SciML/DataDrivenDiffEq.jl

What it solves

It addresses the challenge of structural estimation and identification of differential equations from raw data. Instead of manually deriving a mathematical model, this tool allows users to automatically discover the underlying equations that govern a system's dynamics from observed data, which can then be used to simulate how the system behaves under different conditions.

How it works

The package uses a data-driven approach to identify the structure of differential equations. Users provide observed data (such as a solution to an ODE) and define a basis of potential functions (e.g., polynomial bases). The system then optimizes the selection of these functions to find the simplest and most accurate mathematical representation of the system's dynamics, identifying both the equations and the parameters involved.

Who it’s for

It is designed for researchers and engineers who work with dynamical systems and need to recover mathematical models from experimental or simulated data.

Highlights

• Automatically discovers differential equations from data.
• Supports structural estimation and identification.
• Enables simulation of perturbed dynamics based on discovered models.
• Integrates with the SciML ecosystem, including ModelingToolkit and OrdinaryDiffEq.