arXiv AI By Yuhao Sun, Zekun Wu, Zixun Huang, Peijie Zhou

TracingFlow: A Simulation-Free Trajectory Inference Framework Based on Second-Order Dynamics

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arXiv AI
Sep 7

Simulation-free Unbalanced Dynamic Optimal Transport with General Growth Penalty

The paper introduces SUDO, a simulation‑free framework for unbalanced dynamic optimal transport (UDOT) that supports general convex growth penalties beyond the quadratic Wasserstein‑Fisher‑Rao case. By showing that concave penalties lead to degenerate solutions, the authors focus on convex penalties, learning conditional paths and transport costs to solve a semi‑coupling problem and then applying unbalanced flow matching. On benchmark datasets, SUDO matches the accuracy of analytical WFR solvers while being faster than simulation‑based methods, and it also handles asymmetric penalties that better reflect proliferation‑dominant biological priors.

By Junda Ying, Yuxuan Wang, Bowen Yang, Peijie Zhou, Lei Zhang
arXiv Machine Learning
3d ago

A Variational Optimal Transport Operator on Incompressible Flow

The paper introduces the Variational Incompressible Optimal Transport (VIOT) operator, a generative neural operator that predicts divergence‑free velocity fields for incompressible density transport. VIOT combines a stream‑function representation, a regularized transport objective, and a Fourier Neural Operator backbone to amortize the solve across new source‑target pairs and grid resolutions. Experiments on 2D and 3D benchmarks show that VIOT produces full transport trajectories in seconds, achieving roughly a $10^4 imes$ speedup over per‑instance baselines that require hours of optimization.

By Jinjin He, Shenyifan Lu, Sinan Wang, Zhiqi Li, Duowen Chen, Bo Zhu
arXiv Computer Vision
Sep 11

Two-Parameter Flow Map Learning for Continuous-Time Diffeomorphic Image Registration

The paper introduces a new framework for learning continuous-time diffeomorphic image registration by modeling a non-autonomous ODE as a two-parameter flow map. By enforcing cocycle consistency, the method learns flow maps without time discretization or velocity integration during training, enabling efficient inference with few compositions. Experiments on nine datasets show consistent alignment improvements, including a 2.1% Dice gain on brain MRI, 12% TRE reduction on lung CT, and 2.6% Dice improvement on cardiac MRI and ultrasound.

By Mohammadjavad Matinkia, Nilanjan Ray