Least squares methods for Lorenz trajectories

I’ve been working with Qiqi Wang to implement a continuation method combined with a nonlinear least squares solver to approximate trajectories of the Lorenz equation at different parameter values. I used DOLFIN to build the solver, which interfaces with PETSc’s SNES. Here is a figure of the trajectories as a function of the R parameter. I started with a reference solution at R=30 and used the continuation method with the solver to take R down to 1.

lorenz

Click the figure for higher resolution. Here’s a link to the code. Check out Qiqi’s arXiv paper here.

You know, at some point we’ll update the pictures in the header of this blog. You’d think a blog called “simulation informatics” would have cool pictures.

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