This paper introduces a method for discovering governing equations from data, called Sparse Identification of Nonlinear Dynamical Systems (SINDy). The method combines sparsity-promoting techniques with machine learning to identify the few important terms in nonlinear dynamical systems from measurement data. The key assumption is that physical systems have only a few relevant terms, making the governing equations sparse in a high-dimensional function space. This approach uses sparse regression to determine the minimal set of terms needed to accurately represent the data, resulting in parsimonious models that balance complexity with accuracy. The method is demonstrated on a range of problems, including simple canonical systems like linear and nonlinear oscillators and the chaotic Lorenz system, as well as fluid dynamics. The fluid example shows the method's ability to discover the underlying dynamics of a system that took experts nearly 30 years to resolve. The method also generalizes to parameterized, time-varying, or externally forced systems. The algorithm uses a library of nonlinear functions of the state variables to find the sparse combination of terms that best describe the dynamics. It is implemented using a sequential thresholded least-squares algorithm, which efficiently identifies the sparse solution. Cross-validation is used to determine the sparsification parameter, ensuring a good balance between model complexity and accuracy. The method is extended to handle discrete-time systems, high-dimensional systems, and systems with external forcing or bifurcation parameters. It is shown to work well with noisy data and can identify normal forms associated with bifurcation parameters. The method is applied to various examples, including the logistic map and the Hopf normal form, demonstrating its effectiveness in identifying parameterized dynamics. The results show that the method accurately captures the dynamics of complex systems, including chaotic systems and fluid flows, even with noisy data. The method is particularly effective in identifying the underlying structure of systems that are difficult to model with traditional approaches. The ability to discover governing equations from data represents a significant step toward the long-held goal of intelligent, unassisted identification of dynamical systems.This paper introduces a method for discovering governing equations from data, called Sparse Identification of Nonlinear Dynamical Systems (SINDy). The method combines sparsity-promoting techniques with machine learning to identify the few important terms in nonlinear dynamical systems from measurement data. The key assumption is that physical systems have only a few relevant terms, making the governing equations sparse in a high-dimensional function space. This approach uses sparse regression to determine the minimal set of terms needed to accurately represent the data, resulting in parsimonious models that balance complexity with accuracy. The method is demonstrated on a range of problems, including simple canonical systems like linear and nonlinear oscillators and the chaotic Lorenz system, as well as fluid dynamics. The fluid example shows the method's ability to discover the underlying dynamics of a system that took experts nearly 30 years to resolve. The method also generalizes to parameterized, time-varying, or externally forced systems. The algorithm uses a library of nonlinear functions of the state variables to find the sparse combination of terms that best describe the dynamics. It is implemented using a sequential thresholded least-squares algorithm, which efficiently identifies the sparse solution. Cross-validation is used to determine the sparsification parameter, ensuring a good balance between model complexity and accuracy. The method is extended to handle discrete-time systems, high-dimensional systems, and systems with external forcing or bifurcation parameters. It is shown to work well with noisy data and can identify normal forms associated with bifurcation parameters. The method is applied to various examples, including the logistic map and the Hopf normal form, demonstrating its effectiveness in identifying parameterized dynamics. The results show that the method accurately captures the dynamics of complex systems, including chaotic systems and fluid flows, even with noisy data. The method is particularly effective in identifying the underlying structure of systems that are difficult to model with traditional approaches. The ability to discover governing equations from data represents a significant step toward the long-held goal of intelligent, unassisted identification of dynamical systems.