Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Deep Learning Improvements for Sparse Spatial Field Reconstruction

Robert Sunderhaft, Logan Frank, Jim Davis

TL;DR

The paper addresses reconstructing global spatial fields from sparse observations in geoscience and fluid dynamics by extending a prior ML approach with data-driven input augmentations. It introduces a Distance Transform Mask, Land Mask separation, and normalization to improve reconstruction accuracy and training speed, and tests these on Cylinder, NOAA, Channel, and Antarctic datasets. Results show significant gains for cyclical datasets (Cylinder, NOAA, Antarctic) and mixed or limited benefits for non-cyclical, high-frequency data (Channel), highlighting the method’s domain dependence. The Antarctic application demonstrates substantial RMSE reductions and faster training, indicating practical potential for real-time reanalysis and sensor-placement planning, while pointing to future work in time-series integration and advanced architectures.

Abstract

Accurately reconstructing a global spatial field from sparse data has been a longstanding problem in several domains, such as Earth Sciences and Fluid Dynamics. Historically, scientists have approached this problem by employing complex physics models to reconstruct the spatial fields. However, these methods are often computationally intensive. With the increase in popularity of machine learning (ML), several researchers have applied ML to the spatial field reconstruction task and observed improvements in computational efficiency. One such method in arXiv:2101.00554 utilizes a sparse mask of sensor locations and a Voronoi tessellation with sensor measurements as inputs to a convolutional neural network for reconstructing the global spatial field. In this work, we propose multiple adjustments to the aforementioned approach and show improvements on geoscience and fluid dynamics simulation datasets. We identify and discuss scenarios that benefit the most using the proposed ML-based spatial field reconstruction approach.

Deep Learning Improvements for Sparse Spatial Field Reconstruction

TL;DR

The paper addresses reconstructing global spatial fields from sparse observations in geoscience and fluid dynamics by extending a prior ML approach with data-driven input augmentations. It introduces a Distance Transform Mask, Land Mask separation, and normalization to improve reconstruction accuracy and training speed, and tests these on Cylinder, NOAA, Channel, and Antarctic datasets. Results show significant gains for cyclical datasets (Cylinder, NOAA, Antarctic) and mixed or limited benefits for non-cyclical, high-frequency data (Channel), highlighting the method’s domain dependence. The Antarctic application demonstrates substantial RMSE reductions and faster training, indicating practical potential for real-time reanalysis and sensor-placement planning, while pointing to future work in time-series integration and advanced architectures.

Abstract

Accurately reconstructing a global spatial field from sparse data has been a longstanding problem in several domains, such as Earth Sciences and Fluid Dynamics. Historically, scientists have approached this problem by employing complex physics models to reconstruct the spatial fields. However, these methods are often computationally intensive. With the increase in popularity of machine learning (ML), several researchers have applied ML to the spatial field reconstruction task and observed improvements in computational efficiency. One such method in arXiv:2101.00554 utilizes a sparse mask of sensor locations and a Voronoi tessellation with sensor measurements as inputs to a convolutional neural network for reconstructing the global spatial field. In this work, we propose multiple adjustments to the aforementioned approach and show improvements on geoscience and fluid dynamics simulation datasets. We identify and discuss scenarios that benefit the most using the proposed ML-based spatial field reconstruction approach.
Paper Structure (47 sections, 2 equations, 31 figures, 4 tables)

This paper contains 47 sections, 2 equations, 31 figures, 4 tables.

Table of Contents

  1. Introduction
  2. Contributions and Significance
  3. Organization
  4. Related Work
  5. Naïve Deep Learning
  6. Physics-Informed Neural Networks
  7. In-painting
  8. Meta-Analysis
  9. Methodology
  10. Voronoi
  11. Land Mask
  12. Distance Transform
  13. Circular Images for Circular Datasets
  14. Masked Out Loss
  15. Normalization
  16. ...and 32 more sections

Figures (31)

  • Figure 1: Voronoi Tessellation Example
  • Figure 2: Separating the (a) Masked Voronoi into a (b) Land Mask and an (c) Unmasked Voronoi
  • Figure 3: We apply the distance transform algorithm to sparse image representations such as the (a) Sparse Location Mask and the (c) Land Mask to achieve the dense (b) DT Information Mask and (d) DT Land Mask
  • Figure 4: Circular Image Dataset Calculation
  • Figure 5: Circular DT Correction
  • ...and 26 more figures