Physics-Informed Semi-Supervised Multibranch UKAN for Prestack Fluid-Factor Inversion

Abstract

The Gassmann fluid term is a key parameter for characterizing reservoir properties. To address the limitations of traditional inversion methods in handling nonlinear responses, the constraints imposed by fixed activation functions in conventional deep learning (DL) models, and the gradient conflict problem in multiparameter inversion, this study proposes a physics-informed semi-supervised multibranch U-shaped Kolmogorov–Arnold network (PI-SS-MUKAN). Based on the Kolmogorov–Arnold representation theorem, the proposed method replaces conventional fixed activation functions with learnable B-spline functions, enhancing the model’s capability to approximate the nonlinear relationships in complex seismic signals. A single-encoder–three-decoder decoupled architecture is designed to independently reconstruct density, shear modulus, and the fluid term, effectively reducing gradient interference among different parameters. In addition, a semi-supervised strategy with an embedded differentiable physical forward modeling layer is introduced. By performing forward reconstruction and residual regularization on unlabeled data, this strategy compensates for the scarcity of well-log labels while imposing strict physical constraints. Application results demonstrate that the proposed method effectively resolves gradient conflicts and nonlinear fitting difficulties, significantly improving the accuracy and physical consistency of fluid identification.