超越场精度：逆物理信息神经网络参数误差的双轴诊断
Beyond Field Accuracy: Two-Axis Diagnosis of Inverse-PINN Parameter Error
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中文总结 AI 辅助
针对逆PINNs的参数误差问题，提出双轴后训练诊断方法，经三类合成PDE及耦合双参数达西检验验证，可有效分离有限样本分辨率与参数偏好，助力后续研究方向确定。
中文摘要 AI 辅助
逆物理信息神经网络（Inverse PINNs）可精准重建场，但会返回错误的物理参数。本文提出一种训练后双轴诊断方法，该方法在指定观测与估计协议下，将有限样本分辨率与最终学习到的场及残差指标编码的带符号参数偏好分离开。第一轴通过匹配的正向估计器反复拟合含噪观测值；第二轴在已知合成真值的情况下，冻结场与残差视图，计算指向附近残差轮廓最小值的局部得分位移，再通过端点一致性检验联合训练是否在相同最终视图下实现该偏好。在三个合成一维标量参数偏微分方程（PDE）上，匹配正向平均绝对相对误差范围为2.34%至17.46%；该位移在固定随机种子、架构及含噪重训练时，可追踪冻结轮廓最小值（相关系数r介于0.945至0.982之间），在240次含噪随机边界算法（RBA）运行中，可追踪已实现的带符号对数误差（r=0.994，240次中有237次方向正确）；耦合双参数达西检验验证了完整矩阵计算。这两个轴是互补的诊断坐标，而非可加误差分量或无需先验的可部署估计器，共同为后续研究指明方向：可从观测值、残差证据或端点交付入手。
英文摘要
Inverse physics-informed neural networks (PINNs) can reconstruct a field accurately while returning an incorrect physical parameter. We introduce a two-axis post-training diagnosis that separates finite-sample resolution under a specified observation-and-estimation protocol from the signed parameter preference encoded by the final learned field and residual metric. The first axis repeatedly fits noisy observations with a matched forward estimator. At known synthetic truth, the second freezes the field and residual view and computes a local score displacement toward a nearby residual-profile minimum. Endpoint consistency then tests whether joint training delivers that preference under the same final view. Across three synthetic one-dimensional, scalar-parameter PDEs, matched-forward mean absolute relative error ranges from 2.34 percent to 17.46 percent. The displacement tracks frozen-profile minima across locked seeds, architectures, and fresh-noise retraining (r from .945 to .982), and it tracks delivered signed log-error in 240 fresh-noise RBA runs (r = .994; 237/240 correct directions). A coupled two-parameter Darcy check validates the full matrix calculation. The axes are complementary diagnostic coordinates, not additive error components or a deployable oracle-free estimator. Together, they route follow-up work toward observations, residual evidence, or endpoint delivery.
发表机构
- School of Software Engineering, South China University of Technology（华南理工大学软件学院）
机构由 AI 辅助整理，请以论文原文为准。
