The paper proposes Domain-aware Fourier Features (DaFFs) for Physics-Informed Neural Networks (PINNs), embedding domain-specific geometry and boundary conditions into the positional encoding. DaFFs eliminate the need for explicit boundary loss terms, simplify optimization, and reduce training cost, leading to orders-of-magnitude lower errors and faster convergence compared to vanilla PINNs and RFF-based PINNs. An LRP-based explainability framework further shows that DaFFs produce more physically consistent relevance attributions, improving interpretability.
arXiv:2502. 07209v4 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning.
The paper introduces beignet, a neural field architecture that replaces the random Fourier feature embedding in physics-informed neural networks with a trainable multi‑resolution Fourier feature pyramid. By using Fourier interpolation and spectral derivatives, beignet efficiently computes spatial derivatives and scales accuracy through the feature pyramid rather than the neural network size. Experiments show that beignet achieves more accurate PDE solutions with fewer parameters than existing PINN methods and can reach machine‑precision residuals on the inviscid Burgers blowup problem using the Adam optimizer.
arXiv:2607. 25608v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs) by embedding governing physical laws into deep neural networks.
arXiv:2606. 06164v1 Announce Type: new Abstract: Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data.
arXiv:2601.12971v2 Announce Type: replace Abstract: Physics-informed neural networks (PINNs) can be limited by coordinate representations and conflicting gradients from heterogeneous physical constra...
arXiv:2608. 05892v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) often fail to accurately resolve partial differential equations (PDEs) with high-frequency or multi-scale solutions, as well as strongly nonlinear problems.
arXiv:2510. 19399v2 Announce Type: replace Abstract: Spectral bias, the tendency of neural networks to learn low-frequency features first, is a well-known issue with many training algorithms for physics-informed neural networks (PINNs).
arXiv:2607. 14233v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have had a broad research impact in modeling domains governed by partial differential equations (PDE).
Physics-informed neural operators (PINOs) aim to learn solution operators for partial differential equations by using the governing physics as supervision, rather than relying solely on paired input-output simulation data. By incorporating physical constraints into the training objective, PINOs combine the cross-instance generalization of neural operators with the data efficiency of physics-informed learning.
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
The paper introduces an operator-informed initialization for Fourier Feature Physics-Informed Neural Networks (PINNs) to mitigate spectral bias, where certain frequencies converge slower. By analyzing training dynamics in the Neural Tangent Kernel regime, the authors derive an evolution equation linking convergence rates to the product of the differential operator’s symbol and the spectral density of initialization weights. They propose tailoring the initial weight distribution to the specific PDE, which balances convergence across frequencies and improves prediction accuracy without extra training cost, as confirmed by experiments on linear and nonlinear PDEs.
arXiv:2608. 14619v1 Announce Type: new Abstract: This work proposes a new interpretable neural operator framework, termed the Physics Informed Kernel Function Neural Operator (PIKFNO), which explicitly incorporates physics informed kernel functions derived from governing equations into the neural operator architecture.