论文标题
多因素深神经操作员，用于有效学习部分微分方程，并应用于纳米级热传输的快速逆设计
Multifidelity deep neural operators for efficient learning of partial differential equations with application to fast inverse design of nanoscale heat transport
论文作者
论文摘要
深度神经操作员可以通过深层神经网络学习映射无限维功能空间之间的操作员，并已成为科学机器学习的新兴范式。但是，培训神经操作员通常需要大量的高保真数据，这在实际工程问题中通常很难获得。在这里，我们通过使用多重级学习，即从多重元数据数据集学习来应对这一挑战。我们基于深度操作员网络（DeepOnet）开发了多重神经操作员。多重级DEAVONET包括两个标准的Deponets，结合了残留学习和输入增强。多因素deponet显着减少了所需的高保真数据量，并在使用相同数量的高保真数据时达到了一个较小的误差。我们应用多尺度DeepOnet来学习声子Boltzmann传输方程（BTE），该方程是计算纳米级热传输的框架。通过将训练有素的多二二二二脂化deponet与遗传算法或拓扑优化相结合，我们演示了BTE问题逆设计的快速求解器。
Deep neural operators can learn operators mapping between infinite-dimensional function spaces via deep neural networks and have become an emerging paradigm of scientific machine learning. However, training neural operators usually requires a large amount of high-fidelity data, which is often difficult to obtain in real engineering problems. Here, we address this challenge by using multifidelity learning, i.e., learning from multifidelity datasets. We develop a multifidelity neural operator based on a deep operator network (DeepONet). A multifidelity DeepONet includes two standard DeepONets coupled by residual learning and input augmentation. Multifidelity DeepONet significantly reduces the required amount of high-fidelity data and achieves one order of magnitude smaller error when using the same amount of high-fidelity data. We apply a multifidelity DeepONet to learn the phonon Boltzmann transport equation (BTE), a framework to compute nanoscale heat transport. By combining a trained multifidelity DeepONet with genetic algorithm or topology optimization, we demonstrate a fast solver for the inverse design of BTE problems.
