How to recover models from data using DataDrivenDiffEq.jl

In this talk, we will address the problem of data-driven estimation and approximation of completely or partially unknown systems using DataDrivenDiffEq.jl. We will start by giving a short introduction to the field of symbolic regression in general followed by an example of its practical use. Here we learn how to (a) set up a DataDrivenProblem, (b) use ModelingToolkit.jl to incorporate prior knowledge, (c) use different algorithms to recover the underlying equations.

How do we model the friction in the joint of a robot, biological feedback signal, or the influence of seemingly unrelated parameters on our dynamical system?

With the rise of machine learning the classical domain of modeling is becoming more and more driven by data. While the automated discovery of possibly complex relations can help in gaining new insights, classical equations still dominate state-of-the-art machine learning models in terms of extrapolation capabilities and explainability. DataDrivenDiffEq.jl provides a unified application programming interface to define and solve these problems. It brings together operator-based inference, sparse, and symbolic regression to bridge the gap from black to white-box models.

After a brief theoretical introduction to the theory of system identification, currently implemented algorithms, and their underlying models we will explore the conceptual layer of the software. Within the Hands-on example, we will see how DataDrivenDiffEq.jl API mimics the mathematical formulation, builds upon and extends ModelingToolkit.jl, SymbolicUtils.jl, and Symbolics.jl to allow expression-based modeling, and seamlessly integrates into the Scientific Machine Learning ecosystem to solve a variety of estimation problems.