What is automatic differentiation

What is automatic differentiation? A tutorial and demonstration using JAX

Dr. Matt Bonney

Lecturer (assistance professor equivilant) at Swansea University

March 2026

Abstract:

As we explore the complex nature of nonlinear dynamics and joint mechanics, there is an increasing computational demand for simulation and evaluation of both physics-based and data-based models. However, who ever gets it right on the first go? Oftentimes we need to run some type of optimination, variable exploration, etc. to achieve a reasonable level of accuracy on any model prediction. Traditionally, these processes would require many functional evaluations that can easily lead to infeasibility for any non-academic system. To counteract this, increase computational costs, there has been a recent surge to return to the underlying mathematics and utilise some of the overlooked features of them to provide information that wasn't previously available. One common feature relates to the numerical derivatives of functions where a Taylor series expansion can be used instead of another function evaluation. To obtain this information, the field of automatic differentiation has been blossoming from complex step, to hyper-dual numbers, to graph-based evaluations. This talk will explain some of the fundamental mathematics used to obtain this information and provide a demonstration of how to gather this using the JAX package within python. A copy of the demonstration will be made available to allow for further investigation and learning for students.

Biography:

Dr. Matt Bonney is currently a lecturer (assistance professor equivilant) at Swansea University in Wales, UK. He is an alumni of the initial NOMAD, Joints, and TRC institutes and current investigates the multi-physical effects of thermal-vibration. Additionally, Matt is an expert on the use of Digital Twins and is the Early Career Researcher Lead Chair for the UKRI funded Network Plus for Digital Twins. When he isn't busy causing plastic deformation in the Brake-Reuss beam, he uses his thermal-vibrational chamber to explore the onset of nonlinearity and it's volatility with environmental conditions. Matt got his Ph.D. from the University of Wisconsin-Madison under Prof. Dan Kammer investigating the uncertainty propagation of substructuring models.