Segmented Continuous Optimization

Teymur Aghayev

eess.SPFeb 24, 2026

Segmented Continuous Optimization

Authors: Teymur Aghayev

Organizations: Dept. of Electronic Systems Vilnius Gediminas Technical University Vilnius, Lithuania

Abstract

Segmented curve fitting remains an essential approach for the comprehensive analysis of local patterns in non-stationary time-series data. However, traditional regression algorithms primarily focus on linear or polynomial functions, which can be insufficient for analyzing raw signals with oscillatory or transcendental behavior. In this paper, we propose Segmented Continuous Optimization (SCO), a framework that performs piecewise continuous curve fitting on various non-linear models, including trigonometric, polynomial, and exponential. SCO presents a novel signal representation by optimizing a user-defined model in segments with $C^1$ continuity to properly analyze the data's local and global trends. The framework is tested for accuracy and efficiency across all included models. Finally, we provide examples using velocity and EEG datasets to demonstrate the algorithm's practical usage in examining signal patterns, optimized parameters, derivatives, and integrals of the final fit.

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Enhancing Irregular Time Series Forecasting with Continuous-Time Modeling Framework

Tianen Shen, Zhengyu Li, Yutong Li, Xiangfei Qiu+3

Irregular Time-Series Modeling Multivariate Time Series Forecasting Flow Matching Time Series Modeling Time Series Transformers

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Irregular multivariate time series are widely encountered in applications such as healthcare monitoring, human activity recognition, and environmental sensing. Their core challenges stem from asynchronous observations, non-uniform sampling intervals, and the fact that temporal patterns themselves carry critical dynamic information. Existing approaches either rely on discretization-based preprocessing (e.g., interpolation, imputation, or aggregation), which disrupts the underlying continuous-time semantics, or adopt continuous-time modeling via ODE-based frameworks, which typically require specialized architectures and incur substantial computational overhead due to numerical solvers. To address these limitations, we propose WrapFlow, a continuous-time modeling framework for irregular time series forecasting. On the input side, WrapFlow introduces Continuous-Time Tokenization, which directly encodes raw observation events and explicitly models long unobserved intervals via gap-aware tokens. The resulting continuous-time tokens are then processed by a standard Transformer backbone to capture long-range temporal dependencies. On the output side, we develop a simulation-free training paradigm for Residual Flow Matching, which learns conditional residual vector fields around base predictions while avoiding numerical-solver simulation and backpropagation during training. This design enables high-quality continuous forecasting using only a small number of fixed rollout steps at inference. Extensive experiments on multiple real-world datasets demonstrate that WrapFlow achieves state-of-the-art performance.

Abstract

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