用结构保持方法构建实时数字孪生，支持传感器闭环校准。
Structure-Preserving Digital Twins via Conditional Neural Whitney Forms
- 基于条件注意力机制学习降维基和非线性守恒律，保证数值稳定。
- 在稀疏数据下仍准确预测湍流过渡，推理速度达0.1秒，快3.1亿倍于大涡模拟。
- 可对接传统有限元工具，适合复杂几何与工业场景的实时仿真。
我们提出一种基于结构保持降维有限元模型的实时数字孪生框架，该模型通过潜变量Z进行条件控制。方法利用条件注意力机制，在有限元外微分形式（FEEC）框架内同时学习降维基函数和非线性守恒律，确保数值适定性与守恒量的精确保持，不受数据稀疏或优化误差影响。条件机制支持对参数变量的实时校准，实现与传感器数据的闭环推理与更新。框架以非侵入方式对接传统有限元计算流程，可处理复杂几何，并融合学习模型与经典有限元技术。基准测试涵盖对流扩散、激波流体动力学、静电场及复杂电池热失控问题。在仅25次大涡模拟数据条件下，成功捕捉湍流转捩，实现约0.1秒的实时推理，相较大涡模拟提速3.1×10⁸倍。开源代码已发布于GitHub。
原文摘要 · Abstract (English)
We present a framework for constructing real-time digital twins based on structure-preserving reduced finite element models conditioned on a latent variable Z. The approach uses conditional attention mechanisms to learn both a reduced finite element basis and a nonlinear conservation law within the framework of finite element exterior calculus (FEEC). This guarantees numerical well-posedness and exact preservation of conserved quantities, regardless of data sparsity or optimization error. The conditioning mechanism supports real-time calibration to parametric variables, allowing the construction of digital twins which support closed loop inference and calibration to sensor data. The framework interfaces with conventional finite element machinery in a non-invasive manner, allowing treatment of complex geometries and integration of learned models with conventional finite element techniques. Benchmarks include advection diffusion, shock hydrodynamics, electrostatics, and a complex battery thermal runaway problem. The method achieves accurate predictions on complex geometries with sparse data (25 LES simulations), including capturing the transition to turbulence and achieving real-time inference ~0.1s with a speedup of 3.1x10^8 relative to LES. An open-source implementation is available on GitHub.
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