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Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks
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Proposes MMGN, a context-aware implicit neural representation (auto-decoder with Gabor-filter multiplicative modulation) that reconstructs spatiotemporal physical fields from sparse observations, outperforming INR baselines on CESM2 climate and satellite SST data.
Problem
Reconstructing continuous physical fields from sparse, irregular, and random sensor observations, where the generating process is not well understood and time-index-based INRs lack context awareness.
Approach
Replaces the scalar time-index conditioning of INRs with a trainable per-time-step latent code obtained via auto-decoding, and decodes it with a multiplicative and modulated Gabor filter network (MMGN) instead of Fourier features.
Key results
- MMGN achieves the lowest MSE in all 4 tasks at all sampling ratios on both datasets, e.g., 4.244e-3 vs. 8.927e-3 for second-best FFN+P on simulation Task 1 at 5% sampling.
- Reported relative error reductions vs. second-best model range 56.01%-78.94% on simulation data and 16.74%-37.51% on satellite data at the lowest sampling ratios.
- Ablation: removing Gabor filters raises simulation MSE from 4.073e-3 to 1.758e-2; replacing Gabor with Fourier increases simulation MSE to 4.439e-3 and satellite MSE from 6.290e-4 to 7.422e-4.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use MMGN instead of the strongest baseline | CESM2 simulation reconstruction at 5% sampling · CESM2 simulation, Tasks 1–4 | MSE: 78.24%; 57.79%; 78.94%; 56.01% | Helped |
| Use MMGN instead of the strongest baseline | Satellite SST reconstruction at 0.1% sampling · Satellite SST, Tasks 1–4 | MSE: 37.51%; 29.35%; 20.26%; 16.74% | Helped |
| Remove Gabor filters (ablation) | MMGN · CESM2 simulation | MSE: 4.073$e$-3 -> 1.758$e$-2 | Hurt |
| Remove Gabor filters (ablation) | MMGN · Satellite SST | MSE: 6.290$e$-4 -> 6.883$e$-3 | Hurt |
| Replace Gabor filters with Fourier filters (ablation) | MMGN · CESM2 simulation | MSE: 4.073$e$-3 -> 4.439$e$-3; 9.0% drop | Hurt |
| Replace Gabor filters with Fourier filters (ablation) | MMGN · Satellite SST | MSE: 6.290$e$-4 -> 7.422$e$-4; 18.1% decrease | Hurt |
| Reduce latent size to 1 (ablation) | MMGN · CESM2 simulation and Satellite SST | MSE | Helped |
| Increase latent size (ablation) | MMGN · CESM2 simulation | MSE | Helped |
| Remove an individual latent variable (ablation) | MMGN latent code · CESM2 simulation | MSE | Hurt |
Surprising findings
- Reducing latent size to 1 still gives MMGN a slight consistent edge over ResMLP, suggesting the context-aware indexing helps even with a scalar latent.
- SIREN and FFN+P fail to produce meaningful reconstructions at extremely sparse (0.1%) satellite sampling, while ResMLP is competitive there.
Limitations
- Focuses on reconstructing a single selected trajectory; no generalization to multiple trajectories or climate variables shown.
- Error rises noticeably at 10% noise on simulation data.
- Forecasting and temporal interpolation are discussed only conceptually, without experiments.
Experimental setup
Datasets: CESM2 pre-industrial control run surface temperature GHRSST Level 4 MUR global SST
Benchmarks: CESM2 surface temperature reconstruction (4 tasks, 3 sampling ratios each) GHRSST MUR SST reconstruction (4 tasks)
Metrics: MSE PSNR SSIM inference speed NMSE
Baselines: ResMLP SIREN FFN+P FFN+G
Builds on: multiplicative filter network auto-decoder (DeepSDF-style) Fourier feature networks SIREN
Closest papers by meaning
- Deep Random Features for Scalable Interpolation of Spatiotemporal Data (ICLR 2025 · similarity 0.85)
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- Grids Often Outperform Implicit Neural Representation at Compressing Dense Signals (NeurIPS 2025 · similarity 0.85)
- SINR: Sparsity Driven Compressed Implicit Neural Representations (CVPR 2025 · similarity 0.84)
- CALM-PDE: Continuous and Adaptive Convolutions for Latent Space Modeling of Time-dependent PDEs (NeurIPS 2025 · similarity 0.84)
- Sparsely-Supervised Data Assimilation via Physics-Informed Schrödinger Bridge (NeurIPS 2026 · similarity 0.84)
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