arXiv:2604.03321v1 Announce Type: cross Abstract: Machine learning, especially physics-informed neural networks (PINNs) and their neural network variants, has been widely used to solve problems involving partial differential equations (PDEs). The successful deployment of such methods beyond academic research remains limited. For example, PINN methods primarily consider discrete point-to-point fitting and fail to account for the potential properties of real solutions. The adoption of continuous activation functions in these approaches leads to local characteristics that align with the equation solutions while resulting in poor extensibility and robustness. A general explicit network (GEN) that implements point-to-function PDE solving is proposed in this paper. The "function" component can be constructed based on our prior knowledge of the original PDEs through corresponding basis functions for fitting. The experimental results demonstrate that this approach enables solutions with high robustness and strong extensibility to be obtained.

arXiv:2603.07521v1 Announce Type: cross Abstract: This work investigates large-scale sketch recognition from a graph-native perspective, where free-hand sketches are directly modeled as structured graphs rather than raster images or stroke sequences. We propose SketchGraphNet, a hybrid graph neural architecture that integrates local message passing with a memory-efficient global attention mechanism, without relying on auxiliary positional or structural encodings. To support systematic evaluation, we construct SketchGraph, a large-scale benchmark comprising 3.44 million graph-structured sketches across 344 categories, with two variants (A and R) to reflect different noise conditions. Each sketch is represented as a spatiotemporal graph with normalized stroke-order attributes. On SketchGraph-A and SketchGraph-R, SketchGraphNet achieves Top-1 accuracies of 83.62% and 87.61%, respectively, under a unified training configuration. MemEffAttn further reduces peak GPU memory by over 40% and training time by more than 30% compared with Performer-based global attention, while maintaining comparable accuracy.