arXiv:2606.20655physics.comp-phcs.LG2026-06

提出物理可辨识性证书,提前判断流体代理模型能否准确预测关键变量。

Input-schema identifiability limits in physics-informed surrogates for mechanics-governed flow

论文配图:Input-schema identifiability limits in physics-informed surrogates for mechanics-governed flow
图 1 · 摘自论文原文
  • 基于简化物理模型分解目标场,识别输入信息能捕捉的部分
  • 实验证明提供方向可消除角度误差,仅给大小仍存16%-33%符号翻转
  • 适合做生物流体力学建模前的可行性诊断,避免隐藏错误

物理信息与数据驱动代理模型被广泛用于近似力学控制的流场,但其目标量在预测时可能无法从可用输入变量中唯一确定。本文提出一种输入模式可辨识性证书,从降维物理模型出发,将目标场分解为可由几何测量的部分、依赖边界条件的部分,以及仅能按对称商确定的部分。该方法实现训练前审计:预测哪些通道干预能降低误差,哪些无效,哪些模糊性无法通过改变架构、损失函数、优化器或样本量消除。以不可压缩管状流为例,采用柯塞拉杆降维模型,发现腔内速度可分解为可测切向方向、依赖边界条件的幅值,以及符号方向的不确定性。在患者特异性主动脉CFD几何、解析沃默斯利流和对流-扩散转移问题上的受控实验验证了预测模式:提供符号方向后角度误差降至理想水平,而仅提供幅值不给方向则仍存在预测的符号歧义,导致每节点16%-33%的符号翻转。结果为代理建模任务提供了基于力学的可辨识性诊断,揭示了聚合误差指标可能掩盖的失败模式。

原文摘要 · Abstract (English)

Physics-informed and data-driven surrogates are increasingly used to approximate mechanics-governed flow fields, but the target quantities assigned to such models are not always identifiable from the input variables available at prediction time. We introduce an input-schema identifiability certificate for computational surrogates. Starting from a reduced physical model, the certificate decomposes a target field into components that are measurable from geometry, components that require boundary-condition information, and components identifiable only up to a symmetry quotient. This yields a pre-training audit: it predicts which oracle-channel interventions should reduce error, which should fail, and which ambiguity cannot be removed by changing the architecture, loss, optimizer, or sample size. We instantiate the framework for incompressible tubular flow using a Cosserat-rod reduction, where lumen velocity separates into a mesh-measurable tangent direction, a boundary-condition-dependent magnitude, and a signed-orientation ambiguity. Controlled experiments on patient-specific aortic CFD geometries, analytic Womersley flows, and an advection-diffusion transfer problem confirm the predicted pattern: supplying signed direction collapses angular error to the oracle regime, whereas supplying magnitude without orientation leaves the predicted sign ambiguity and yields 16-33 percent per-node sign flips. The results provide a mechanics-based diagnostic for deciding whether a surrogate modelling task is physically identifiable before training, and expose failure modes that aggregate error metrics can hide.

代理模型流体仿真可辨识性生物力学

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