Deep learning in frequency domain for inverse identification of nonhomogeneous material properties

The inverse identification of nonhomogeneous material properties from measured displacement/strain fields, especially when noise exists, is crucial for both engineering and material science. The conventional physics-based solutions either require time-consuming iterative calculations, or are sensitive to noise. While the new machine learning methods either need excess data for high-dimensional matchups, or mainly apply to case-by-case analyses with informed physics. In this paper, to solve the complex matchup between the measured displacement/strain fields and the randomly distributed modulus field rapidly and robustly, a novel method of deep learning in frequency domain is proposed, with discrete cosine transform (DCT) to achieve frequency domain transformation as well as dimensionality reduction and convolutional neural network (CNN) to implement learning in frequency domain. Results show that our method not only has high prediction accuracy on zero-noise samples (with L₁-error of 4.249%) but also presents great robustness to noise (with L₁-error of 5.085% on large-noise samples). Besides, by our method, only one-time training on a dataset with mixed noise is basically enough to deal with arbitrary levels of noise (with L₁-errors below 5.202%), improving the efficiency significantly in practical applications. Moreover, our method can be directly transferred to neighbor sampling spaces with different sampling points, showing a great generalization. The study provides a powerful approach for inverse identification of material properties and promises for wide applications such as real-time elastography and high-throughput non-destructive evaluation techniques.