Question about the reaction_inverse.py

[Xilun1995]

As the code shown, we used the training data to solve the inverse problem.

But I am confused what if observe_x1 is different from observe_x2?(anchor should be equal to observe_x1+observe_x2?) If not, how to define the anchor. Thank in advance.

observe_y1 = dde.PointSetBC(observe_x1, Ca, component=0) observe_y2 = dde.PointSetBC(observe_x2, Cb, component=1)

data = dde.data.TimePDE(
    geomtime,
    pde,
    [bc_a, bc_b, ic1, ic2, observe_y1, observe_y2],
    num_domain=2000,
    num_boundary=100,
    num_initial=100,
    anchors=????????????????????????????,
    num_test=50000,
)

[lululxvi]

Use the union of observe_x1 and observe_x2.

[engsbk]

anchors=geomtime.union((observe_x1, observe_x2, observe_x3))

shows an error:

AttributeError: 'GeometryXTime' object has no attribute 'union'

How to perform the union for 3 point sets?

Thank you in advance!

[lululxvi]

np.vstack

[santoss2020]

hello, I want to know how to solve a fractional differential equation in time with derivative of caputo using your framework for example u_t(caputo)-u_xx=f(x). thanks

[lululxvi]

No. But you can implement time derivative similar as the space derivative, see the fPINN paper.

[wangxiao2019]

Hello, I'm wondering if this framework can only solve spatial fractional derivatives of the Laplace operator. Also, in your paper titled "fPINNs: Fractional Physics-Informed Neural Networks", where in the framework's code module is the finite difference schemes for fractional derivatives, specifically the following equation, implemented? Finite difference schemes for fractional derivatives，$\begin{aligned} \frac{\partial^\gamma \tilde{u}(\boldsymbol{x}, t)}{\partial t^\gamma} \approx \mathcal{L}{\Delta t}^\gamma \tilde{u}(\boldsymbol{x}, t):=\frac{1}{\Gamma(2-\gamma)(\Delta t)^\gamma}\left{-c{\lceil\lambda t\rceil-1} \tilde{u}(\boldsymbol{x}, 0)+c0 \tilde{u}(\boldsymbol{x}, t)\right. & \ & \left.+\sum{k=1}^{\lceil\lambda t\rceil-1}\left(c{\lceil\lambda t\rceil-k}-c{\lceil\lambda t\rceil-k-1}\right) \tilde{u}(\boldsymbol{x}, k \Delta t)\right}\end{aligned}$ Where in the code is this part implemented?