Figure 3 - uploaded by Zachary Cooper-Baldock
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Visual depiction of GMSE loss function operation. The reference ground truth CFD image from the dataset (a) is used to first produce a disparity array (b). The disparity array is then blurred, resulting in the blurred array (c). Finally, a weighting array (d) is produced, used to score the individual pixel loss during training for each new instance the generator provides. The grey appearance of (d) results due to the non-zero lowerbound, used to give weighting to the freestream of the flowfield.
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Computational fluid dynamics (CFD) simulations are crucial in automotive, aerospace, maritime and medical applications, but are limited by the complexity, cost and computational requirements of directly calculating the flow, often taking days of compute time. Machine-learning architectures, such as controlled generative adversarial networks (cGANs)...
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... of the GMSE loss function is sufficiently generalised to allow for velocity, pressure or density fields to be used to determine the weighting used for the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions ...
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... pressure or density fields to be used to determine the weighting used for the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions by the relative difference between adjacent cells/pixels, similar to a ...
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... the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions by the relative difference between adjacent cells/pixels, similar to a unidirectional spatial highpass filter. W d,x denotes the x-axis pixel disparity. This ...
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... of the GMSE loss function is sufficiently generalised to allow for velocity, pressure or density fields to be used to determine the weighting used for the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions ...
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... pressure or density fields to be used to determine the weighting used for the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions by the relative difference between adjacent cells/pixels, similar to a ...
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... the loss calculation. To calculate the Gradient Mean Squared Error (GMSE) loss, a series of modifications were made to the MSE loss equation. A visual depiction of this process is provided in Fig. 3, showing the process undertaken to determine the 2D weighting array (Fig. 3d) for the GMSE loss function operation using the ground truth flow field (Fig. 3a), disparity array ( First, element-wise subtraction was conducted with respect to the x (Eq. 3) and y axis (Eq. 4) of the ground truth field. This determined the gradient regions by the relative difference between adjacent cells/pixels, similar to a unidirectional spatial highpass filter. W d,x denotes the x-axis pixel disparity. This ...
