# BLISSNet: Deep Operator Learning for Fast and Accurate Flow Reconstruction from Sparse Sensor Measurements

arXiv: https://arxiv.org/abs/2602.24228 · HTML: https://mlsanity.com/paper/2602.24228/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 30 references that are in the map.
- First posted on arXiv 27 Feb 2026.

## Builds on (most cited first, 14 of 14)

- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Transformer for Partial Differential Equations' Operator Learning](https://mlsanity.com/paper/2205.13671/) (2022)
- [A Physics-informed Diffusion Model for High-fidelity Flow Field Reconstruction](https://mlsanity.com/paper/2211.14680/) (2022)
- [DiffusionPDE: Generative PDE-Solving Under Partial Observation](https://mlsanity.com/paper/2406.17763/) (2024)
- [Learnable Fourier Features for Multi-Dimensional Spatial Positional Encoding](https://mlsanity.com/paper/2106.02795/) (2021)
- [Image Reconstruction: From Sparsity to Data-adaptive Methods and Machine Learning](https://mlsanity.com/paper/1904.02816/) (2019)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Variable-Input Deep Operator Networks](https://mlsanity.com/paper/2205.11404/) (2022)
- [Neural Chaos: A Spectral Stochastic Neural Operator](https://mlsanity.com/paper/2502.11835/) (2025)
- [Deep Learning Improvements for Sparse Spatial Field Reconstruction](https://mlsanity.com/paper/2408.12531/) (2024)
- [DynORecon: Dynamic Object Reconstruction for Navigation](https://mlsanity.com/paper/2409.19928/) (2024)
- [On the inadequacy of nudging data assimilation algorithms for non-dissipative systems](https://mlsanity.com/paper/2411.08273/) (2024)

## Built on by (most cited first, 1 of 1)

- [Energy-efficient operation of neural operators for virtual sensing](https://mlsanity.com/paper/2609.30580/) (2026)

## Abstract (arXiv)

Reconstructing fluid flows from sparse sensor measurements is a fundamental challenge in science and engineering. Widely separated measurements and complex, multiscale dynamics make accurate recovery of fine-scale structures difficult. In addition, existing methods face a persistent tradeoff: high-accuracy models are often computationally expensive, whereas faster approaches typically compromise fidelity. In this work, we introduce BLISSNet, a model that strikes a strong balance between reconstruction accuracy and computational efficiency for both flow reconstruction and nudging-based data assimilation. The model follows a DeepONet-like architecture, enabling zero-shot inference on domains of arbitrary size. After the first model call on a given domain, certain network components can be precomputed, leading to low inference cost for subsequent evaluations on large domains. Consequently, the model can achieve faster inference than classical interpolation methods such as radial basis function or bicubic interpolation. This combination of high accuracy, low cost, and zero-shot generalization makes BLISSNet well-suited for large-scale real-time flow reconstruction and data assimilation tasks.