Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks

Xihaier Luo1, †, Wei Xu1, Yihui Ren1, Shinjae Yoo1, Balu Nadiga2
1Brookhaven National Laboratory
2Los Alamos National Lab
The International Conference on Learning Representations (ICLR) 2024
†Indicates the corresponding author
Paper Code arXiv

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 Dataset

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.

Method

Conventional spatiotemporal disentangled representation utilizes the time index (t) primarily as a reference to indicate a specific time instance. Motivated by the desire for a more context-aware indexing mechanism, we pose the question: Can the pointing process be improved? A natural approach to incorporate available context information in field reconstruction involves using measurements of the underlying physical process at time $t$. As the number and positions of available measurements change over time, we propose a design wherein an encoder extracts a latent representation from actual measurements. This latent representation is subsequently employed to guide the model to the target time instance. When coupled with an INR-based decoder, this proposed method achieves continuous field reconstruction.

Model

We introduce a neural network reconstruction method, MMGN (Multiplicative and Modulated Gabor Network), that features an encoder-decoder architecture.

Quantitative Results

Performance comparison with four INR baselines on both high-fidelity climate simulation data and real-world satellite-based benchmarks. MSE is recorded. A smaller MSE denotes superior performance. For clarity, we highlight the best result in bold and underline the second-best. We have also included the promotion metric, which indicates the reduction in relative error compared to the second-best model for each task.

Quantitative Results

Visualizations of true and reconstructed fields: (1) global surface temperature derived from multi-scale high-fidelity climate simulations and (2) 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.

BibTeX

@inproceedings{
        luo2024continuous,
        title={Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks},
        author={Xihaier Luo and Wei Xu and Balu Nadiga and Yihui Ren and Shinjae Yoo},
        booktitle={The Twelfth International Conference on Learning Representations},
        year={2024},
        url={https://openreview.net/forum?id=kuTZMZdCPZ}
        }