从稀疏快照中学习随机动态，无需先验知识即可重建发育轨迹。
Learning stochastic dynamics from snapshots through regularized unbalanced optimal transport
- 基于正则化非平衡最优传输的深度学习方法
- 准确识别生长与转移模式，消除虚假路径
- 适合单细胞数据、基因网络等动态建模场景
从稀疏时间采样的快照中重建动态过程，是自然科学与机器学习中的关键问题。本文提出一种求解正则化非平衡最优传输（RUOT）的深度学习方法，可直接从观测快照中推断连续的非平衡随机动态，无需预先知道增殖或消亡过程。理论上，我们揭示了RUOT与Schrödinger桥问题的联系，并讨论了核心挑战与解决方案。在合成基因调控网络、高维高斯混合模型及血液发育的单细胞RNA-seq数据上验证了方法的有效性。相比现有方法，本方法能准确识别生长与转移模式，消除虚假过渡路径，并构建出Waddington发育景观。代码已开源：https://github.com/zhenyiizhang/DeepRUOT。
原文摘要 · Abstract (English)
Reconstructing dynamics using samples from sparsely time-resolved snapshots is an important problem in both natural sciences and machine learning. Here, we introduce a new deep learning approach for solving regularized unbalanced optimal transport (RUOT) and inferring continuous unbalanced stochastic dynamics from observed snapshots. Based on the RUOT form, our method models these dynamics without requiring prior knowledge of growth and death processes or additional information, allowing them to be learned directly from data. Theoretically, we explore the connections between the RUOT and Schrödinger bridge problem and discuss the key challenges and potential solutions. The effectiveness of our method is demonstrated with a synthetic gene regulatory network, high-dimensional Gaussian Mixture Model, and single-cell RNA-seq data from blood development. Compared with other methods, our approach accurately identifies growth and transition patterns, eliminates false transitions, and constructs the Waddington developmental landscape. Our code is available at: https://github.com/zhenyiizhang/DeepRUOT.
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