用于从低分辨率和噪声位移数据估计非均匀弹性特性的概率物理信息神经网络
Probabilistic Physics-Informed Neural Networks for Estimating Heterogeneous Elastic Properties from Low-Resolution and Noisy Displacement Data
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中文总结 AI 辅助
针对从低分辨率和噪声位移数据估计非均匀弹性特性的不适定问题，提出PIE - PINN框架，结合B样条引导位移网络与分层半柯西模型，用交替最大似然训练策略，能稳健估计杨氏模量和泊松比，案例研究验证了其稳健性。
中文摘要 AI 辅助
从低分辨率位移测量中估计空间非均匀弹性特性是一个严重不适定的逆弹性问题，因为低分辨率模糊了区分非均匀特性变化所需的空间细节，且小的测量扰动或拟合误差会在逆估计中放大。现有逆方法常依赖高保真观测和手动预设损失权重，限制了适应性且对噪声和分辨率退化敏感。我们提出概率逆弹性物理信息神经网络（PIE - PINN）框架，用于从噪声、低分辨率位移数据中稳健估计杨氏模量和泊松比。PIE - PINN在统一概率模型中使用拉普拉斯分布对位移观测、应变差异和平衡残差进行建模。为提高稳健性，该框架将B样条引导的位移网络与用于位移残差尺度的分层半柯西模型相结合。通过交替最大似然训练策略更新均值和尺度。系统案例研究表明了PIE - PINN的稳健性。
英文摘要
Estimating spatially heterogeneous elastic properties from low-resolution displacement measurements is a severely ill-posed inverse elasticity problem because low resolution obscures spatial details needed to distinguish heterogeneous property variations, and small measurement perturbations or fitting errors are amplified through inverse estimation. Existing inverse methods often rely on high-fidelity observations and manually prespecified loss weights, limiting their adaptability and making them sensitive to noise and resolution degradation. We propose a Probabilistic Inverse Elasticity Physics-Informed Neural Network (PIE-PINN) framework for robust estimation of Young's modulus and Poisson's ratio from noisy, low-resolution displacement data. PIE-PINN models displacement observation, strain-discrepancy, and equilibrium residuals using Laplace distributions within a unified probabilistic model. To improve robustness, the framework combines a B-spline-guided displacement network with a hierarchical half-Cauchy model for displacement residual scales. The B-spline provides a smooth global representation of the displacement field, while the neural network correction captures local variations. The hierarchical scale model adaptively downweights severe displacement fitting errors, enabling more robust recovery of the latent mean displacement field. An alternating maximum-likelihood training strategy updates the mean through weighted residual minimization and updates the scales to adjust the loss weights. Systematic case studies across varying noise levels and observation resolutions demonstrate the robustness of PIE-PINN.
发表机构
- Texas A&M University（德克萨斯A&M大学）
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