发表机构
Princeton University; Stanford University（普林斯顿大学; 斯坦福大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
triangulax是一个基于JAX的Python库，利用三角网格和离散微分几何实现可微分模拟，支持强变形曲面，自动计算力并拟合参数，应用于膜力学、顶点模型及逆向设计。
AI 中文摘要
许多物理和生物系统——泡沫、膜、弹性壳或组织片——可以被数学描述为二维曲面。这些曲面可以承载复杂的动力学，如反应-扩散系统，并经历剧烈的变形。在这里，我们介绍triangulax，一个开源的Python库，用于模拟和几何处理，通过三角网格对曲面进行离散化，可在https://this URL获取。它结合了两个特性。首先，离散微分几何提供了无坐标离散化，这使得模拟强烈变形的曲面成为可能。其次，该库构建在机器学习框架JAX之上，因此基于网格的能量和整个模拟可以自动微分（包括具有随机力或拓扑修改的模拟）。这通过自动计算力简化了多物理模拟，并允许将模型参数拟合到实验数据或设计目标。我们实现了一种算法来保持强烈变形曲面中的网格质量，并将其应用于与膜上浓度场耦合的膜力学模型。我们针对精确解和现有软件验证了我们的方法，并在一系列问题上展示了triangulax，包括膜力学、顶点模型和形状变形弹性体片的逆向设计。
英文摘要
Many physical and biological systems -foams, membranes, elastic shells, or tissue sheets- can be mathematically described as 2D surfaces. These surfaces can host complex dynamics, like reaction-diffusion systems, and undergo drastic deformations. Here, we present triangulax, an open-source Python library for simulations and geometry processing that discretizes surfaces using triangular meshes available at https://github.com/nikolas-claussen/triangulax. It combines two features. First, discrete differential geometry provides coordinate-free discretization, which allows simulating strongly deforming surfaces. Second, the library is built on the machine-learning framework JAX, so mesh-based energies and entire simulations can be differentiated automatically (including simulations with stochastic forces or topological modifications). This simplifies multi-physics simulations by computing forces automatically and allows fitting model parameters to experimental data or design objectives. We implement an algorithm to preserve mesh quality in strongly deforming surfaces and apply it to a model of membrane mechanics coupled to an on-membrane concentration field. We validate our approach against exact solutions and existing software, and demonstrate triangulax across a range of problems, including membrane mechanics, vertex models, and inverse design of a shape-morphing elastomer sheet.
Comments20 pages, 11 figures
