Continuous Field Reconstruction from Sparse Observations with Implicit
  Neural Networks
Xihaier Luo Wei Xu Yihui Ren Shinjae Yoo Balu Nadiga
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
state-of-the-art climate model and a second dataset that comprises ultra-high
resolution satellite-based sea surface temperature fields.