用B样条插值改进生成模型，更精准模拟动态系统演化过程。
SplineFlow: Flow Matching for Dynamical Systems with B-Spline Interpolants
- 采用B样条基函数构建稳定平滑的条件路径，避免高阶多项式振荡问题。
- 在多时间点观测下满足多边缘约束，有效建模复杂动态系统轨迹。
- 适用于不规则采样数据，尤其适合细胞轨迹推断等生物动力学任务。
流匹配是一种可扩展的生成框架，用于表征连续归一化流，在多种场景中具有广泛应用。然而，现有先进方法在建模动态系统时表现不佳，因其使用线性插值构造条件路径，难以捕捉真实的状态演化，尤其是在从不规则采样数据中学习高阶动态时。构建满足多边缘约束的统一路径极具挑战，因朴素的高阶多项式易引发不稳定与振荡。本文提出SplineFlow，一种理论严谨的流匹配算法，通过B样条插值联合建模跨观测点的条件路径。SplineFlow利用B样条基的光滑性与稳定性，以结构化方式学习复杂底层动态，同时确保满足多边缘约束。在多种确定性和随机动态系统（含不同复杂度）以及细胞轨迹推断任务上的综合实验表明，SplineFlow显著优于现有基线方法。代码已开源：https://github.com/santanurathod/SplineFlow。
原文摘要 · Abstract (English)
Flow matching is a scalable generative framework for characterizing continuous normalizing flows with wide-range applications. However, current state-of-the-art methods are not well-suited for modeling dynamical systems, as they construct conditional paths using linear interpolants that may not capture the underlying state evolution, especially when learning higher-order dynamics from irregular sampled observations. Constructing unified paths that satisfy multi-marginal constraints across observations is challenging, since naïve higher-order polynomials tend to be unstable and oscillatory. We introduce SplineFlow, a theoretically grounded flow matching algorithm that jointly models conditional paths across observations via B-spline interpolation. Specifically, SplineFlow exploits the smoothness and stability of B-spline bases to learn the complex underlying dynamics in a structured manner while ensuring the multi-marginal requirements are met. Comprehensive experiments across various deterministic and stochastic dynamical systems of varying complexity, as well as on cellular trajectory inference tasks, demonstrate the strong improvement of SplineFlow over existing baselines. Our code is available at: https://github.com/santanurathod/SplineFlow.
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