arXiv:2609.24947v1 Announce Type: new Abstract: Neural operators evaluate parametric partial differential equations cheaply but degrade sharply outside their training distribution. Physics-informed n...
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:2602.08515v3 Announce Type: replace-cross Abstract: This work investigates shallow physics-informed neural networks (PINNs) for solving forward and inverse problems governed by nonlinear partia...
arXiv:2606. 19754v1 Announce Type: new Abstract: Partial differential equations (PDEs) play a central role in modeling complex physical, biological, and engineering systems.
arXiv:2608. 00850v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) have emerged as a versatile approach for solving nonlinear partial differential equations (PDEs), yet achieving high accuracy efficiently using these techniques remains challenging for high-dimensional or multiscale systems.
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.
Gen-PINNs introduces a deterministic residual-adversarial framework that combines Generative Adversarial Networks with Physics-Informed Neural Networks to solve partial differential equations. The method addresses limitations of standard PINNs—such as spectral bias, loss imbalance, and optimizer stagnation—by using a generator that learns the PDE solution with dynamically weighted physics-informed losses and discriminators that assess residuals against zero-residual states. Experiments on nonlinear and higher-order PDEs (Burgers, Allen‑Cahn, Kuramoto‑Sivashinsky) show significant gains in accuracy and convergence, especially for sharp-front, stiff, and high-order problems.
arXiv:2607. 26490v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful paradigm for solving partial differential equations (PDEs), yet their performance heavily relies on the manual, trial-and-error engineering of neural representations, loss formulations, and optimization dynamics.
The paper introduces a physics-constrained neural network surrogate that learns the microstructural evolution of binary mixtures governed by the Cahn‑Hilliard equation. By imposing conservation of the order parameter as a hard constraint on the network output, the model accurately predicts long‑time phase‑separation dynamics for both critical and off‑critical mixtures, maintaining mixture composition and matching the Lifshitz‑Slyozov domain‑growth law. A variant that enforces conservation only through a penalty term drifts from the initial composition and loses predictive accuracy over long rollouts, underscoring the necessity of the hard constraint for stability.
arXiv:2604. 07366v2 Announce Type: replace Abstract: Partial differential equations (PDEs) govern nearly every physical process in science and engineering, but solving them at scale remains prohibitively expensive.
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:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.