Irregularly Sampled Time Series Interpolation for Binary Evolution Simulations Using Dynamic Time Warping

2026-04-15

AI Summary

This study addresses the challenges posed by irregular sampling, trajectory offsets, and physical discontinuities in binary star evolutionary tracks due to complex interactions, which conventional interpolation methods struggle to handle effectively. To overcome these limitations, this work introduces multivariate joint dynamic time warping (DTW) into the field for the first time and proposes an interpolation framework that integrates joint alignment with iterative averaging. The method synchronizes multiple evolutionary trajectories onto a unified time grid while rigorously preserving fundamental physical constraints, such as the Stefan–Boltzmann law. Evaluated across diverse binary configurations, the approach significantly outperforms existing techniques, enabling efficient generation of high-fidelity stellar population samples at substantially reduced computational cost.

Technology Category

• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems

Application Category

• Web Mining and Content Analysis: Models for Web evolution
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Data management and stream processing for Web, mobile and wireless applications

Abstract

Binary stellar evolution simulations are computationally expensive. Stellar population synthesis relies on these detailed evolution models at a fundamental level. Producing thousands of such models requires hundreds of CPU hours, but stellar track interpolation provides one approach to significantly reduce this computational cost. Although single-star track interpolation is straightforward, stellar interactions in binary systems introduce significant complexity to binary evolution, making traditional single-track interpolation methods inapplicable. Binary tracks present fundamentally different challenges compared to single stars, which possess relatively straightforward evolutionary phases identifiable through distinct physical properties. Binary systems are complicated by mutual interactions that can dramatically alter evolutionary trajectories and introduce discontinuities difficult to capture through standard interpolation. In this work, we introduce a novel approach for track alignment and iterative track averaging based on Dynamic Time Warping to address misalignments between neighboring tracks. Our method computes a single shared warping path across all physical parameters simultaneously, placing them on a consistent temporal grid that preserves the causal relationships between parameters. We demonstrate that this joint-alignment strategy maintains key physical relationships such as the Stefan-Boltzmann law in the interpolated tracks. Our comprehensive evaluation across multiple binary configurations demonstrates that proper temporal alignment is crucial for track interpolation methods. The proposed method consistently outperforms existing approaches and enables the efficient generation of more accurate binary population samples for astrophysical studies.

Problem

• Binary stellar evolution
• Time series interpolation
• Irregular sampling
• Dynamic Time Warping
• Stellar population synthesis

Innovation

• Dynamic Time Warping
• Binary Stellar Evolution
• Time Series Interpolation
• Track Alignment
• Stellar Population Synthesis