arXiv:2602. 02547v2 Announce Type: replace-cross Abstract: Physics-Informed Neural Networks (PINNs) are effective methods for solving inverse problems and discovering governing equations from observational data.
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:2602. 09303v2 Announce Type: replace Abstract: We propose a physics-informed consistency modeling framework for solving partial differential equations (PDEs) via fast, few-step generative inference.
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: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.
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:2607. 15180v1 Announce Type: new Abstract: Ordinary differential equations (ODEs) are widely used to model dynamical systems in physics, biology, neuroscience, and physiology, but in many applications some equations of the dynamics are unknown and only a subset of the state variables are measured.
arXiv:2608. 04778v1 Announce Type: new Abstract: Physics-informed neural networks (PINNs) incorporate governing equations into neural-network training and can approximate PDE solutions without requiring large observational datasets.
arXiv:2607. 23940v1 Announce Type: new Abstract: Physics-Informed Neural Networks (PINNs) solve differential equations by minimizing the residual of a nonlinear operator over a neural parameterization of the solution.
arXiv:2601. 21284v2 Announce Type: replace-cross Abstract: Diffusion models have emerged as powerful generative tools for modeling complex data distributions, yet their purely data-driven nature limits applicability in engineering and scientific problems where physical laws must be respected.
arXiv:2509. 00203v3 Announce Type: replace Abstract: Parameterized partial differential equations (PDEs) underpin the mathematical modeling of complex systems in diverse domains, including engineering, healthcare, and physics.
arXiv:2409. 08958v3 Announce Type: replace-cross Abstract: Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability.
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.