Fourier Double Gate Physics-Informed Neural Networks for Multiscale PDE Solutions and Spatiotemporal Field Modeling
Abstract
Abstract Physics-Informed Neural Networks (PINNs) provide an effective framework for forward and inverse problems by jointly optimizing the residuals of partial differential equations together with initial and boundary conditions. However, standard multilayer perceptrons exhibit a pronounced spectral bias, and the different loss terms in PINNs often suffer from gradient and scale imbalance. As a result, PINNs may converge slowly or inadequately satisfy local constraints in mixed-frequency and multiscale problems. To address these issues, this paper combines multiscale Fourier feature encoding, a Double Gate network architecture, and adaptive loss weighting to construct a Fourier Double Gate PINN (FDG-PINN). Experiments on mixed-frequency partial differential equations (PDEs) demonstrate that FDG-PINN achieves lower relative errors under a unified frequency configuration. The FDG-PINN framework is subsequently applied to real-world temperature-field reconstruction and temporal extrapolation over northern South Asia and North China to evaluate its ability to reconstruct and extrapolate temperature fields characterized by complex nonlinear spatiotemporal dynamics.
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