How to include non-linear derivative terms

[reveperdu]

I'm trying to use pysindy to find the governing equations from data, but preliminary attempts do not converge, and I suspect the equations might contain non-linear derivatives, such as dx/dt=x(dx/dt)^2+(d2x/dt2). But I'm not sure how to do this, as function library does not seem to specify derivative terms. Is this feature supported?

[Jacob-Stevens-Haas]

You need to pre-calculate the dx/dt term and pass it as a system coordinate. As your example is linear in d2x/dt2, you should be able to discover d2x/dt2 = dx/dt - x(dx/dt)^2 with a PolynomialLibrary of degree 3