  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.

Geophysics;Machine Learning;Quantum Physics