量子张量网络在地球科学中的应用
Quantum-inspired tensor network for Earth science
摘要：
深度学习（DL）是许多成功的方法之一，可以从不断增加的噪声大规模数据集（在我们的例子中，是卫星图像）中提取信息模式和见解。然而，DL模型由几千到几百万个训练参数组成，并且这些训练参数需要大量的电力来从有噪声的大规模数据集（例如，计算成本高）。因此，我们采用量子启发张量网络压缩物理信息神经网络（PINN）在地球科学的可训练参数。PINN是通过强制执行物理定律而受到惩罚的DL模型;特别是，物理定律嵌入DL模型中。此外，我们将张量分解应用于高光谱图像（HSI），以提高其光谱分辨率。受量子启发的张量网络也是在GPU张量核心上的大数据集上有效表示和训练量子机器学习模型的原生公式。此外，本文的主要贡献是双重的：（I）我们减少了一些可训练参数的PINN通过使用量子启发张量网络，（II）我们提高了光谱分辨率的遥感图像通过采用张量分解。作为一个基准偏微分方程，我们解决了伯格方程。作为实际的卫星数据，我们采用了印度松，美国和帕维亚大学，意大利的HSI。
英文摘要：
Deep Learning (DL) is one of many successful methodologies to extract informative patterns and insights from ever increasing noisy large-scale datasets (in our case, satellite images). However, DL models consist of a few thousand to millions of training parameters, and these training parameters require tremendous amount of electrical power for extracting informative patterns from noisy large-scale datasets (e.g., computationally expensive). Hence, we employ a quantum-inspired tensor network for compressing trainable parameters of physics-informed neural networks (PINNs) in Earth science. PINNs are DL models penalized by enforcing the law of physics; in particular, the law of physics is embedded in DL models. In addition, we apply tensor decomposition to HyperSpectral Images (HSIs) to improve their spectral resolution. A quantum-inspired tensor network is also the native formulation to efficiently represent and train quantum machine learning models on big datasets on GPU tensor cores. Furthermore, the key contribution of this paper is twofold: (I) we reduced a number of trainable parameters of PINNs by using a quantum-inspired tensor network, and (II) we improved the spectral resolution of remotely-sensed images by employing tensor decomposition. As a benchmark PDE, we solved Burger's equation. As practical satellite data, we employed HSIs of Indian Pine, USA and of Pavia University, Italy.
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。
