[firedrake] Problem with Jacobian

[Lawrence Mitchell]

> On 5 Nov 2015, at 10:26, Stephan Kramer <s.kramer at imperial.ac.uk> wrote:
> 
> On 05/11/15 10:08, Lawrence Mitchell wrote:
>> 
>>> On 5 Nov 2015, at 09:49, Buesing, Henrik <HBuesing at eonerc.rwth-aachen.de> wrote:
>>> 
>>> Dear all,
>>> 
>>> I’m having a variable Sw, which I calculate pointwise in a routine calc_Sw (see attachment). This variable depends on my primary unknown h: Sw = (h-hn)/(hw-hn) (hn,hw known values).
>>> 
>>> But now it seems like automatic differentiation for this routine does not work. I’m getting zero entries for the Jacobian, whereas d(Sw)/dh = 1.0 should hold.
>> 
>> Yes, this is because the AD doesn't know about the relationship between Sw and dh.  UFL has a facility for this, but I notice we don't expose it in firedrake (however, it is straightforward to do):
>> 
>> 
>> We want
>> 
>> derivative(F, u)
>> 
>> But F contains a coefficient, S, whose derivative wrt u is 1.0 (however, they are not symbolically related in a way UFL understands).  So we build a mapping from this coefficient to its derivative wrt u:
>> 
>> coefficient_derivatives = {S: 1.0}
>> 
>> and then pass this additional information to the derivative call.
>> 
>> derivative(F, u, coefficient_derivatives=coefficient_derivatives)
>> 
>> Firedrake uses the UFL derivative function, but does not expose this extra argument in the interface.  It is straightforward to alter the definition in firedrake/ufl_expr.py to take this extra argument and pass it through.  If this works for you, do you want to propose a patch that adds this functionality?
>> 
>> Cheers,
>> 
>> Lawrence
>> 
> 
> Are you sure the problem isn't that he needs bounds for his solve? AFAICS dS/dh=0 for h<hw or h>hn. Otherwise shouldn't rewriting this with conditionals have worked? Henrik, I presume you are looking for a solution hw<h<hn ?


I didn't think hard about this, I simply considered that there's a functional relationship which UFL doesn't know about if you just pass in unrelated coefficients.

Lawrence
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