פירמידות תכונות פורייה לרשתות נוירונים מודעות פיזיקה

תקציר מקורי באנגליתarXiv:2605.24278v2 Announce Type: replace Abstract: We present an improved neural field architecture for solving partial differential equations (PDEs). Current physics-informed neural networks (PINNs) provide a flexible framework for solving PDEs, but they struggle to achieve highly accurate solutions and require computation that scales poorly with parameter count. Our model, which we call beignet (Bandlimited Embedding with Interpolated Grid Network), replaces the random Fourier feature embedding used by existing PINN models with a trainable multi-resolution Fourier feature pyramid. To query beignet at a continuous coordinate, we use Fourier interpolation at each level of the pyramid to return features at the input coordinate, and then decode this vector with a fully-connected neural netw