arXiv:2510.00884cs.CEcs.LG2025-10被引 6

用批量向量化加速材料本构计算,让有限元模拟快了上千倍。

COMMET: orders-of-magnitude speed-up in finite element method via batch-vectorized neural constitutive updates

  • 设计新架构支持批量向量化本构求解,取代传统逐个计算。
  • 相比传统方法,计算速度提升超过三个数量级(即1000倍以上)。
  • 适合需要大规模高精度仿真的工程与力学研究者使用。

复杂材料模型在有限元(FE)仿真中常使本构计算成为主要性能瓶颈。神经本构模型(NCMs)虽能灵活建模复杂材料行为,但因需反复计算应力和刚度,导致计算开销巨大,其庞大的计算图使得传统自动微分方法难以应对,限制了其在大规模问题中的应用。本文提出COMMET,一个从底层重构的开源有限元框架,通过新型批处理向量化装配算法、优化计算图的导数计算替代自动微分,以及基于MPI的分布式内存并行机制,显著降低运行时间。实验表明,相较传统非向量化自动微分实现,该方法在速度上实现超三个数量级的提升。尽管主要针对NCMs验证,但其原理可推广至所有受循环遍历装配或本构更新限制性能的场景,为计算力学中的大规模高保真仿真树立了新标准。

原文摘要 · Abstract (English)

Constitutive evaluations often dominate the computational cost of finite element (FE) simulations whenever material models are complex. Neural constitutive models (NCMs) offer a highly expressive and flexible framework for modeling complex material behavior in solid mechanics. However, their practical adoption in large-scale FE simulations remains limited due to significant computational costs, especially in repeatedly evaluating stress and stiffness. NCMs thus represent an extreme case: their large computational graphs make stress and stiffness evaluations prohibitively expensive, restricting their use to small-scale problems. In this work, we introduce COMMET, an open-source FE framework whose architecture has been redesigned from the ground up to accelerate high-cost constitutive updates. Our framework features a novel assembly algorithm that supports batched and vectorized constitutive evaluations, compute-graph-optimized derivatives that replace automatic differentiation, and distributed-memory parallelism via MPI. These advances dramatically reduce runtime, with speed-ups exceeding three orders of magnitude relative to traditional non-vectorized automatic differentiation-based implementations. While we demonstrate these gains primarily for NCMs, the same principles apply broadly wherever for-loop based assembly or constitutive updates limit performance, establishing a new standard for large-scale, high-fidelity simulations in computational mechanics.

有限元神经本构加速计算高性能

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