# Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks

arXiv: https://arxiv.org/abs/2401.11611 · HTML: https://mlsanity.com/paper/2401.11611/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Builds on 26 of its 54 references that are in the map.
- First posted on arXiv 21 Jan 2024.

## Builds on (most cited first, 26 of 26)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [Occupancy Networks: Learning 3D Reconstruction in Function Space](https://mlsanity.com/paper/1812.03828/) (2018)
- [Diffusion Posterior Sampling for General Noisy Inverse Problems](https://mlsanity.com/paper/2209.14687/) (2022)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [Generative Image Inpainting with Contextual Attention](https://mlsanity.com/paper/1801.07892/) (2018)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Fundamentals of Recurrent Neural Network (RNN) and Long Short-Term Memory (LSTM) Network](https://mlsanity.com/paper/1808.03314/) (2018)
- [Deep Fluids: A Generative Network for Parameterized Fluid Simulations](https://mlsanity.com/paper/1806.02071/) (2018)
- [MeshfreeFlowNet: A Physics-Constrained Deep Continuous Space-Time Super-Resolution Framework](https://mlsanity.com/paper/2005.01463/) (2020)
- [Any-resolution Training for High-resolution Image Synthesis](https://mlsanity.com/paper/2204.07156/) (2022)
- [Dynamic CT Reconstruction from Limited Views with Implicit Neural Representations and Parametric Motion Fields](https://mlsanity.com/paper/2104.11745/) (2021)
- [Neural Implicit Flow: a mesh-agnostic dimensionality reduction paradigm of spatio-temporal data](https://mlsanity.com/paper/2204.03216/) (2022)
- [Bayesian parameter estimation using conditional variational autoencoders for gravitational-wave astronomy](https://mlsanity.com/paper/1909.06296/) (2019)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [Arbitrary-Scale Image Synthesis](https://mlsanity.com/paper/2204.02273/) (2022)
- [PDE-Driven Spatiotemporal Disentanglement](https://mlsanity.com/paper/2008.01352/) (2020)
- [Learning Vortex Dynamics for Fluid Inference and Prediction](https://mlsanity.com/paper/2301.11494/) (2023)
- [SPIN: Simplifying Polar Invariance for Neural networks Application to vision-based irradiance forecasting](https://mlsanity.com/paper/2111.14507/) (2021)
- [Faster Kernel Interpolation for Gaussian Processes](https://mlsanity.com/paper/2101.11751/) (2021)
- [Inferring propagation paths for sparsely observed perturbations on complex networks](https://mlsanity.com/paper/1801.01179/) (2017)

## Built on by (most cited first, 20 of 20)

- [Deep Operator Learning for High-Fidelity Fluid Flow Field Reconstruction from Sparse Sensor Measurements](https://mlsanity.com/paper/2412.08009/) (2024)
- [Explorable INR: An Implicit Neural Representation for Ensemble Simulation Enabling Efficient Spatial and Parameter Exploration](https://mlsanity.com/paper/2504.00904/) (2025)
- [Spatiotemporal Implicit Neural Representation as a Generalized Traffic Data Learner](https://mlsanity.com/paper/2405.03185/) (2024)
- [Breaking the Discretization Barrier of Continuous Physics Simulation Learning](https://mlsanity.com/paper/2509.17955/) (2025)
- [SENDAI: A Hierarchical Sparse-measurement, EfficieNt Data AssImilation Framework](https://mlsanity.com/paper/2601.21664/) (2026)
- [From Sparse Sensors to Continuous Fields: STRIDE for Spatiotemporal Reconstruction](https://mlsanity.com/paper/2602.04201/) (2026)
- [Implicit Neural Representations for Simultaneous Reduction and Continuous Reconstruction of Multi-Altitude Climate Data](https://mlsanity.com/paper/2409.17367/) (2024)
- [STACI: Spatio-Temporal Aleatoric Conformal Inference](https://mlsanity.com/paper/2505.21658/) (2025)
- [FA-INR: Adaptive Implicit Neural Representations for Interpretable Exploration of Simulation Ensembles](https://mlsanity.com/paper/2506.06858/) (2025)
- [LASER: Learning Active Sensing for Continuum Field Reconstruction](https://mlsanity.com/paper/2604.19355/) (2026)
- [Studying the Impact of Latent Representations in Implicit Neural Networks for Scientific Continuous Field Reconstruction](https://mlsanity.com/paper/2404.06418/) (2024)
- [Collaborative Imputation of Urban Time Series through Cross-city Meta-learning](https://mlsanity.com/paper/2501.11306/) (2025)
- [Generalizable Implicit Neural Representations via Parameterized Latent Dynamics for Baroclinic Ocean Forecasting](https://mlsanity.com/paper/2503.21588/) (2025)
- [Dynamical Implicit Neural Representations](https://mlsanity.com/paper/2511.21787/) (2025)
- [Performance and Efficiency of Climate In-Situ Data Reconstruction: Why Optimized IDW Outperforms kriging and Implicit Neural Representation](https://mlsanity.com/paper/2512.11832/) (2025)
- [Sparsely-Supervised Data Assimilation via Physics-Informed Schr"odinger Bridge](https://mlsanity.com/paper/2603.22319/) (2026)
- [WindINR: Latent-State INR for Fast Local Wind Query and Correction in Complex Terrain](https://mlsanity.com/paper/2605.09511/) (2026)
- [TRACE: Retrospective Streaming Generation of Physical Fields under Sparse Structured Sensing](https://mlsanity.com/paper/2608.26219/) (2026)
- [REACT: Physically and Chemically Consistent Reconstruction of Marine Active Tracers](https://mlsanity.com/paper/2610.03888/) (2026)
- [Refined Grid Sampling for Efficient Implicit Neural Representations of Large-Scale Scientific Data](https://mlsanity.com/paper/2610.14205/) (2026)

## Abstract (arXiv)

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.