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arXiv 2307.09623cond-mat.mtrl-sci
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揭示神经算子对数字复合材料中应变演化的预测能力

Revealing the Predictive Power of Neural Operators for Strain Evolution in Digital Composites

Meer Mehran Rashid, Souvik Chakraborty, N. M. Anoop Krishnan

AI总结:

针对基于物理的复合材料应变演化模拟计算成本高的问题,研究对比三种神经算子的预测能力,发现FNO性能最优、推理速度比有限元快近三个数量级,可加速复合材料微结构设计。

摘要:

对高性能材料的需求,结合增材制造与3D打印等先进合成技术,推动了具备优异性能的层级复合材料的发展。然而,使用基于物理的求解器对此类复合材料进行计算建模,虽能实现最优微结构的发现,但其计算成本高得令人望而却步,阻碍了实际应用。\n在此背景下,我们证明神经算子(Neural Operators,NOs)可用于学习和预测二维数字复合材料中的应变演化。具体而言,我们研究了三种架构,即傅里叶神经算子(Fourier NO,FNO)、小波神经算子(Wavelet NO,WNO)和多小波神经算子(Multi-wavelet NO,MWT)。我们证明,仅需提供少量初始应变帧作为输入,神经算子就能以极高的数据效率准确预测多个未来时间步,其中WNO表现尤为突出。此外,一旦训练完成,神经算子可针对完全未见的边界条件预测应变轨迹。\n在各类神经算子中,仅FNO具备多尺度应变估计的超分辨率能力,可提供更高的材料分辨率和像素级分辨率。我们还表明,神经算子无需额外训练,就能泛化到具有更精细域分辨率的任意几何结构。基于所有呈现的结果,我们指出FNO在神经算子中表现最佳,同时推理时间最短,比传统有限元解低近三个数量级。因此,FNO可作为替代模型,用于加速复杂微结构中应变演化的模拟,以设计下一代复合材料。

英文摘要:

The demand for high-performance materials, along with advanced synthesis technologies such as additive manufacturing and 3D printing, has spurred the development of hierarchical composites with superior properties. However, computational modelling of such composites using physics-based solvers, while enabling the discovery of optimal microstructures, have prohibitively high computational cost hindering their practical application. To this extent, we show that Neural Operators (NOs) can be used to learn and predict the strain evolution in 2D digital composites. Specifically, we consider three architectures, namely, Fourier NO (FNO), Wavelet NO (WNO), and Multi-wavelet NO (MWT). We demonstrate that by providing a few initial strain frames as input, NOs can accurately predict multiple future time steps in an extremely data-efficient fashion, especially WNO. Further, once trained, NOs forecast the strain trajectories for completely unseen boundary conditions. Among NOs, only FNO offers super-resolution capabilities for estimating strains at multiple length scales, which can provide higher material and pixel-wise resolution. We also show that NOs can generalize to arbitrary geometries with finer domain resolution without the need for additional training. Based on all the results presented, we note that the FNO exhibits the best performance among the NOs, while also giving minimum inference time that is almost three orders magnitude lower than the conventional finite element solutions. Thus, FNOs can be used as a surrogate for accelerated simulation of the strain evolution in complex microstructures toward designing the next composite materials.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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