Table 1.

Example 3.1: viscous Burgers’ equation. The feature space is made up of the terms from a third-order Taylor expansion using up to second-order derivatives. The coefficients are identified to within 1% in relative error. As the noise level increases, the approximation to the coefficients stays within two significant digits.

terms	coefficients, noise=2.0%	noise=19.5%	noise=94.5%
1	0	0	0
u	0	0	0
u2	0	0	0
u3	0	0	0
ux	0	0	0
$u_x^2$	0	0	0
$u_x^3$	0	0	0
uux	0.9953	0.9949	0.9948
u2ux	0	0	0
$u{u}_x^2$	0	0	0
uxx	0.0099	0.0099	0.0099
$u_{xx}^2$	0	0	0
$u_{xx}^3$	0	0	0
uuxx	0	0	0
u2uxx	0	0	0
$u{u}_{xx}^2$	0	0	0
uxuxx	0	0	0
$u_x^2{u}_{xx}$	0	0	0
$u_x{u}_{xx}^2$	0	0	0
uuxuxx	0	0	0