How do I use this package to pass analytical jvp?

[rveltz]

Hi,

Say I have the following vector field:

f(du,u,p,t) = @. du = -u^2

I know that the jacobian is given by

myjac(out,in,u,p,t) = @. out = -2 * u * in

How do I pass this information to ODEFunction or ODEProblem?

SciMLOperators.FunctionOperator is just asking for the linear op in the form op(out, in, p, t), but where is the information about u?

[ChrisRackauckas]

@avik-pal you just took a look through this could you comment?

[avik-pal]

myjac(out,in,u,p,t) = @. out = -2 * u * in

What is in? This looks like the JVP / VJP and not the Jacobian itself.

[rveltz]

yes that's the jvp

[avik-pal]

Right, see how the JacVec operator is defined. Instead of using ad for the internal op, you will have to specify it analytically for every u. The other option is the use the kwargs interface for FunctionOperator and pass in in as a kwarg, for this see the VecJac implementation. Both are in https://github.com/JuliaDiff/SparseDiffTools.jl/blob/master/src/differentiation/jaches_products.jl & https://github.com/JuliaDiff/SparseDiffTools.jl/blob/master/src/differentiation/vecjac_products.jl

[rveltz]

I thought DE would provide a built in solution like DiffEqOperator used to.

[ChrisRackauckas]

This seems like a mistake. You could use parameters here, but it feels off. The function operator is L(u,p,t) so that it defines mul!(y,L,x) to be y = L(u,p,t)*x. The u seems to just be lopped off here. You can do L((u,p),t)*x but that seems like a mistake. input isn't u: you're not necessarily always doing L(u,p,t)*u, so the state of the operator needs to update independent of the vector that is being multiplied.

Wouldn't this make JacVec easier to implement too?

[ChrisRackauckas]

We talked, FunctionOperator is just wrong. We need to fix that.

[rveltz]

👍

[vpuri3]

We have come across this issue before when trying to form nonlinear operators eg, f(u) * u, df(u)/du * u, etc with ComposedOperator (#159). This seemed like a design constraint for SciMLOperators, and so when writing SparseDiffTools.VecJac, we created the kwarg interface for FunctionOperator (#125). That would allow calls to VecJac like L(v, u, p, t; VJP_input = w) which is equivalent to v .= df(w)/dw * u (JuliaDiff/SparseDiffTools.jl#245). This interface wasn't extended to SparseDiffTools.JacVec but maybe it should have. I don't know what the current problem you're facing is, but maybe a similar solution for JacVec could help alleviate the problem?

[ChrisRackauckas]

That would allow calls to VecJac like L(v, u, p, t; VJP_input = w) which is equivalent to v .= df(w)/dw * u (JuliaDiff/SparseDiffTools.jl#245).

Let's standardize our notation.

w = L(u,p,t)*v

[ChrisRackauckas]

The L someone would define here is just L = FunctionOperator((w,v,u,p,t)-> ..., u, p, t), where update_coefficients!(L,u,p,t) updates the internal states.

[ChrisRackauckas]

L should have two calls:

• L(v,u,p,t) out of place
• L(w,v,u,p,t) in place

[rveltz]

Let's standardize our notation.

If I understand you well, L(u,p,t) is a linear operator representing the differential of say F(u,p,t) wrt to the first variable at position u.

[rveltz]

How is the progress on this issue?