神经算子解决本构模型发现的逆问题
Neural operators solve inverse problems for constitutive model discovery
AI总结：
研究旨在解决材料力学响应表征中优化问题计算成本高且耗时的问题，提出PANO和CANO两种神经算子架构，通过拉普拉斯特征函数编码位移场，训练后能快速表征材料，还测试了其对多种数据的预测能力。
AI中文摘要：
传统上，表征材料的力学响应需要解决优化问题，校准或训练模型参数以最小化模型预测与实验数据之间的差异，此过程计算成本高且耗时。为克服这一限制，我们提出了两种神经算子架构：物理增强神经算子（PANO）和本构人工神经算子（CANO）。它们将实验测量数据直接映射到控制材料力学响应的本构函数。通过拉普拉斯特征函数对位移场进行编码，使预测与离散化无关且抗噪声。框架将输出空间限制为满足基本物理要求的物理上可接受的材料模型。在一系列材料模型的位移场和反作用力模拟数据元组上训练神经算子。训练后，神经算子可实现近乎即时的材料表征，只需一次前向传递就能从给定实验数据集中推断应变能密度函数。我们测试了神经算子对未见数据、噪声数据、缺失信息数据、不同空间离散化数据以及不同尺寸几何数据的预测能力。
英文摘要：
Characterizing the mechanical response of materials traditionally requires solving optimization problems in which model parameters are calibrated or trained to minimize the discrepancy between model predictions and experimental data. This process can be computationally expensive and time-consuming. To overcome this limitation, we propose two neural operator architectures that directly map experimentally measured data to the constitutive functions governing the mechanical response of the material: Physics-Augmented Neural Operators (PANO) and Constitutive Artificial Neural Operators (CANO). The proposed neural operators approximate the mapping between the infinite-dimensional input space of full-field displacement measurements and net reaction forces, and the infinite-dimensional output space of hyperelastic strain-energy density functions. The displacement fields are encoded through Laplacian eigenfunctions to obtain discretization-independent and noise-robust predictions. Our framework constrains the output space to physically admissible material models that satisfy fundamental physical requirements by design. The neural operators are trained on simulated data tuples of displacement fields and reaction forces for a range of material models. Once trained, the neural operators enable near-instantaneous material characterization and require only a single forward pass to infer the strain-energy density function from a given experimental dataset. We test the predictive power of the neural operators for unseen data, noisy data, data with missing information, data from different spatial discretizations, and data from geometries of different sizes.
