You signed in with another tab or window. Reload to refresh your session.You signed out in another tab or window. Reload to refresh your session.You switched accounts on another tab or window. Reload to refresh your session.Dismiss alert
I am currently working with DeepXDE to solve a two-dimensional inverse problem by identifying five model parameters of a mathematical system composed of three partial differential equations (PDEs). I have a critical question regarding the initial conditions.
I understand that if I know the mathematical expression required to define the initial conditions, I can implement something like the following:
In this case, x[:, 0:1] represents the longitudinal coordinate (x-direction), and x[:, 1:2] represents the lateral coordinate (y-direction).
However, my question pertains to a situation where I do not have a formula for defining the initial condition but have known values at specific spatial points in matrix form. How can I use this matrix (or vector) in place of the formula? Specifically, I am uncertain about the values of x[:, 0:1] and x[:, 1:2]. Should these correspond to the points in the training dataset, or are they distinct from them?
I would greatly appreciate any guidance you could provide on this matter.
reacted with thumbs up emoji reacted with thumbs down emoji reacted with laugh emoji reacted with hooray emoji reacted with confused emoji reacted with heart emoji reacted with rocket emoji reacted with eyes emoji
-
Dear @lululxvi and the rest of the community,
I am currently working with DeepXDE to solve a two-dimensional inverse problem by identifying five model parameters of a mathematical system composed of three partial differential equations (PDEs). I have a critical question regarding the initial conditions.
I understand that if I know the mathematical expression required to define the initial conditions, I can implement something like the following:
def T_i_func(x):
return (0.57 * np.exp( - ((((x[:, 0:1] - 0.4) ** 2.0) / (0.1 ** 2.0)) +
(((x[:, 1:2] - 0.4) ** 2.0) / (0.1 ** 2.0)))) + 0.19)
ic_T = dde.icbc.IC(
spacetime, T_i_func, lambda _, on_initial: on_initial, component=0
)
In this case, x[:, 0:1] represents the longitudinal coordinate (x-direction), and x[:, 1:2] represents the lateral coordinate (y-direction).
However, my question pertains to a situation where I do not have a formula for defining the initial condition but have known values at specific spatial points in matrix form. How can I use this matrix (or vector) in place of the formula? Specifically, I am uncertain about the values of x[:, 0:1] and x[:, 1:2]. Should these correspond to the points in the training dataset, or are they distinct from them?
I would greatly appreciate any guidance you could provide on this matter.
Thank you in advance for your assistance.
Best regards,
K.V.
Beta Was this translation helpful? Give feedback.
All reactions