arXiv:2608. 10389v1 Announce Type: cross Abstract: In recent years, neural networks have significantly advanced numerical solutions of partial differential equations (PDEs).
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2607. 15291v1 Announce Type: cross Abstract: We develop a physics-informed neural network (PINN) framework for nonlocal partial differential equations arising in dynamic density functional theory (DDFT).
arXiv:2607. 28762v1 Announce Type: new Abstract: This work embeds feature interaction modules derived from factorization machines (FMs) into physics-informed neural networks (PINNs) and neural operator learning, to enhance model expressiveness for solution manifolds of parameterized partial differential equations (PDEs).
arXiv:2601. 00473v4 Announce Type: replace-cross Abstract: We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms.
arXiv:2607. 20541v1 Announce Type: cross Abstract: We introduce HypNO, a graph-based neural operator for scalar hyperbolic conservation laws.
arXiv:2606. 01179v1 Announce Type: cross Abstract: Entropy production governs irreversibility and uncertainty in both physical and information-theoretic systems.
arXiv:2606. 07982v1 Announce Type: new Abstract: High-dimensional transient heat diffusion under noisy boundary conditions exposes a fundamental limitation of classical numerical methods: accuracy degrades catastrophically where physical noise is unavoidable.