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Studying the Impact of Latent Representations in Implicit Neural Networks for Scientific Continuous Field Reconstruction

Wei Xu, Derek Freeman DeSantis, Xihaier Luo, Avish Parmar, Klaus Tan, Balu Nadiga, Yihui Ren, Shinjae Yoo

TL;DR

This paper tackles reconstructing continuous physical fields from sparse measurements using implicit neural representations. It introduces MMGN, an encoder–decoder framework where an encoder maps real-time observations to a latent code $z_t$ and a decoder fuses spatial coordinates with $z_t$ via Gabor-Fourier features and a multiplicative filter network to reconstruct $u(x,t)$. To interpret the latent space, the authors apply explainability techniques including t-SNE clustering, PCA/CCA correlation analyses, and Tucker tensor factorizations, plus ablation studies. Results on climate-model data show that $z_t$ encodes measurement context, that higher latent dimensions better capture the global data distribution and dominant spatio-temporal modes, and that MMGN can recover key dynamics with low relative error. These findings support the use of structured explainability to increase trust and guide future extensions in scientific continuous field reconstruction.

Abstract

Learning a continuous and reliable representation of physical fields from sparse sampling is challenging and it affects diverse scientific disciplines. In a recent work, we present a novel model called MMGN (Multiplicative and Modulated Gabor Network) with implicit neural networks. In this work, we design additional studies leveraging explainability methods to complement the previous experiments and further enhance the understanding of latent representations generated by the model. The adopted methods are general enough to be leveraged for any latent space inspection. Preliminary results demonstrate the contextual information incorporated in the latent representations and their impact on the model performance. As a work in progress, we will continue to verify our findings and develop novel explainability approaches.

Studying the Impact of Latent Representations in Implicit Neural Networks for Scientific Continuous Field Reconstruction

TL;DR

This paper tackles reconstructing continuous physical fields from sparse measurements using implicit neural representations. It introduces MMGN, an encoder–decoder framework where an encoder maps real-time observations to a latent code and a decoder fuses spatial coordinates with via Gabor-Fourier features and a multiplicative filter network to reconstruct . To interpret the latent space, the authors apply explainability techniques including t-SNE clustering, PCA/CCA correlation analyses, and Tucker tensor factorizations, plus ablation studies. Results on climate-model data show that encodes measurement context, that higher latent dimensions better capture the global data distribution and dominant spatio-temporal modes, and that MMGN can recover key dynamics with low relative error. These findings support the use of structured explainability to increase trust and guide future extensions in scientific continuous field reconstruction.

Abstract

Learning a continuous and reliable representation of physical fields from sparse sampling is challenging and it affects diverse scientific disciplines. In a recent work, we present a novel model called MMGN (Multiplicative and Modulated Gabor Network) with implicit neural networks. In this work, we design additional studies leveraging explainability methods to complement the previous experiments and further enhance the understanding of latent representations generated by the model. The adopted methods are general enough to be leveraged for any latent space inspection. Preliminary results demonstrate the contextual information incorporated in the latent representations and their impact on the model performance. As a work in progress, we will continue to verify our findings and develop novel explainability approaches.
Paper Structure (8 sections, 1 equation, 4 figures)

This paper contains 8 sections, 1 equation, 4 figures.

Table of Contents

  1. Introduction
  2. Related Work
  3. Methodology
  4. The MMGN model
  5. Explainability approaches
  6. Results
  7. Conclusion
  8. Acknowledgments

Figures (4)

  • Figure 1: The t-SNE distribution changes in three latent spaces: (left) 4-D, (middle) 512-D, and (right) the original data; the color represents the temporal indexing.
  • Figure 2: Left: The standard deviations of clusters diminish across latent spaces and they are compared with the ones of the original data (the rightmost boxplot). Middle: The trendings of explained variance ratios of the principal components for all latent spaces (illustrating only the top 5 sizes) and compare them with the trending of the original data. Right: Ablation result indicating spatial linkage of temporal indexing.
  • Figure 3: Top: Correlation plots for the three variables. Bottom: Complexity of Tucker core for different multi-ranks.
  • Figure 4: Latitude modes $1,2,3$ in blue versus latitude modes $101,102,103$ in red. Higher order modes capture higher frequency information compared to lower order modes.