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:2608.29892v1 Announce Type: new
Abstract: Learning solution operators for partial differential equations (PDEs) on irregular and geometry-dependent domains remains a central challenge in scient...
By Abdolmehdi Behroozi, Chaopeng Shen
Quantum SEDONet is a quantum-enhanced deep operator network that embeds spectral features—Fourier for periodic coordinates and Chebyshev for bounded, non‑periodic coordinates—directly into the trunk network. This coordinate‑wise spectral embedding is achieved without adding qubits or circuit depth under unary amplitude encoding, and it reduces mean relative L2 error by up to 54.1% across four PDE benchmarks compared to the baseline Quantum DeepONet. The method demonstrates that quantum and classical inference paths agree to within 10⁻⁸, and it allows simultaneous use of both spectral bases within a single problem, as shown in a mixed‑boundary Poisson channel example.
By Muhammad Abid, Arth Sojitra, Bipin Tiwari, Omer San
arXiv:2607. 22516v1 Announce Type: cross Abstract: A central design principle in modern machine learning and artificial intelligence is to align a model's inductive bias with the structure of its input data.
By Peiyong Wang, Udaya Parampalli, Casey R. Myers
arXiv:2608. 08207v1 Announce Type: cross Abstract: Multivariate Time Series Classification (MTSC) demands models that can effectively capture complex temporal patterns across multiple scales while remaining computationally efficient.
By Pingping Liu, Muyao Wang, Zijian Zhang, Tongshun Zhang, Hao Miao, Guorui Xie, Qingliang Li, Qiuzhan Zhou
arXiv:2606. 11518v1 Announce Type: cross Abstract: Fourier neural operators (FNOs) are effective and efficient surrogates for approximating solutions of PDEs and generalize across discretizations.
By Pengqing Shi, Jie Yin, Stephen Tierney, Junbin Gao
Euclidean Fourier Neural Operators (EFNOs) extend Fourier neural operators by making the spectral kernel a continuous function of physical wavevectors, thereby removing dependence on specific periodic domain shapes and sizes. This domain‑independent formulation allows EFNOs to learn operators that generalize across different grid resolutions and domain geometries. Experiments on a heat equation and a materials‑science task demonstrate that EFNOs can successfully transfer learned mappings to unseen grid sizes and crystal structures.
By Nathanael Bosch, Niklas Frederik Schmitz, Michael F. Herbst
arXiv:2604. 07421v3 Announce Type: replace Abstract: Full-waveform inversion (FWI) is pivotal for reconstructing high-resolution subsurface velocity models but remains computationally intensive and ill-posed.
By Zhenyu Wang, Peiyuan Li, Yongxiang Shi, Ruoyu Wu, Chenfei Liao, Lei Zhang
Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges. A major difficulty arises from the time reparameterization invariance of time series data, which complicates the extraction of meaningful temporal features.
The paper introduces Neural Fourier Surrogates (NFS), a stochastic classical neural network that learns coefficients over a finite Fourier series support similar to quantum neural networks (QNNs). By testing on tabular benchmark datasets, NFS demonstrates competitive classification performance against established classical baselines and data‑reuploading QNNs. The authors also compare the learned Fourier spectra of QNNs and NFS on synthetic data, positioning NFS as a natural classical baseline for evaluating QNN performance.
By Oliver Knitter, Jonathan Mei, Sang Hyub Kim, Chi Chen, Masako Yamada, Martin Roetteler
arXiv:2607. 07634v1 Announce Type: cross Abstract: Time series analysis plays a vital role across a wide range of scientific and engineering domains but poses substantial computational challenges.
By Leonardo Nogueira Falabella, Vasily Sazonov
arXiv:2606. 27815v1 Announce Type: cross Abstract: Dynamic Time Warping (DTW) is a cornerstone for time series classification, but its reliance on Euclidean distances fails to capture latent cross-channel correlations in complex multivariate data.
By Diego Alvarez-Estevez, Alejandro Mayorga-Redondo, Eduardo Mosqueira-Rey