How to run parameters optimization for my model using the GPU

Essentially, I have a model with given a set of parameters is able to calculate different thermodynamic properties for different compounds, let's say liquid densities and vapor pressures for example.

When I want to regress the model parameters (e.g. a,b,c,d,e) by fitting data for different compounds, I usually do a lot of sequential operations that I am sure I can easily improve their efficiency. I am thinking about multiobjective optimization or even better-using GPU or multicores of the CPU. But I am a bit lost on where to start from reading just the documentation.

So within my objetive function I usually have something like:

[fval]= objective_function(a,b,c,d,e)
input_comp1=f(constants,a,b,c,d,e)
input_comp2=f(constants,a,b,c,d,e)
exp_density1=load some text file or so.
exp_density2=load some text file or so.
exp_vaporpressure1=load some text file or so.
exp_vaporpressure2=load some text file or so.
densities_1=density(a,b,c,d,e,input_comp1)
vapor_pressures1=vapor_pressures(a,b,c,d,e,input_comp1)
densities_2=density(a,b,c,d,e,input_comp2)
vapor_pressures=vapor_pressures (a,b,c,d,e,input_comp2)
ARD_d1=expression for deviations between experimental and calculated values for density of comp.1
ARD_d2=...
ARD_p1=...
ARD_p2=...
fval= ARD_d1+ARD_d2+ARD_p1+ARD_p2

Which is then evaluated by something like fminsearch but I have also used others in the past, fminsearch worked the best for me. When I do this for just one component It works fast enough for my purpose (but I am a patient man). But now I've extended the model in a way that I need to regress parameters simultaneous from more than one component and it becomes impossible.

I am quite sure this way of doing the calculations can be improved because I can run the calculations for the different compounds simultaneous instead of doing them sequentially, and then evaluate fval when the calculations for all components are done. But how?

[Joss Knight]

Have you tried the UseParallel setting of optimoptions? I'm not sure it works for fminsearch though, you might have to change your solver.

[Matt J]

@Emanuel,

Are the number of parameters and data points always the same across the set of regressions you are trying to do?

[Emanuel Crespo]

@Joss Knight fminsearch does not support useparallel but assuming I could use other optimization routine, I could try to have a parfor cycle that goes between 1 to the number of different components to which I want to fit my parameters. But I am not sure if that will work.

@Matt J The number of parameters is the same with those 5 or 6 parameters I know everything to calculate any component. However, the number of experimental data points may differ between components. But assuming I can decide to use the same number of data points for each component. I am not understanding why would that be helpful? Can you please ellaborate on it?

Thank you