Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks

Reliably reconstructing physical fields from sparse sensor data is a challenge that frequently arises in many scientific domains. In practice, the process generating the data often is not understood to sufficient accuracy. Therefore, there is a growing interest in using the deep neural network route to address the problem. This work presents a novel approach that learns a continuous representation of the physical field using implicit neural representations (INRs). Specifically, after factorizing spatiotemporal variability into spatial and temporal components using the separation of variables technique, the method learns relevant basis functions from sparsely sampled irregular data points to develop a continuous representation of the data. In experimental evaluations, the proposed model outperforms recent INR methods, offering superior reconstruction quality on simulation data from a stateof-the-art climate model and a second dataset that comprises ultra-high resolution satellite-based sea surface temperature fields. Achieving accurate and comprehensive representation of complex physical fields is pivotal for tasks spanning system monitoring and control, analysis, and design. However, in a multitude of applications, encompassing geophysics (Reichstein et al., 2019), astronomy (Gabbard et al., 2022), biochemistry (Zhong et al., 2021), fluid mechanics (Deng et al., 2023), and others, using a sparse sensor network proves to be the most practical and effective solution. In meteorology and oceanography, variables such as atmospheric pressure, temperature, salinity/humidity, and wind/current velocity must be reconstructed from sparsely sampled observations. Currently, two distinct approaches are used to reconstruct full fields from sparse observations. Traditional physics model-based approaches are based on partial differential equations (PDEs). These approaches draw upon theoretical techniques to derive PDEs rooted in conservation laws and fundamental physical principles (Hughes, 2012). Yet, in complex systems such as weather (Brunton et al., 2016) and epidemiology (Massucci et al., 2016), deriving comprehensive models that are both sufficiently accurate and computationally efficient remains elusive.