Bayesian Calibration with Functional Outputs Using Elastic Partial Matching

2026-09-21

AI Summary

本文通过引入部分弹性对齐方法，解决模拟与实验曲线时间轴不匹配问题，改进了贝叶斯校准方法，并应用于状态方程的校准。

Abstract

Calibrating a simulation model involves estimating its parameters by comparing model outputs with experimental data, so that simulation results faithfully reproduce the experimental observations. When the outputs are functions of time, there are multiple ways to quantify the discrepancy between experimental and simulated curves. A recent approach based on elastic functional data analysis decomposes a functional output into two components: a function temporally aligned to a template, and the corresponding warping function. This decomposition splits the problem into two independent calibration tasks, thereby addressing functional misalignment. However, it assumes that experimental and simulated curves share the same temporal support, an assumption often violated in practice when initial or end times are themselves uncertain or depend on the calibration parameters. In this work, we reinterpret the decomposition step as an approximation to a more general Bayesian calibration problem that incorporates an error term on the time axis. This perspective allows us to naturally extend the framework to a broader family of time warpings with varying initial or end times, using partial elastic alignment. We illustrate the method on a synthetic test case, comparing it with existing Bayesian calibration methods and demonstrating improved surrogate performance and error modeling. We then apply the proposed approach to the calibration of an equation of state (a thermodynamic equation relating the state variables of a material).

Problem

• Bayesian Calibration
• Functional Outputs
• Elastic Partial Matching
• Time Warping
• Temporal Support

Innovation

• Bayesian Calibration
• Elastic Functional Data Analysis
• Partial Elastic Alignment
• Time Warping