# Physics-Aware Neural Operators for Direct Inversion in 3D Photoacoustic Tomography

arXiv: https://arxiv.org/abs/2509.09894 · HTML: https://mlsanity.com/paper/2509.09894/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 11 of its 45 references that are in the map.
- First posted on arXiv 11 Sep 2025.

## Builds on (most cited first, 11 of 11)

- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [High-Resolution Image Synthesis with Latent Diffusion Models](https://mlsanity.com/paper/2112.10752/) (2021)
- [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)
- [3D U-Net: Learning Dense Volumetric Segmentation from Sparse Annotation](https://mlsanity.com/paper/1606.06650/) (2016)
- [InverseBench: Benchmarking Plug-and-Play Diffusion Priors for Inverse Problems in Physical Sciences](https://mlsanity.com/paper/2503.11043/) (2025)
- [Neural Operators with Localized Integral and Differential Kernels](https://mlsanity.com/paper/2402.16845/) (2024)
- [Scalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions](https://mlsanity.com/paper/2209.13603/) (2022)
- [A Unified Model for Compressed Sensing MRI Across Undersampling Patterns](https://mlsanity.com/paper/2410.16290/) (2024)
- [Ultrasound Lung Aeration Map via Physics-Aware Neural Operators](https://mlsanity.com/paper/2501.01157/) (2025)
- [Single-shot 3D photoacoustic computed tomography with a densely packed array for transcranial functional imaging](https://mlsanity.com/paper/2306.14471/) (2023)

## Built on by (most cited first, 3 of 3)

- [From Black Hole to Galaxy: Neural Operator: Framework for Accretion and Feedback Dynamics](https://mlsanity.com/paper/2512.01576/) (2025)
- [Self-Supervised Learning via Flow-Guided Neural Operator on Time-Series Data](https://mlsanity.com/paper/2602.12267/) (2026)
- [A library for differentiable signal processing and machine learning on the sphere](https://mlsanity.com/paper/2609.39737/) (2026)

## Abstract (arXiv)

Learning physics-constrained inverse operators-rather than post-processing physics-based reconstructions-is a broadly applicable strategy for problems with expensive forward models. We demonstrate this principle in three-dimensional photoacoustic computed tomography (3D PACT), where current systems demand dense transducer arrays and prolonged scans, restricting clinical translation. We introduce PANO (PACT imaging neural operator), an end-to-end physics-aware neural operator-a deep learning architecture that generalizes across input sampling densities without retraining-that directly learns the inverse mapping from raw sensor measurements to a 3D volumetric image. Unlike two-step methods that reconstruct then denoise, PANO performs direct inversion in a single pass, jointly embedding physics and data priors. It employs spherical discrete-continuous convolutions to respect hemispherical sensor geometry and Helmholtz equation constraints to ensure physical consistency. PANO reconstructs high-quality images from both simulated and real data across diverse sparse acquisition settings, achieves real-time inference and outperforms the widely-used UBP algorithm by approximately 33 percentage points in cosine similarity on simulated data and 14 percentage points on real phantom data. These results establish a pathway toward more accessible 3D PACT systems for preclinical research, and motivate future in-vivo validation for clinical translation.