Nonlinear Tikhonov regularization within a Bayesian framework is incorporated into a computer program called pyReSpect, which infers the continuous and discrete relaxation spectra from oscillatory shear experiments. It uses Bayesian inference to provide uncertainty estimates for the continuous spectrum h ( τ ) by propagating the uncertainty in the regularization parameter λ . The new algorithm is about 6–9 times faster than an older version of the program (ReSpect) in which the optimal λ was determined by the L-curve method. About half of the speedup arises from the Bayesian formulation by restricting the window of λ explored. The other half arises from the nonlinear formulation for which the spectrum is a weak function of λ , allowing us to use a coarse mesh for λ . The program is tested and validated on three examples: a synthetic spectrum, a H-polymer, and an elastomer with a nonzero terminal plateau.

中文翻译：

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使用具有贝叶斯准则的非线性 Tikhonov 正则化的弛豫谱

贝叶斯框架内的非线性 Tikhonov 正则化被合并到一个名为 pyReSpect 的计算机程序中，该程序从振荡剪切实验中推断出连续和离散的弛豫谱。它使用贝叶斯推理通过传播正则化参数 λ 中的不确定性来为连续谱 h ( τ ) 提供不确定性估计。新算法比旧版本的程序 (ReSpect) 快 6-9 倍，其中最佳 λ 由 L 曲线方法确定。通过限制探索的 λ 窗口，大约一半的加速来自贝叶斯公式。另一半来自非线性公式，其中频谱是 λ 的弱函数，允许我们对 λ 使用粗网格。该程序在三个示例上进行了测试和验证：合成光谱，