Table 1 Comparison of variables and parameters between the two PINN models.
Category | Symbol | Meaning | Type | Classical PINN | Hybrid PINN |
|---|---|---|---|---|---|
State Variable | \(\:\theta\:(z,t)\) | Water Content | Model output | Objective Function of the Network Prediction | |
Input Variable | \(\:z/t\) | Depth/Time | Model Input | Range [0, Z]/Range [0, t] | |
\(\:\theta\:(z,0)\) | Initial Water Content | Residual of Initial Conditions Incorporated into the Loss Function | |||
\(\:\theta\:\left(0,t\right)\) \(\:\:\theta\:({z}_{0},t)\) | Upper and Lower Boundary Conditions | Residual of Boundary Conditions Incorporated into the Loss Function | |||
Hydrus-1D Data | \(\:{\theta\:}_{data}(z,t)\) | Water Content Field | Data-Driven Input | Not Incorporated | Incorporation |
Soil Parameters | \(\:{\theta\:}_{s}\),/\(\:{\theta\:}_{r}\) | Saturated/Residual Water Content | Calibrated Parameters | See Table 2 | |
\(\:{K}_{s}\) | Saturated Hydraulic Conductivity | ||||
\(\:\alpha\:/m/n\) | VG Model Parameters | ||||
