The paper presents a modified physics-informed DeepONet (PI-DeepONet) architecture that reduces computational cost by eliminating redundancy in the Branch network’s handling of input functions across collocation points. The new formulation is mathematically equivalent to the original but uses smaller input tensors and fewer network evaluations, leading to faster training while maintaining comparable predictive accuracy on 1D, 2D, and 3D linear advection problems. Experiments show up to a 3.75× speed‑up in 2D and enable feasible training of 3D models on an NVIDIA A100 GPU, where the original architecture fails due to memory limits.
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.
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.
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:2609.14841v1 Announce Type: new Abstract: Scientific machine learning methods such as physics-informed neural networks (PINNs) increasingly rely on domain decomposition for better scalability w...
arXiv:2607. 18020v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
arXiv:2607. 18020v2 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) solve PDEs by incorporating physical constraints into neural-network training, but large-scale problems are limited by automatic-differentiation memory overhead and inefficient execution of grid-based PDE operators.
arXiv:2606. 04736v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have become a promising framework for simulating partial differential equations (PDEs) by embedding physical laws directly into neural network training.
arXiv:2602. 04940v2 Announce Type: replace Abstract: Deep learning has emerged as a transformative tool for the neural surrogate modeling of partial differential equations (PDEs), known as neural PDE solvers.
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).
arXiv:2607. 08025v1 Announce Type: new Abstract: While neural PDE solvers have demonstrated significant potential for accelerating engineering simulations, existing architectures remain constrained by high memory consumption and the single node bottleneck, where the maximum processable mesh resolution is strictly limited by the VRAM of a single compute unit.
arXiv:2608. 13629v1 Announce Type: cross Abstract: Clinically actionable, patient-specific hemodynamic assessment, specifically wall shear stress, vortex structure and pressure distributions, is critical for determining risky or unfavorable evolution in Abdominal Aortic Aneurysms (AAA).
arXiv:2502. 07209v4 Announce Type: replace Abstract: Physics-Informed Neural Networks (PINNs) seek to solve partial differential equations (PDEs) with deep learning.