An Introduction to Sparse Identification of Nonlinear Dynamics for Engineering Applications

Overview of SINDy for Engineering

Many engineering systems are governed by complex, nonlinear dynamics that are often only partially understood. While black-box models like neural networks can predict system behavior, they lack physical interpretability and typically require massive datasets. The Sparse Identification of Nonlinear Dynamics (SINDy) framework offers an alternative by identifying the sparse, governing differential equations directly from time-series data. By selecting only the most relevant terms from a library of candidate functions, SINDy produces models that are both compact and physically meaningful.

Methodological Extensions

Standard SINDy is often insufficient for real-world engineering data, which is frequently noisy, irregularly sampled, or high-dimensional. This paper outlines several critical extensions to the core algorithm:

• Noise Robustness: Techniques such as total variation regularization and weak-form formulations allow the model to handle noisy sensor data without relying on unreliable numerical differentiation.
• Dimensionality Reduction: For high-dimensional systems, SINDy can be integrated with Proper Orthogonal Decomposition (POD), Dynamic Mode Decomposition (DMD), or autoencoders to discover dynamics in a compressed latent space.
• Constrained Learning: Incorporating prior physical knowledge—such as known kinematic constraints—allows the model to enforce specific structures while learning unknown force or moment terms.
• Uncertainty Quantification: Ensemble methods (bagging/bragging) and active learning strategies help quantify model uncertainty, which is essential when data is limited or expensive to acquire.

Practical Applications

The authors demonstrate these techniques through two primary case studies: the system identification of a quadcopter UAV and a chaotic thermosyphon heat exchanger. By using a constrained SINDy approach, the authors show that one can retain known rigid-body kinematics while simultaneously discovering the unknown aerodynamic forces and moments from flight test data. The accompanying tutorial provides a modular, step-by-step implementation that guides users from basic ODE identification to advanced, constrained, and noise-robust modeling.