# Fitting a multivariate PDE (using Java)

I'm doing simulations of 2 coupled PDE's with Comsol Multiphysics. I want to fit some data (using the Application method, whose language is Java) to those simulations.

In order to answer my question you don't need to know what is Comsol Multiphysics or what is an Application Builder don't worry :)

So basically the equations look like : $$\phi_t=\nabla.(\lambda\nabla\mu(\phi))+\Gamma(\phi,n)\tau_1$$ and $$n_t=D\nabla^2+G(\phi,n)\tau_2$$.

And I have 3 parameters to fit :$$\lambda,\tau_1,\tau_2$$.

Here is a curve of the data with a curve of a simulation : So I heard about many methods to fit univariate functions like the Bisection method, or the Brent-Decker, but I was wondering about how to apply them to a multivariate function, and more than this to my case with the simulation.

I was also wondering if there was a tool in Java to do it.

If I omitted some things are not clear in what I wrote please ask :)