Discovering-governing-equations_figure

Figure 1

Schematic of our algorithm for sparse identification of nonlinear dynamics, demonstrated on the Lorenz equations. Data is collected from measurements of the system, including a time history of the states X and derivatives Ẋ . Next, a library of nonlinear functions of the states, Θ(X), is constructed. This nonlinear feature library is used to find the fewest terms needed to satisfy Ẋ = Θ(X)Ξ. The few entries in the vectors of Ξ, solved for by sparse regression, denote the relevant terms in the right-hand side of the dynamics. Parameter values are σ = 10, β = 8/3, ρ = 28, (x0, y0, z0)T = (−8, 7, 27)T . The trajectory on the Lorenz attractor is colored by the adaptive time-step required, with red requiring a smaller tilmestep.