Abstract
Finite element methods typically require a high resolution to satisfactorily approximate micro and even macro patterns of an underlying physical model. This issue can be circumvented by appropriate multiscale strategies that are able to obtain reasonable approximations on under-resolved scales. In this paper, we study the implicit neural representation and propose a continuous super-resolution network as a correction strategy for multiscale effects. It can take coarse finite element data to learn both in-distribution and out-of-distribution high-resolution finite element predictions. Our highlight is the design of a local implicit transformer, which is able to learn multiscale features. We also propose Gabor wavelet-based coordinate encodings, which can overcome the bias of neural networks learning low-frequency features. Finally, perception is often preferred over distortion, so scientists can recognize the visual pattern for further investigation. However, implicit neural representation is known for its lack of local pattern supervision. We propose to use stochastic cosine similarities to compare the local feature differences between prediction and ground truth. It shows better performance on structural alignments. Our experiments show that our proposed strategy achieves superior performance as an in-distribution and out-of-distribution super-resolution strategy.
Abstract (translated)
有限元方法通常需要高分辨率才能满意地近似底层物理模型的微尺度和宏尺度模式。这一问题可以通过适当的多尺度策略来解决，这些策略能够获得在低分辨率下合理近似的解。本文研究了隐式神经表示，并提出了一种连续超分辨率网络作为多重尺度效应的校正策略。该方法可以利用粗糙的有限元数据学习分布内及分布外的高分辨率有限元预测。 我们的亮点在于设计了一个局部隐式变压器，它可以学习多尺度特征。此外，我们还提出了基于Gabor小波的坐标编码，这可以克服神经网络在学习低频特征时产生的偏差。然而，感知通常比失真更受科学家们的青睐，因此他们可以通过视觉模式进一步进行研究。 尽管隐式神经表示缺乏局部模式监督，我们提出使用随机余弦相似度来比较预测和真实值之间的局部特征差异。这种方法在结构对齐上表现更好。 我们的实验表明，在分布内及分布外的超分辨率策略中，所提出的策略表现出优越性。
URL
https://arxiv.org/abs/2411.07576
