# SurgFormer: Scalable Learning of Organ Deformation with Resection Support and Real-Time Inference

arXiv: https://arxiv.org/abs/2603.06543 · HTML: https://mlsanity.com/paper/2603.06543/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 22 references that are in the map.
- First posted on arXiv 6 Mar 2026.

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

- [PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation](https://mlsanity.com/paper/1612.00593/) (2016)
- [FlashAttention: Fast and Memory-Efficient Exact Attention with IO-Awareness](https://mlsanity.com/paper/2205.14135/) (2022)
- [Learning Mesh-Based Simulation with Graph Networks](https://mlsanity.com/paper/2010.03409/) (2020)
- [Fourier Neural Operator with Learned Deformations for PDEs on General Geometries](https://mlsanity.com/paper/2207.05209/) (2022)
- [Point-Voxel CNN for Efficient 3D Deep Learning](https://mlsanity.com/paper/1907.03739/) (2019)
- [GNOT: A General Neural Operator Transformer for Operator Learning](https://mlsanity.com/paper/2302.14376/) (2023)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [Geometry Aware Operator Transformer as an Efficient and Accurate Neural Surrogate for PDEs on Arbitrary Domains](https://mlsanity.com/paper/2505.18781/) (2025)
- [Harnessing Scale and Physics: A Multi-Graph Neural Operator Framework for PDEs on Arbitrary Geometries](https://mlsanity.com/paper/2411.15178/) (2024)
- [MeshGraphNet-Transformer: Scalable Mesh-based Learned Simulation for Solid Mechanics](https://mlsanity.com/paper/2601.23177/) (2026)
- [Neural-Initialized Newton: Accelerating Nonlinear Finite Elements via Operator Learning](https://mlsanity.com/paper/2511.06802/) (2025)
- [A Review on Organ Deformation Modeling Approaches for Reliable Surgical Navigation using Augmented Reality](https://mlsanity.com/paper/2408.02713/) (2024)
- [Soft Tissue Simulation and Force Estimation from Heterogeneous Structures using Equivariant Graph Neural Networks](https://mlsanity.com/paper/2509.10125/) (2025)
- [Neural-Augmented Kelvinlet for Real-Time Soft Tissue Deformation Modeling](https://mlsanity.com/paper/2506.08043/) (2025)

## Abstract (arXiv)

We introduce SurgFormer, a multiresolution gated transformer for data driven soft tissue simulation on volumetric meshes. High fidelity biomechanical solvers are often too costly for interactive use, so we train SurgFormer on solver generated data to predict nodewise displacement fields at near real time rates. SurgFormer builds a fixed mesh hierarchy and applies repeated multibranch blocks that combine local message passing, coarse global self attention, and pointwise feedforward updates, fused by learned per node, per channel gates to adaptively integrate local and long range information while remaining scalable on large meshes. For cut conditioned simulation, resection information is encoded as a learned cut embedding and provided as an additional input, enabling a unified model for both standard deformation prediction and topology altering cases. We also introduce two surgical simulation datasets generated under a unified protocol with XFEM based supervision: a cholecystectomy resection dataset and an appendectomy manipulation and resection dataset with cut and uncut cases. To our knowledge, this is the first learned volumetric surrogate setting to study XFEM supervised cut conditioned deformation within the same volumetric pipeline as standard deformation prediction. Across diverse baselines, SurgFormer achieves strong accuracy with favorable efficiency, making it a practical backbone for both tasks. Code, data, and project page: hrefhttps://mint-vu.github.io/SurgFormer/available here