发表机构
TU Dresden（德累斯顿工业大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究提出一种无监督学习框架，结合全场实验数据校准物理增强神经网络，通过平衡间隙法等优化算法实现小应变粘弹性模型的高效校准，在带噪合成数据上验证了其优异性能。
AI 中文摘要
我们提出一种无监督学习框架，用于通过全场数据校准用于小应变粘弹性的物理增强神经网络（PANN）。该框架仅需真实实验中可直接获取的量进行训练，即全局反作用力和表面位移。底层PANN嵌入广义标准材料理论中，其中两个标量势使本构模型在构建上具有热力学一致性，而基于不变量的自由能表示和对偶耗散势进一步确保材料对称性。考虑平面应力假设下的薄试样，我们基于平衡间隙方法结合拟牛顿优化器和自动微分构建约束优化问题。由此，未知的面外应变由平面应力条件得出，内部变量的演化由隐式时间积分格式捕捉。所得非线性方程组在积分点和时间步通过局部牛顿迭代求解。为大幅降低训练的计算成本，采用伴随反向法计算目标损失的梯度，而非反向传播所有牛顿迭代步骤。所提框架在合成数据（含带噪位移和力）上得到验证，在宽范围变形速率和载荷路径下均表现出优异一致性。
英文摘要
We propose an unsupervised learning framework for calibrating a physics-augmented neural network (PANN) for small-strain viscoelasticity via full-field data. It only requires quantities that are directly accessible in real experiments for training, namely global reaction forces and surface displacements. The underlying PANN is embedded in the generalized standard materials theory, in which two scalar-valued potentials render the constitutive model thermodynamically consistent by construction, while invariant-based representations of the free energy and the dual dissipation potential additionally ensure material symmetry. Considering a thin specimen under the plane stress assumption, we formulate a constrained optimization problem based on the equilibrium gap method in combination with quasi-Newton optimizers and automatic differentiation. Thereby, the unknown out-of-plane strain follows from the plane stress condition and the evolution of the internal variables is captured by an implicit time integration scheme. The resulting system of nonlinear equations is solved via a local Newton iteration at quadrature point and time step. To drastically reduce the computational cost of training, the backward adjoint method is employed to compute the gradient of the target loss, instead of backpropagating through all Newton iteration steps. The proposed framework is demonstrated for synthetic data, including noisy displacements and forces, showing excellent agreement across a wide range of deformation rates and load paths.
