arXiv:2608. 08788v1 Announce Type: cross Abstract: Koopman theory offers a linear-operator view of nonlinear sequence dynamics by lifting observations into a space where evolution is governed by a linear time-invariant Koopman operator.
arXiv:2410. 23467v3 Announce Type: replace Abstract: Recurrent neural networks are a successful neural architecture for many time-dependent problems, including time series analysis, forecasting, and modeling of dynamical systems.
The paper introduces K$^2$SVD, a method that learns the leading singular functions of the Koopman operator by optimizing a Hilbert-Schmidt objective, producing a low‑rank, interpretable Koopman representation with a compact latent space. In this space, temporal evolution is modeled with a linear Gaussian state‑space model and inference is performed via Kalman filtering to reduce noise accumulation in multi‑step predictions. Experiments demonstrate that K$^2$SVD outperforms state‑of‑the‑art methods on multiple datasets, achieving faster prediction speeds and lower computational cost.
The paper introduces m-WCN, an end‑to‑end deep learning framework that neuralizes multi‑wavelet decomposition to jointly extract temporal patterns and frequency components from time series. Two task‑specific architectures built on m‑WCN—TFBC for classification and FTB for forecasting—are shown to outperform baseline models on 64 UCR datasets and seven forecasting benchmarks, achieving average improvements of nearly 20% in both tasks. The approach leverages trainable convolutional operators and orthogonality constraints to produce interpretable multi‑resolution representations.
The paper introduces m-WCN, an end‑to‑end deep learning framework that neuralizes multi‑wavelet decomposition to jointly extract temporal patterns and frequency components from time series. It enforces orthogonality constraints to produce interpretable multi‑resolution representations, and builds two task‑specific architectures—TFBC for classification and FTB for forecasting—on top of this foundation. Experiments on 64 UCR datasets and seven forecasting benchmarks show that TFBC and FTB outperform baseline models, achieving average improvements of about 20% in both classification and forecasting tasks.
arXiv:2605. 11287v2 Announce Type: replace-cross Abstract: A persistent paradox in time-series forecasting is that structurally simple MLP and linear models often outperform high-capacity Transformers.
arXiv:2606. 17996v1 Announce Type: cross Abstract: Cyclicity and trend are important components of time series data and many studies based on cyclicity and trend have achieved good results in long-term time series forecasting.
arXiv:2607. 00197v1 Announce Type: new Abstract: Long-horizon multivariate time series forecasting (LTSF) remains challenging due to non-stationarity, regime shifts, and error accumulation.
arXiv:2607. 08234v1 Announce Type: cross Abstract: Real-world time series exhibit complex dynamics characterized by multiple simultaneous temporal patterns: short-term fluctuations, periodic seasonal cycles, long-term trends, and irregular abrupt changes.
arXiv:2606. 17070v1 Announce Type: cross Abstract: Accurate oceanic forecasting is critical for climate monitoring and disaster early warning.
The paper introduces DNBNet, a Debiased Neural Basis-Function Network designed for irregular time series forecasting. It addresses two main limitations of existing methods: asymptotic bias from ignoring timestamp sampling density and limited adaptability of predefined basis functions. DNBNet employs importance sampling to correct bias, neural‑network parameterized basis functions for flexibility, a multi‑scale decomposition with mass‑aware fusion for sparse data, and a dual‑branch decoder, achieving strong performance across diverse real‑world datasets.
arXiv:2609.37435v1 Announce Type: new Abstract: Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabli...
arXiv:2608. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.