system, which is a new contribution to the falling paper
Summary
Complex physical phenomena are often governed by highly non-linear, multidimensional dynamics. It can be challenging to understand these systems using traditional modelling tools, as we lack knowledge of the underlying physical phenomena required to implement these. The obvious course of action, is to infer these phenomena via physical experimentation. Schmidt and Lipson [1] developed an algorithm to automatically discover analytical relationships in dynamical systems, ranging from simple harmonic oscillators to more complex chaotic double pendulum systems. This was preceded by a method of non-linear model synthesis from directly observed data using co-evolution [2]. Data-driven approaches to modelling have shown the ability to predict behaviours of dynamic systems [4, 5]
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