Predicting geological features in 3D seismic data

• The matrix M is a ground metric matrix, , with d the distance between two output locations k, k’. • T is a transport plan which matches the mass in the prediction to the ground truth . • Major difference with standard divergences: the Wasserstein loss differentiates between outputs that are small and large shifts of ground truth, with respect to the ground metric. • Learning requires computing gradient of the loss: this is a linear program, O(K3 log K) – often prohibitively complex. • A regularized approximation is efficient to compute: