论文标题
与神经操作员（BINO）进行建模的贝叶斯反演：前进和反问题
Bayesian Inversion with Neural Operator (BINO) for Modeling Subdiffusion: Forward and Inverse Problems
论文作者
论文摘要
分数扩散方程已成为建模复杂系统中异常扩散的有效工具。但是，传统的数值方法需要昂贵的计算成本和存储资源，因为时间分数衍生物的卷积积分所带来的记忆效应。我们提出了与神经操作员（BINO）的贝叶斯反演，以克服传统方法的难度如下。我们采用深层运算符网络来学习分数扩散方程的解决方案操作员，从而使我们能够迅速而精确地解决给定输入（包括分数顺序，扩散系数，源术语等）的正向问题。此外，我们将深层操作员网络与贝叶斯倒置方法集成在一起，用于通过次扩散过程进行建模问题并解决逆量扩散问题，从而大大降低了时间成本（没有压倒性存储资源）。大量的数值实验表明，这项工作中提出的操作员学习方法可以有效地解决左扩散方程的远期问题和贝叶斯反向问题。
Fractional diffusion equations have been an effective tool for modeling anomalous diffusion in complicated systems. However, traditional numerical methods require expensive computation cost and storage resources because of the memory effect brought by the convolution integral of time fractional derivative. We propose a Bayesian Inversion with Neural Operator (BINO) to overcome the difficulty in traditional methods as follows. We employ a deep operator network to learn the solution operators for the fractional diffusion equations, allowing us to swiftly and precisely solve a forward problem for given inputs (including fractional order, diffusion coefficient, source terms, etc.). In addition, we integrate the deep operator network with a Bayesian inversion method for modelling a problem by subdiffusion process and solving inverse subdiffusion problems, which reduces the time costs (without suffering from overwhelm storage resources) significantly. A large number of numerical experiments demonstrate that the operator learning method proposed in this work can efficiently solve the forward problems and Bayesian inverse problems of the subdiffusion equation.
