arXiv:2602. 05352v3 Announce Type: replace Abstract: Modern neural networks have shown promise for solving partial differential equations over surfaces, often by discretizing the surface as a mesh and learning with a mesh-aware graph neural network.
Summary generated by The Flow from the publisher's feed. The full article lives at arXiv Machine Learning.
arXiv:2607. 11672v1 Announce Type: new Abstract: Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs.
Industrial design in fields such as vehicle and aerospace engineering often relies on large-scale numerical simulations to evaluate fluid dynamics performance, which can incur substantial computational costs. Deep neural networks have shown promise in improving simulation efficiency, especially graph neural networks (GNNs), which demonstrate great potential due to their flexibility with unstructured data.
arXiv:2607. 18309v1 Announce Type: new Abstract: Unsteady aerodynamic phenomena, such as gusts, turbulence, and fluid-structure interactions affect an aircraft during flight.
arXiv:2605. 21247v3 Announce Type: replace Abstract: Graph Neural Networks (GNNs) have emerged as a cornerstone of deep learning, with most existing methods rooted in graph signal processing and diffusion equations to model message passing.
arXiv:2608. 13827v1 Announce Type: new Abstract: Machine-learned physical surrogate models have become promising alternatives to mesh-based numerical solvers.
arXiv:2403. 11199v2 Announce Type: replace-cross Abstract: Unitarity is a useful principle for stabilizing deep neural networks, but in graph neural networks (GNNs) instability is induced not only by learnable parameters but also by the graph propagation operator.