How can I use Automatic differentiation tools to specify gradient to fsolve?

Hello reader,

I have a nonlinear ODE system. I intend on using an iterative solver to calculate the steady-state(SS) solution of the system. I am aware that I can just wait for the ODE to settle to the steady-state value but that would take much longer as I need to calculate the SS response for few hundred conditions.

Currently I am using fsolve to find the root of the ODE function. However, it takes too long to estimate the Jacobian using the finite difference method. A MWE of my implementation is as follows,

classdef myClass < handle
    properties
        someProperty = [];
    end
    
    methods
        function response = steadyStateResponse(self,inp)
            % Some preprocesssing
            
            options =   optimoptions('fsolve','Algorithm','trust-region-dogleg','Display','off');
            
            [tOut, x]   =   fsolve(@(x)self.myODE(x,inp),xInit,options);
        end
    end
    
    methods (Access = private)
        function [dXdt] = myODE(self,x,inp)
            % Some output
            dXdt = [];      % Array of n x 1; n being number of equations
        end
    end
end

The problem that I face now is that for each iteration fsolve has to compute the Jacobian using finite differences. It is not possible to get an analytical expression of the Jacobian, so I was thinking of using AD to calculate the jacobian at each point. I found dlgradient as the implementation of AD in matlab. However, it works with dlarray. Some functions that I am using don't support dlarray.

How can I make this work? Any help is appreciated.

Thank you very much.

Answer 1

[Ranjeet]

As per my understanding, there is data incompatibility issue while using some functions. It is suggested to first convert the 'dlarray' type data to 'matrix' and then use with the functions not accepting 'dlarray' as input.

You may use the 'extractdata' method to get the underlying data from 'dlarray' to a 'matrix' type.

The following MATLAB answer can also be referred -

https://www.mathworks.com/matlabcentral/answers/505775-how-to-convert-dlarray-into-matrix

[Dhruv Thakkar]

Hi Ranjeet, I have already tried 'extractdata' for this. But I still run into errors and I seems I am adding the overhead to convert the data. Is there a more efficient way to provide the gradients?