Optimizing Parallel Schemes with Lyapunov Exponents and kNN-LLE Estimation

Inverse parallel schemes remain indispensable tools for computing the roots of nonlinear systems, yet their dynamical behavior can be unexpectedly rich, ranging from strong contraction to oscillatory or chaotic transients depending on the choice of algorithmic parameters and initial states. A unified analytical-data-driven methodology for identifying, measuring, and reducing such instabilities in a family of uni-parametric inverse parallel solvers is presented in this study. On the theoretical side, we derive stability and bifurcation characterizations of the underlying iterative maps, identifying parameter regions associated with periodic or chaotic behavior. On the computational side, we introduce a micro-series pipeline based on kNN-driven estimation of the local largest Lyapunov exponent (LLE), applied to scalar time series derived from solver trajectories. The resulting sliding-window Lyapunov profiles provide fine-grained, real-time diagnostics of contractive or unstable phases and reveal transient behaviors not captured by coarse linearized analysis. Leveraging this correspondence, we introduce a Lyapunov-informed parameter selection strategy that identifies solver settings associated with stable behavior, particularly when the estimated LLE indicates persistent instability. Comprehensive experiments on ensembles of perturbed initial guesses demonstrate close agreement between the theoretical stability diagrams and empirical Lyapunov profiles, and show that the proposed adaptive mechanism significantly improves robustness. The study establishes micro-series Lyapunov analysis as a practical, interpretable tool for constructing self-stabilizing root-finding schemes and opens avenues for extending such diagnostics to higher-dimensional or noise-contaminated problems.

Trend-Adjusted Time Series Models with an Application to Gold Price Forecasting

Time series data play a critical role in various fields, including finance, healthcare, marketing, and engineering. A wide range of techniques (from classical statistical models to neural network-based approaches such as Long Short-Term Memory (LSTM)) have been employed to address time series forecasting challenges. In this paper, we reframe time series forecasting as a two-part task: (1) predicting the trend (directional movement) of the time series at the next time step, and (2) forecasting the quantitative value at the next time step. The trend can be predicted using a binary classifier, while quantitative values can be forecasted using models such as LSTM and Bidirectional Long Short-Term Memory (Bi-LSTM). Building on this reframing, we propose the Trend-Adjusted Time Series (TATS) model, which adjusts the forecasted values based on the predicted trend provided by the binary classifier. We validate the proposed approach through both theoretical analysis and empirical evaluation. The TATS model is applied to a volatile financial time series (the daily gold price) with the objective of forecasting the next days price. Experimental results demonstrate that TATS consistently outperforms standard LSTM and Bi-LSTM models by achieving significantly lower forecasting error. In addition, our results indicate that commonly used metrics such as MSE and MAE are insufficient for fully assessing time series model performance. Therefore, we also incorporate trend detection accuracy, which measures how effectively a model captures trends in a time series.

Wavelet-Driven Masked Multiscale Reconstruction for PPG Foundation Models

Wearable foundation models have the potential to transform digital health by learning transferable representations from large-scale biosignals collected in everyday settings. While recent progress has been made in large-scale pretraining, most approaches overlook the spectral structure of photoplethysmography (PPG) signals, wherein physiological rhythms unfold across multiple frequency bands. Motivated by the insight that many downstream health-related tasks depend on multi-resolution features spanning fine-grained waveform morphology to global rhythmic dynamics, we introduce Masked Multiscale Reconstruction (MMR) for PPG representation learning - a self-supervised pretraining framework that explicitly learns from hierarchical time-frequency scales of PPG data. The pretraining task is designed to reconstruct randomly masked out coefficients obtained from a wavelet-based multiresolution decomposition of PPG signals, forcing the transformer encoder to integrate information across temporal and spectral scales. We pretrain our model with MMR using ~17 million unlabeled 10-second PPG segments from ~32,000 smartwatch users. On 17 of 19 diverse health-related tasks, MMR trained on large-scale wearable PPG data improves over or matches state-of-the-art open-source PPG foundation models, time-series foundation models, and other self-supervised baselines. Extensive analysis of our learned embeddings and systematic ablations underscores the value of wavelet-based representations, showing that they capture robust and physiologically-grounded features. Together, these results highlight the potential of MMR as a step toward generalizable PPG foundation models.

TimeMar: Multi-Scale Autoregressive Modeling for Unconditional Time Series Generation

Generative modeling offers a promising solution to data scarcity and privacy challenges in time series analysis. However, the structural complexity of time series, characterized by multi-scale temporal patterns and heterogeneous components, remains insufficiently addressed. In this work, we propose a structure-disentangled multiscale generation framework for time series. Our approach encodes sequences into discrete tokens at multiple temporal resolutions and performs autoregressive generation in a coarse-to-fine manner, thereby preserving hierarchical dependencies. To tackle structural heterogeneity, we introduce a dual-path VQ-VAE that disentangles trend and seasonal components, enabling the learning of semantically consistent latent representations. Additionally, we present a guidance-based reconstruction strategy, where coarse seasonal signals are utilized as priors to guide the reconstruction of fine-grained seasonal patterns. Experiments on six datasets show that our approach produces higher-quality time series than existing methods. Notably, our model achieves strong performance with a significantly reduced parameter count and exhibits superior capability in generating high-quality long-term sequences. Our implementation is available at https://anonymous.4open.science/r/TimeMAR-BC5B.

Nonlinear Dynamic Factor Analysis With a Transformer Network

The paper develops a Transformer architecture for estimating dynamic factors from multivariate time series data under flexible identification assumptions. Performance on small datasets is improved substantially by using a conventional factor model as prior information via a regularization term in the training objective. The results are interpreted with Attention matrices that quantify the relative importance of variables and their lags for the factor estimate. Time variation in Attention patterns can help detect regime switches and evaluate narratives. Monte Carlo experiments suggest that the Transformer is more accurate than the linear factor model, when the data deviate from linear-Gaussian assumptions. An empirical application uses the Transformer to construct a coincident index of U.S. real economic activity.

IceWatch: Forecasting Glacial Lake Outburst Floods (GLOFs) using Multimodal Deep Learning

Glacial Lake Outburst Floods (GLOFs) pose a serious threat in high mountain regions. They are hazardous to communities, infrastructure, and ecosystems further downstream. The classical methods of GLOF detection and prediction have so far mainly relied on hydrological modeling, threshold-based lake monitoring, and manual satellite image analysis. These approaches suffer from several drawbacks: slow updates, reliance on manual labor, and losses in accuracy when clouds interfere and/or lack on-site data. To tackle these challenges, we present IceWatch: a novel deep learning framework for GLOF prediction that incorporates both spatial and temporal perspectives. The vision component, RiskFlow, of IceWatch deals with Sentinel-2 multispectral satellite imagery using a CNN-based classifier and predicts GLOF events based on the spatial patterns of snow, ice, and meltwater. Its tabular counterpart confirms this prediction by considering physical dynamics. TerraFlow models glacier velocity from NASA ITS_LIVE time series while TempFlow forecasts near-surface temperature from MODIS LST records; both are trained on long-term observational archives and integrated via harmonized preprocessing and synchronization to enable multimodal, physics-informed GLOF prediction. Both together provide cross-validation, which will improve the reliability and interpretability of GLOF detection. This system ensures strong predictive performance, rapid data processing for real-time use, and robustness to noise and missing information. IceWatch paves the way for automatic, scalable GLOF warning systems. It also holds potential for integration with diverse sensor inputs and global glacier monitoring activities.

How does downsampling affect needle electromyography signals? A generalisable workflow for understanding downsampling effects on high-frequency time series

Automated analysis of needle electromyography (nEMG) signals is emerging as a tool to support the detection of neuromuscular diseases (NMDs), yet the signals' high and heterogeneous sampling rates pose substantial computational challenges for feature-based machine-learning models, particularly for near real-time analysis. Downsampling offers a potential solution, but its impact on diagnostic signal content and classification performance remains insufficiently understood. This study presents a workflow for systematically evaluating information loss caused by downsampling in high-frequency time series. The workflow combines shape-based distortion metrics with classification outcomes from available feature-based machine learning models and feature space analysis to quantify how different downsampling algorithms and factors affect both waveform integrity and predictive performance. We use a three-class NMD classification task to experimentally evaluate the workflow. We demonstrate how the workflow identifies downsampling configurations that preserve diagnostic information while substantially reducing computational load. Analysis of shape-based distortion metrics showed that shape-aware downsampling algorithms outperform standard decimation, as they better preserve peak structure and overall signal morphology. The results provide practical guidance for selecting downsampling configurations that enable near real-time nEMG analysis and highlight a generalisable workflow that can be used to balance data reduction with model performance in other high-frequency time-series applications as well.

Split-and-Conquer: Distributed Factor Modeling for High-Dimensional Matrix-Variate Time Series

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise) and allocated to node servers, where each node estimates the row (or column) loading matrix via two-dimensional tensor PCA. These local estimates are then transmitted to a central server and aggregated, followed by a final PCA step to obtain the global row (or column) loading matrix estimator. Given the estimated loading matrices, the corresponding factor matrices are subsequently computed. Unlike existing distributed approaches, our framework preserves the latent matrix structure, thereby improving computational efficiency and enhancing information utilization. We also discuss row- and column-wise clustering procedures for settings in which the group memberships are unknown. Furthermore, we extend the analysis to unit-root nonstationary matrix-variate time series. Asymptotic properties of the proposed method are derived for the diverging dimension of the data in each computing unit and the sample size $T$. Simulation results assess the computational efficiency and estimation accuracy of the proposed framework, and real data applications further validate its predictive performance.

EvoMorph: Counterfactual Explanations for Continuous Time-Series Extrinsic Regression Applied to Photoplethysmography

Wearable devices enable continuous, population-scale monitoring of physiological signals, such as photoplethysmography (PPG), creating new opportunities for data-driven clinical assessment. Time-series extrinsic regression (TSER) models increasingly leverage PPG signals to estimate clinically relevant outcomes, including heart rate, respiratory rate, and oxygen saturation. For clinical reasoning and trust, however, single point estimates alone are insufficient: clinicians must also understand whether predictions are stable under physiologically plausible variations and to what extent realistic, attainable changes in physiological signals would meaningfully alter a model's prediction. Counterfactual explanations (CFE) address these "what-if" questions, yet existing time series CFE generation methods are largely restricted to classification, overlook waveform morphology, and often produce physiologically implausible signals, limiting their applicability to continuous biomedical time series. To address these limitations, we introduce EvoMorph, a multi-objective evolutionary framework for generating physiologically plausible and diverse CFE for TSER applications. EvoMorph optimizes morphology-aware objectives defined on interpretable signal descriptors and applies transformations to preserve the waveform structure. We evaluated EvoMorph on three PPG datasets (heart rate, respiratory rate, and oxygen saturation) against a nearest-unlike-neighbor baseline. In addition, in a case study, we evaluated EvoMorph as a tool for uncertainty quantification by relating counterfactual sensitivity to bootstrap-ensemble uncertainty and data-density measures. Overall, EvoMorph enables the generation of physiologically-aware counterfactuals for continuous biomedical signals and supports uncertainty-aware interpretability, advancing trustworthy model analysis for clinical time-series applications.

Kolmogorov Arnold Networks and Multi-Layer Perceptrons: A Paradigm Shift in Neural Modelling

The research undertakes a comprehensive comparative analysis of Kolmogorov-Arnold Networks (KAN) and Multi-Layer Perceptrons (MLP), highlighting their effectiveness in solving essential computational challenges like nonlinear function approximation, time-series prediction, and multivariate classification. Rooted in Kolmogorov's representation theorem, KANs utilize adaptive spline-based activation functions and grid-based structures, providing a transformative approach compared to traditional neural network frameworks. Utilizing a variety of datasets spanning mathematical function estimation (quadratic and cubic) to practical uses like predicting daily temperatures and categorizing wines, the proposed research thoroughly assesses model performance via accuracy measures like Mean Squared Error (MSE) and computational expense assessed through Floating Point Operations (FLOPs). The results indicate that KANs reliably exceed MLPs in every benchmark, attaining higher predictive accuracy with significantly reduced computational costs. Such an outcome highlights their ability to maintain a balance between computational efficiency and accuracy, rendering them especially beneficial in resource-limited and real-time operational environments. By elucidating the architectural and functional distinctions between KANs and MLPs, the paper provides a systematic framework for selecting the most suitable neural architectures for specific tasks. Furthermore, the proposed study highlights the transformative capabilities of KANs in progressing intelligent systems, influencing their use in situations that require both interpretability and computational efficiency.