We present an efficient adjoint model based on the deep‐learning surrogate to address high‐dimensional inverse modeling with an application to subsurface transport. The proposed method provides a completely code nonintrusive and computationally feasible way to approximate the model derivatives, which subsequently can be used to derive gradients for inverse modeling. This conceptual deep‐learning framework, that is, an architecture of deep convolutional neural network through combining autoencoder and autoregressive structure, efficiently produces an analogously analytical adjoint with the help of auto‐differentiation module in the popular deep‐learning packages. We intentionally retain training data at the specific time instances where the measurements are taken, the storage of the intermediate states and computation of their adjoint, therefore, are completely avoided. This proposed adjoint state method is tested on a synthetic two‐dimensional model for parameter estimations. The preliminary results reveal the feasibility of the proposed adjoint state method in term of computational efficiency and programming flexibility.

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基于深度学习的伴随状态方法：方法和在逆建模中的初步应用

我们提出了一种基于深度学习代理的有效伴随模型，以解决高维逆建模及其在地下运输中的应用。所提出的方法提供了一种完全编码的非介入式方法，并且在计算上可行，可以近似于模型导数，随后可用于导出逆模型的梯度。这种概念性的深度学习框架，即通过将自编码器和自回归结构相结合的深度卷积神经网络架构，借助流行的深度学习包中的自动分化模块，可以有效地产生类似的分析伴随物。因此，我们有意地在进行测量的特定时间点，中间状态的存储和伴随状态的计算中保留了训练数据，因此，完全避免。该拟议的伴随状态方法在用于参数估计的合成二维模型上进行了测试。初步结果揭示了所提出的伴随状态方法在计算效率和编程灵活性方面的可行性。