Tutorial: a beginner’s guide to building a representative model of dynamical systems using the adjoint method

Building a representative model of a complex dynamical system from empirical evidence remains a highly challenging problem. Classically, these models are described by systems of differential equations that depend on parameters that need to be optimized by comparison with data. In this tutorial, we introduce the most common multi-parameter estimation techniques, highlighting their successes and limitations. We demonstrate how to use the adjoint method, which allows efficient handling of large systems with many unknown parameters, and present prototypical examples across several fields of physics. Our primary objective is to provide a practical introduction to adjoint optimization, catering for a broad audience of scientists and engineers. Multiple parameter estimation techniques are employed to empirically validate theoretical propositions regarding complex systems by discerning relevant free parameters from often scarce experimental data. In this tutorial, the authors provide a beginner’s guide to parameter estimation via adjoint optimization, and show its efficiency in prototypical problems across different fields of physics.