Coupled equations

[dmaionchi]

Hi! I am trying to implement 2 pdes, solving one at a time. From the first one I obtain a variable that I need to include in the second one. The implementation of the first and second equations are: def pde1(x, y): rhoS=100 dUs_z = dde.grad.jacobian(y, x, i=0, j=0)
return rhoS*dUs_z - 1

def bio(x, y): Us = model.predict(x) y2 = Us*y drho_z = dde.grad.jacobian(y2, x, i=0, j=0) drho_t = dde.grad.jacobian(y, x, i=0, j=1)
return drho_t + drho_z - 1

But I'm getting the following error:

def array(self, dtype=None): 990 del dtype --> 991 raise NotImplementedError( 992 "Cannot convert a symbolic Tensor ({}) to a numpy array." 993 " This error may indicate that you're trying to pass a Tensor to" 994 " a NumPy call, which is not supported".format(self.name))

NotImplementedError: Cannot convert a symbolic Tensor (Placeholder_302:0) to a numpy array. This error may indicate that you're trying to pass a Tensor to a NumPy call, which is not supported. Could you please help me? I think it is something wrong with Us = model.predict(x). Thanks in advance.

[lululxvi]

This is not supported directly, but it is doable to re-implement code in another way to solve the problem.

[dmaionchi]

Hi! I implemented all equations in the same function. But I am having a problem with a second order equation. I define many variables as,
Us = y[:, 0:1] rhoS = [y[:, 1:2], y[:, 2:3], y[:, 3:4]] rhoGm = y[:,4:5] Ug = y[:,5:6] rhoG = [y[:,6:7]] and identify each derivative according to the component index. For example, for this case I use d2rhoG_z = dde.grad.hessian(y, x, component=6, j=0)
to write the equation: y_rhoG = d2rhoG_z However, it does not obtain a linear equation as expected. I also used the following boundary conditions: def boundaryL(x, on_boundary): return on_boundary and np.isclose(x[0], 0) def boundaryR(x, on_boundary): return on_boundary and np.isclose(x[0], 0.655) bcL_rhoG0 = dde.DirichletBC(geomtime, lambda x: 10, boundaryL) bcR_rhoG0 = dde.DirichletBC(geomtime, lambda x: 0, boundaryR) ic_rhoG0 = dde.IC(geomtime, lambda x: 0, lambda _, on_initial: on_initial) I don't know what the error can be. I tried to write the function just for rhoG, not needing the component and it worked. Then, it has something to do with the component? Thanks in advance for your answer.

[lululxvi]

I cannot understand your question. Could you explain more with a better code style?