AI 中文总结
该研究提出无生成模型的自由形式变形方法，通过将变形建模为ODE流，用FFD参数化速度场，证明其理论表达性，结合生成方法实现高效采样等，在变形体流动基准测试中提升了降阶模型的精度和效率。
AI 中文摘要
我们通过将变形建模为常微分方程（ODE）的流，引入了一个与拓扑无关的框架，用于匹配具有非同构网格图的三维形状的变形。速度场由与时间相关的自由形式变形（FFD）参数化，通过粗控制晶格的位移表示，产生一个平滑且低维的表示，使变形模型与源表面和目标表面的离散化解耦。在适度的正则性假设下，我们证明了诱导的ODE映射是亏格为0的表面之间映射的通用逼近器（在sup范数下），提供了理论上的表达保证。为了进一步压缩表示并实现概率推理，我们将ODE - FFD模型与TarFlow框架中基于流的生成方法相结合，学习FFD映射时间序列上的紧凑潜在参数化。所得方法支持对合理变形轨迹进行高效采样和优化，同时保持网格质量，并实现可扩展的降阶建模。在变形体流动基准测试上的实验表明，从学习到的潜在动力学构建的降阶模型具有更高的精度和计算效率。
英文摘要
We introduce a topology-agnostic framework for matching deformations of three-dimensional shapes with non-isomorphic mesh graphs by modelling the deformation as the flow of an Ordinary Differential Equation (ODE). The velocity field is parameterised by a time-dependent Free Form Deformation (FFD), expressed through displacements of a coarse control lattice, yielding a smooth and low-dimensional representation that decouples the deformation model from the discretisation of the source and target surfaces. Under mild regularity assumptions, we prove that the induced ODE map is a universal approximator (in the sup norm) for mappings between genus-0 surfaces, providing a theoretical expressivity guarantee. To further compress the representation and enable probabilistic inference, we couple the ODE--FFD model with a flow-based generative approach in the TarFlow framework, learning a compact latent parametrisation over time series of FFD maps. The resulting method supports efficient sampling and optimisation of plausible deformation trajectories while preserving mesh quality, and it enables scalable reduced-order modelling. Experiments on deforming-body flow benchmarks demonstrate improved accuracy and computational efficiency of reduced-order models constructed from the learned latent dynamics.
Comments48 pages, 14 figures
