sup3r.utilities.loss_metrics.GeothermalConductiveHeatTransferLoss

class GeothermalConductiveHeatTransferLoss(dx, dy, depths=range(0, 8000, 1000), temperature_prefix='t', heat_flux_prefix='q', thermal_conductivity_prefix='k')

Bases: Sup3rLoss

Deviation from three-dimensional conductive heat transfer.

This loss evaluates the conductive heat-transfer PDE residual described in [1] using predicted temperature, thermal conductivity, and surface heat flow. Temperature features are expected in C, thermal conductivity features in W/m-K, and heat-flow features in mW/m^2.

The loss requires temperature and thermal conductivity channels at each requested depth and a single surface heat-flow channel at 0 m. Expected feature names are <temperature_prefix>_<depth>m (e.g. “t_1000m”), <thermal_conductivity_prefix>_<depth>m (e.g. “k_1000m”), and q_0m.

References

[1]

Aljubran, M. J., and Horne, R. N., “Thermal Earth model for the conterminous United States using an interpolative physics-informed graph neural network,” Geothermal Energy, vol. 12, no. 1, article 25, 2024. doi:10.1186/s40517-024-00304-7.

Initialize the conductive heat-transfer loss

Parameters:

• dx (float) – Horizontal grid spacing along the x dimension in m.

• dy (float) – Horizontal grid spacing along the y dimension in m.

• depths (iterable of int, optional) – Depth levels in m used to assemble the temperature and thermal conductivity feature channels. Depths must include 0 m and be uniformly spaced so the vertical derivative can be evaluated.

• temperature_prefix (str, optional) – Prefix used for temperature channels in C. Expected feature names are <temperature_prefix>_<depth>m.

• heat_flux_prefix (str, optional) – Prefix used for heat-flow channels in mW/m^2. This loss requires a surface heat-flow feature only, named <heat_flux_prefix>_0m.

• thermal_conductivity_prefix (str, optional) – Prefix used for thermal-conductivity channels in W/m-K. Expected feature names are <thermal_conductivity_prefix>_<depth>m.

Methods

call(y_true, y_pred)	Invokes the Loss instance.
from_config(config)	Instantiates a Loss from its config (output of get_config()).
get_config()	Returns the config dictionary for a Loss instance.

Attributes

LOSS_METRIC

__call__(__, x_gen)

Evaluate the conductive heat-transfer loss

Parameters:

• x_true (tf.tensor) – Ground truth data (unused).

• x_gen (tf.tensor) – Synthetic generator output used to compute the conductive heat-transfer residual. The feature axis must contain temperature channels in C, thermal conductivity channels in W/m-K, and a surface heat-flow channel in mW/m^2. Shape must be either: (n_observations, spatial_1, spatial_2, features) or (n_observations, spatial_1, spatial_2, temporal, features)

Returns:

tf.tensor – 0D tensor loss value

abstract call(y_true, y_pred)

Invokes the Loss instance.

Args:

y_true: Ground truth values. shape = [batch_size, d0, .. dN],

except sparse loss functions such as sparse categorical crossentropy where shape = [batch_size, d0, .. dN-1]

y_pred: The predicted values. shape = [batch_size, d0, .. dN]

Returns:

Loss values with the shape [batch_size, d0, .. dN-1].

classmethod from_config(config)

Instantiates a Loss from its config (output of get_config()).

Args:

config: Output of get_config().

Returns:

A Loss instance.

get_config()

Returns the config dictionary for a Loss instance.