Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks

TL;DR

This work tackles reconstructing a continuous spatiotemporal field u(x,t) from sparse observations. It introduces MMGN, a context-aware implicit neural representation that uses a trainable latent code z_t to condition a coordinate-based decoder built from shift-invariant Gabor filters, enabling flexible temporal handling and high-frequency fidelity. The key contributions include a context-aware indexing mechanism, an auto-decoder training regime for latent codes, and a multiplicative Gabor-based decoder that yields superior reconstruction accuracy over state-of-the-art INR baselines on climate and sea-surface temperature data, especially under extreme sparsity. The results suggest MMGN can deliver accurate field reconstructions from very sparse sensor networks and could inform sensor placement and multi-trajectory generalization in future work, with potential impact across geosciences and remote sensing.

Abstract

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.

Figures (22)

• Figure 1: Field reconstruction from sparse observations: The Prior approach uses the time index ($t$) as a reference to indicate a specific time instance. Our approach is context-aware, leveraging available context information by incorporating measurements at time $t$.
• Figure 2: Architecture of the MMGN Model. The MMGN model employs auto-decoding to infer the latent variable ${\bm{z}}$. Consequently, only the decoder is explicitly defined, and encoding takes place through stochastic optimization. More precisely, the latent code ${\bm{z}}=\arg \min _{{\bm{z}}} \mathcal{L}({\bm{z}}, \Theta)$ is obtained by minimizing a loss function $\mathcal{L}$ calculated as an expectation over a dataset.
• Figure 3: Visualizations of true and reconstructed fields. Global surface temperature derived from multiscale high-fidelity climate simulations and sea surface temperature assimilated using satellite imagery observations. For each dataset, the first column displays the ground truth, the first row showcases predictions from different models, and the second row presents corresponding error maps relative to the reference data. In the error maps, darker pixels indicate lower error levels.
• Figure 4: Model performance with different levels of noise.
• Figure 5: Ablation on context-aware indexing mechanism.