An autoencoder compression approach for accelerating large-scale inverse problems
An autoencoder compression approach for accelerating large-scale inverse problems
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DOI：
10.1088/1361-6420/acfbe1
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发表时间：
2023-04
期刊：
影响因子：
2.1
通讯作者：
J. Wittmer;Jacob Badger;H. Sundar;T. Bui-Thanh
中科院分区：
文献类型：
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作者：
J. Wittmer;Jacob Badger;H. Sundar;T. Bui-Thanh
偏微分方程 (PDE) 约束反问题是当今计算科学中最具挑战性和计算要求最高的问题。精确计算偏微分方程解所需的精细网格会引入大量参数，并且需要大规模计算资源（例如更多处理器和更多内存）才能在合理的时间内求解此类系统。对于受时间相关 PDE 约束的逆问题，通常采用伴随方法来有效计算梯度和高阶导数，需要求解时间反转的所谓伴随 PDE，该方法取决于每个时间步的前向 PDE 解。这需要在每个时间步存储高维前向解向量。这样的过程很快就会耗尽可用的内存资源。为了缓解内存瓶颈，人们提出了几种以额外计算换取减少内存占用的方法，包括检查点和压缩策略。在这项工作中，我们提出了一种接近理想的可扩展压缩方法，使用自动编码器来消除对检查点和大量内存存储的需求，从而减少解决方案的时间和内存需求。我们将我们的方法与检查点和现成的压缩方法在地球尺度不适定地震反问题上进行比较。结果验证了使用所提出的自动编码器压缩方法对梯度和 Hessian 向量积的预期接近理想的加速。为了强调所提出方法的实用性，我们将自动编码器压缩与数据通知的活动子空间（DIAS）结合起来，展示了如何将 DIAS 方法经济地扩展到大规模问题，而不需要检查点和大内存。
Partial differential equation (PDE)-constrained inverse problems are some of the most challenging and computationally demanding problems in computational science today. Fine meshes required to accurately compute the PDE solution introduce an enormous number of parameters and require large-scale computing resources such as more processors and more memory to solve such systems in a reasonable time. For inverse problems constrained by time-dependent PDEs, the adjoint method often employed to compute gradients and higher order derivatives efficiently requires solving a time-reversed, so-called adjoint PDE that depends on the forward PDE solution at each timestep. This necessitates the storage of a high-dimensional forward solution vector at every timestep. Such a procedure quickly exhausts the available memory resources. Several approaches that trade additional computation for reduced memory footprint have been proposed to mitigate the memory bottleneck, including checkpointing and compression strategies. In this work, we propose a close-to-ideal scalable compression approach using autoencoders to eliminate the need for checkpointing and substantial memory storage, thereby reducing the time-to-solution and memory requirements. We compare our approach with checkpointing and an off-the-shelf compression approach on an earth-scale ill-posed seismic inverse problem. The results verify the expected close-to-ideal speedup for the gradient and Hessian-vector product using the proposed autoencoder compression approach. To highlight the usefulness of the proposed approach, we combine the autoencoder compression with the data-informed active subspace (DIAS) prior showing how the DIAS method can be affordably extended to large-scale problems without the need for checkpointing and large memory.