时间依赖参数多保真模型的收敛加速
Convergence Acceleration for Time Dependent Parametric Multifidelity Models
AI总结：
本文提出一种数值方法加速参数常微分方程多保真模型的收敛，通过多保真代理模型构建三级算法，结合样条插值和Richardson外推提升收敛精度。
摘要：
我们提出了一种数值方法，用于加速参数常微分方程多保真模型的收敛。模型的层次结构定义为在时间积分方案中使用不同时间步长计算的轨迹。我们的第一个贡献是多保真过程的新分析，提供了收敛估计。我们的第二个贡献是开发了一个三级算法，利用多保真代理模型加速收敛：第一步使用三级多保真过程获得准确预测，利用低成本（大时间步长）模型；第二步使用高阶样条构建时间连续轨迹；第三步结合三级样条预测推断收敛阶并计算序列变换预测（特别是使用Richardson外推）以实现更优的误差。我们在线性和非线性参数常微分方程系统上展示了该方法。
英文摘要：
We present a numerical method for convergence acceleration for multifidelity models of parameterized ordinary differential equations. The hierarchy of models is defined as trajectories computed using different timesteps in a time integration scheme. Our first contribution is in novel analysis of the multifidelity procedure, providing a convergence estimate. Our second contribution is development of a three-step algorithm that uses multifidelity surrogates to accelerate convergence: step one uses a multifidelity procedure at three levels to obtain accurate predictions using inexpensive (large timestep) models. Step two uses high-order splines to construct continuous trajectories over time. Finally, step three combines spline predictions at three levels to infer an order of convergence and compute a sequence transformation prediction (in particular we use Richardson extrapolation) that achieves superior error. We demonstrate our procedure on linear and nonlinear systems of parameterized ordinary differential equations.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
