As a crucial approach for constructing subsurface velocity models, traveltime tomography derives the velocity distribution of the subsurface medium by solving an inverse problem constrained by observed traveltime data. However, in physics-informed neural network (PINN) traveltime tomography, the weighting between the data misfit term and the physical constraint term often relies on manual experience, making adaptive balancing difficult. This can lead to slow convergence or even cause the network to be trapped in local optima. Therefore, a neural tangent kernel (NTK) based adaptive weight optimization method for PINN traveltime tomography is proposed. First, to address the challenge of optimizing multi-objective loss functions, a dynamic weight adjustment mechanism is constructed based on the NTK theory. Second, the trace of the NTK is used to characterize gradient flow and to adaptively balance the contributions from the data and physical constraint terms. Finally, this mechanism optimizes the training process by addressing gradient imbalance, accelerating convergence of the PINN, and enhancing inversion stability. Synthetic benchmarks and field-data applications demonstrate that the proposed method improves training stability for complex velocity models and yields superior inversion results compared to traditional fixed-weight PINNs.
Tang et al. (Mon,) studied this question.