Conventional neural networks learn predominantly through affine transformations followed by nonlinear activations, while elapsed time is often treated as an auxiliary feature or assumed to be uniforml...
The paper introduces the Spatiotemporal Conditional Operator (STCO), a framework for learning neural operators that can incorporate prescribed target‑time condition fields—such as body motion, inflow disturbances, or body‑force actuation—into time‑dependent PDE simulations. STCO combines a Flow‑Aware Graph Leaf (FAGL) partitioning scheme with Dual‑Site Feature‑wise Linear Modulation (DSFiLM) to inject these conditions before and after the core operator computation. Evaluated on twelve backbone architectures across an immersed‑boundary CFD benchmark, STCO achieves significant reductions in relative‑L2 field error (31.1%) and pressure‑derived load error (24.7%) while improving long‑lead predictions for most backbones.
By Xingxin Yang, Zhan Zhang, Juan Li
arXiv:2609. 19039v1 Announce Type: cross Abstract: We introduce the Long-Short-Range Neural Network (LSR-Net), a novel neural operator architecture designed for data-driven forward evolution modeling, and extends it to the prediction of nonlinear fluid dynamics.
By Qian Hou, Sutrisno, Yuqing Li, Zecheng Gan
The paper introduces the Frequency Selective Neural Network (FSNN), a new foundation architecture for time‑series learning that embeds advanced signal‑processing mathematics into its neural topology. By using a fully differentiable Wiener‑like filter bank optimized with complex‑domain backpropagation, FSNN autonomously discovers and isolates the precise physical modes of a given task, thereby avoiding the spectral entanglement that plagues CNNs, RNNs, and Transformers. Extensive evaluations show that FSNN achieves state‑of‑the‑art predictive performance, attaining 77.0 % average accuracy on the 10 multivariate UEA datasets and leading all major metrics on the imbalanced PTB‑XL ECG benchmark, while converging directly on physically meaningful frequency bands such as the cardiac QRS complex.
By Hui Huang, Ye Sun, Shiyan Hu
arXiv:2606. 16575v1 Announce Type: new Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.
By Yong Wang, Tao Zhou, Xuhui Meng
arXiv:2606. 16575v2 Announce Type: replace Abstract: Deep neural networks (DNNs) have achieved remarkable success in scientific computing, yet they often suffer from spectral bias in capturing oscillatory and multiscale behaviors.
By Yong Wang, Tao Zhou, Xuhui Meng