基于模型降维和递归神经网络的油藏参数反演

Model-reduced Autoregressive Neural Network for Parameter Inversion

提出一种基于映射递归神经网络(aNN)的代理模型,借助于深度学习框架中易于使用的自动微分工具,有效生成模型降阶伴随算子,实现高效反演建模。与降阶切线线性模型相似,基于投影的神经网络(POD-aNN)结构加速降阶子空间的伴随模型的建立。POD-aNN由一个降维单元和一个用于投影的中间非线性过渡单元组成,二者分别用于将状态系统分解为低维子空间和近似系统状态的时变演化。因此,伴随模型在缩减的空间中运行,计算量和内存需求可以忽略不计。结合二维石油模型展开油藏参数反演研究。结果表明:该方法在显著降低计算量的前提下取得了满意的参数反演结果,从而证明了该方法的有效性,并为应用神经网络模型到实际参数反演案例提供理论基础。

We present an architecture of projection-based autoregressive neural network(aNN)where model-reduced adjoint is efficiently produced with the help of an easy-to-use auto-differentiation(AD)tool in deep-learning frameworks.Analogy to reduced-order tangent linear model,a projection-based aNN(POD-aNN)structure is proposed to accelerate the construction of adjoint model based on reduced subspace.The POD-aNN consists of a dimensionality reduction and an intermediate non-linear transition unit which is used to project a state system to a low-dimensional subspace and approximate time-varying evolution of system states in low dimension,respectively.The adjoint model is run in reduced space with negligible computational cost and memory requirement.Once the gradient is obtained in reduced space it is projected back in full space and then the inversion modeling is conducted.Characteristics and performance of the method are illustrated with two sets of inverse modeling experiments in a synthetic 2 D fluid flow model with random spatially dependent parameters.It shows that the proposed POD-aNN obtains satisfactory results with significantly reduced computational cost and,therefore,demonstrates promising applicability to practical reservoir models.