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.
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.
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.
arXiv:2511. 06609v4 Announce Type: replace Abstract: The accurate forecasting of complex, high-dimensional dynamical systems from observational data is a fundamental task across numerous scientific and engineering disciplines.
arXiv:2608. 13215v1 Announce Type: new Abstract: Forecasting the long-horizon evolution of mechanical systems from position-only observations is a pivotal yet difficult task, as hidden velocities and trajectory-specific physical properties must be inferred simultaneously.
arXiv:2608.29579v1 Announce Type: new Abstract: Chaotic time series forecasting is a challenging task due to its sensitivity to initial conditions and long-term unpredictability. Traditional methods...
arXiv:2608. 04471v1 Announce Type: cross Abstract: Time series in real-world applications are often generated by nonlinear dynamical systems, making accurate forecasting challenging.
arXiv:2606. 19984v1 Announce Type: new Abstract: Reservoir computing offers a lightweight framework for forecasting dynamical systems but may struggle to capture long-range dependencies due to limited representational capacity.
The paper introduces a data‑adaptive nonlinear vector autoregression (NVAR) model that replaces fixed polynomial or random feature maps with a shallow, trainable multilayer perceptron (MLP). By jointly training the MLP and a linear readout via gradient‑based optimization, the model learns data‑driven nonlinearities while maintaining a simple readout structure, improving scalability in high‑dimensional settings. Experiments on several chaotic systems, both noise‑free and synthetically noisy, show that this adaptive NVAR outperforms standard NVAR, a leaky echo state network (ESN), and a hybrid ESN in predictive accuracy, demonstrating robust forecasting under noisy conditions.
This paper introduces a data‑driven neural power‑iteration algorithm for approximating the dominant eigenfunctions (modes) of the Koopman operator in nonlinear dynamical systems. By avoiding explicit construction of the operator’s projection, the method sidesteps the curse of dimensionality that plagues expressive neural templates. The authors provide theoretical convergence guarantees tied to sample size and network width, and demonstrate through numerical experiments that the approach yields accurate, smooth mode approximations without the drawbacks of traditional techniques such as extended dynamic mode decomposition.
arXiv:2607. 11272v1 Announce Type: cross Abstract: Accurate dengue forecasting is crucial for public health planning, but remains challenging because incidence series are often short, noisy, non-stationary, nonlinear, and often affected by long-range temporal dependence.
A modular deep Recurrent Neural Network (RNN) is presented that enables easy deployment of various RNN architectures and automatic derivative computation for gradient-based learning. The modular design introduces new architectures, notably one with feedforward inter‑layer connections, which markedly improves the RNN’s ability to learn high‑order dynamics and nonlinearities while mitigating vanishing/exploding gradients. These advantages are illustrated through a quadrotor altitude dynamics case study, where the proposed network learns the model more quickly and generalizes better than existing methods.
arXiv:2506.12809v2 Announce Type: replace Abstract: The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects o...