A quantum-inspired tensor network for physics-informed neural networks and satellite images

Abstract

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, which require tremendous 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 the 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.