Table 1 Data comparison of PINN predicted values for cavity with Ref.11 at \(Ra=10^{3}\), \(10^{4}\), \(10^{5}\), and \(10^{6}\). The order of magnitude of the MSE loss and the runtime are also tabulated.
From: Physics-informed neural network simulation of thermal cavity flow
Parameter | \(Ra=10^3\) | \(Ra=10^4\) | \(Ra=10^5\) | \(Ra=10^6\) |
|---|---|---|---|---|
Nu | a | b | c | d |
\(|\psi |_{ref}\) location (x, z) | (0.5, 0.5) | (0.5, 0.5) | (0.5, 0.5) | (0.5, 0.5) |
\(|\psi |_{ref}\) | 1.174 | 5.071 | 9.111 | 16.32 |
\(|\psi |_{pred}\) | 1.173 | 5.065 | 9.116 | 16.38 |
\(u_{ref}\) location (x, z) | (0.5, 0.813) | (0.5, 0.823) | (0.5, 0.855) | (0.5, 0.850) |
\(u_{ref}\) | 3.649 | 16.178 | 34.73 | 64.63 |
\(u_{pred}\) | 3.643 | 16.135 | 34.74 | 64.81 |
\(w_{ref}\) location (x, z) | (0.178, 0.5) | (0.119, 0.5) | (0.066, 0.5) | (0.0379, 0.5) |
\(w_{ref}\) | 3.697 | 19.617 | 68.59 | 219.36 |
\(w_{pred}\) | 3.691 | 19.590 | 68.64 | 220.52 |
Loss order of magnitude | \(10^{-4}\) | \(10^{-4}\) | \(10^{-7}\) | \(10^{-6}\) |
Runtime | 24 min | 24 min | 4 h 2 min | 3 h 55 min |
