how to use pybamm.diff()

[xrfe]

when I create my submodel, one of the term on the right hand side depends on the time derivative, I then use pybamm.diff(),
e.g., dcdt = K*pybamm.diff(j_n, pybamm.t)
but got error:

` return self.left.diff(variable) + self.right.diff(variable)

File /pybamm/lib/python3.11/site-packages/pybamm/expression_tree/unary_operators.py:345 in diff
raise NotImplementedError

NotImplementedError`

Does anyone know how to solve the issue?
Thanks!

[brosaplanella]

I suspect this is to do with how j_n is defined. Can you provide a minimum working example?

[xrfe]

Thanks for the reply.
sorry for confision, my problem is
when creating models, how to implement time-derivatives of internal variables of pybamm, such as current density (j_n----d j_n / dt), overpotential (η ----- dη/dt)?
for example, (https://github.com/pybamm-team/PyBaMM/blob/develop/examples/scripts/create_model.py):
in Line 41:

N = -(1 / L) * D(c) * pybamm.grad(c) # solvent flux,

now if N depends on the derivative of any intermediate varialbles, e.g.,
N = -(1 / L) t0 d(D(c)/dt * pybamm.grad(c)
seems the function pybamm.Symbol.diff() does not work here.

[valentinsulzer]

It's best to refactor your equations so that the d/dt term is on the left-hand side and then add the rhs to model.rhs. If the d/dt term appears in multiple places then you can reuse the rhs expression. e.g.

da/dt = 2*a
db/dt = da/dt - b

becomes

da/dt = 2*a
db/dt = 2*a - b

If you have a system that can't be rearranged in this way let us know

[xrfe]

That's probably the standard way to implement d/dt. in case I don't have explicit expression for the right hand side, I tried to use pybamm.VariableDot(), e.g.,
j_n = pybamm.Variables("Negative electrode interfacial current density [A.m-2]")
dj_ndt = pybamm.VariableDot(j_n)
the error messege says the time derivative is on the right hand side.

[valentinsulzer]

Can you share the full system of equations? Number of equations should be equal to the number of variables, otherwise the system is not well defined

[xrfe]

besides the standard DFN equations, we have an additional equation for side reactions (li plating):
d c_Li/ dt = - a*exp(-k*dj_n/dt)*N_Li
the above equation quite resembles the default one in pybamm but add a coefficient function exp(k*dj_n/dt). so I have to access the derivative of the current density j_n, but it seems not able to directly use pybamm.VariableDot(j_n).

[brosaplanella]

If j_n is defined as d j_n / dt = ... then you can do what Valentin suggested above. If it is not, you can probably write d j_n / dt in terms of the other variables and apply the approach above.