A Dual-Objective Meta-Learning Physics-Informed Neural Network for multi-condition hydraulic fracture geometry prediction

Dynamic adjustment of hydraulic fracturing operating parameters to achieve rapid and accurate predict ion of hydraulic fracture geometry (HFG) under multiple operating conditions is essential for optimizing fracturing schemes and quantitatively evaluating reservoir stimulation effects. However, existing studies on multi-condition HFG prediction remain limited. Parameterized PINNs and neural operators can reduce repetitive training to some extent, but the former may encounter optimization difficulties as the operating range expands, while the latter often suffers from accuracy degradation when training data are insufficient. Therefore, this paper proposes a Dual-Objective Meta-Learning Physics-Informed Neural Network (DOM-PINN) framework. This framework constructs a PINN model based on the PKN model for hydraulic fracture propagation and introduces two objective modules: (1) a multi-condition PINN transferable parameter initialization module; and (2) a multi-condition PINN loss weight adaptive prediction module. The proposed method adopts a bi-level meta-learning strategy. In the inner loop, PINN parameters are adapted to the current operating condition. In the outer loop, the adapted PINN parameters are used to construct the loss and jointly update the two modules. The updated modules are then used to initialize PINN parameters and assign loss weights for new operating conditions, enabling fast and accurate prediction with only a few samples and update steps. Experiments on multi-condition HFG prediction with varying fracturing-fluid viscosity and Young’s modulus show that DOM-PINN achieves faster convergence and higher accuracy than baseline methods using fewer update steps.