用于逆 PDE 算子的伪微分积分自动编码器网络

IF 4.6 Q2 MATERIALS SCIENCE, BIOMATERIALS
Ke Chen, Jasen Lai, Chunmei Wang
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引用次数: 0

摘要

偏微分方程(PDE)在物理现象建模中发挥着基础性作用。本研究解决了从测量数据中确定偏微分方程中可变系数这一具有挑战性的任务。我们引入了一种新型神经网络 "伪差分 IAEnet"(pd-IAEnet),它从伪差分算子中汲取灵感。与传统模型相比,pd-IAEnet 以更少的参数显著提高了计算速度和精度。在电阻抗层析成像、光学层析成像和地震成像等一系列逆问题上进行了广泛的基准评估,一致证明 pd-IAEnet 具有卓越的准确性。值得注意的是,pd-IAEnet 在存在测量噪声的情况下也表现出很强的鲁棒性,这是实际应用中的一个关键特性。它的一个突出特点是离散不变性,可以对来自不同离散方案的数据进行有效训练,同时保持不同网格的精度。总之,pd-IAEnet 为解决逆 PDE 问题提供了一个强大而高效的解决方案,有助于提高计算效率、鲁棒性和对各种数据源的适应性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Pseudo-differential integral autoencoder network for inverse PDE operators
Partial differential equations (PDEs) play a foundational role in modeling physical phenomena. This study addresses the challenging task of determining variable coefficients within PDEs from measurement data. We introduce a novel neural network, ‘pseudo-differential IAEnet’ (pd-IAEnet), which draws inspiration from pseudo-differential operators. pd-IAEnet achieves significantly enhanced computational speed and accuracy with fewer parameters compared to conventional models. Extensive benchmark evaluations are conducted across a range of inverse problems, including electrical impedance tomography, optical tomography, and seismic imaging, consistently demonstrating pd-IAEnet’s superior accuracy. Notably, pd-IAEnet exhibits robustness in the presence of measurement noise, a critical characteristic for real-world applications. An exceptional feature is its discretization invariance, enabling effective training on data from diverse discretization schemes while maintaining accuracy on different meshes. In summary, pd-IAEnet offers a potent and efficient solution for addressing inverse PDE problems, contributing to improved computational efficiency, robustness, and adaptability to a wide array of data sources.
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来源期刊
ACS Applied Bio Materials
ACS Applied Bio Materials Chemistry-Chemistry (all)
CiteScore
9.40
自引率
2.10%
发文量
464
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