# Reconstruction of 4D Mitral Regurgitation Hemodynamics from Sparse Planar Data using Deep Operator Networks with Test-Time Adaptation

arXiv: https://arxiv.org/abs/2609.20857 · HTML: https://mlsanity.com/paper/2609.20857/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 31 Aug 2026.

## Builds on (most cited first, 10 of 10)

- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Sigmoid-Weighted Linear Units for Neural Network Function Approximation in Reinforcement Learning](https://mlsanity.com/paper/1702.03118/) (2017)
- [A Comprehensive Survey on Test-Time Adaptation under Distribution Shifts](https://mlsanity.com/paper/2303.15361/) (2023)
- [Physics-Informed Deep Neural Operator Networks](https://mlsanity.com/paper/2207.05748/) (2022)
- [Deep transfer operator learning for partial differential equations under conditional shift](https://mlsanity.com/paper/2204.09810/) (2022)
- [Reliable extrapolation of deep neural operators informed by physics or sparse observations](https://mlsanity.com/paper/2212.06347/) (2022)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Recent Advances on Machine Learning for Computational Fluid Dynamics: A Survey](https://mlsanity.com/paper/2408.12171/) (2024)
- [Constrained optimization of sensor placement for nuclear digital twins](https://mlsanity.com/paper/2306.13637/) (2023)
- [Enhanced Vascular Flow Simulations in Aortic Aneurysm via Physics-Informed Neural Networks and Deep Operator Networks](https://mlsanity.com/paper/2503.17402/) (2025)

## Abstract (arXiv)

Quantifying mitral regurgitation severity remains limited by the assumptions of clinical flow convergence methods, while high-fidelity simulation and volumetric velocimetry are too slow for routine use. We investigate whether a learned solution operator can reconstruct transient three-dimensional transvalvular hemodynamics from the sparse observation an in-vitro experiment actually provides: a single planar velocity slice and two boundary pressure traces. A Deep Operator Network is pretrained on an experimentally benchmarked URANS database spanning eleven mitral regurgitation orifice phantoms, learning a mapping from a masked two-component planar velocity snapshot to the surrounding volumetric field, and is subsequently adapted to unseen target cases by fine-tuning on their sparse measurements. Adaptation reliably corrects the flow topology within the supervised plane, reorienting a strongly eccentric jet that the pretrained operator predicts as straight, and yields full-field predictions in minutes rather than the days required by the underlying simulations. Its influence decays sharply with distance from that plane, however: measured against phase-resolved particle image velocimetry, the reconstruction error rises from 24.6% at 2mm to 52.6% at 6mm, and the resulting mismatch between corrected and uncorrected layers degrades physical consistency. Single-plane supervision thus constrains the observed plane far more effectively than the surrounding volume, which we identify as the principal obstacle to coherent 4D reconstruction from sparse planar data.