Non-invasive Inference of Thrombus Material Properties with Physics-Informed Neural Networks.
Non-invasive Inference of Thrombus Material Properties with Physics-Informed Neural Networks.
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DOI：
10.1016/j.cma.2020.113603
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发表时间：
2020-05
影响因子：
7.2
通讯作者：
Minglang Yin;Xiaoning Zheng;J. Humphrey;G. Karniadakis
中科院分区：
文献类型：
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作者：
Minglang Yin;Xiaoning Zheng;J. Humphrey;G. Karniadakis
我们使用物理信息神经网络（pinn）来推断使用合成数据的生物材料的性质。特别地，我们成功地应用PINNs从血栓变形数据中提取渗透率和粘弹性模量，这些数据可以用四阶Cahn-Hilliard和Navier-Stokes方程来描述。在pinn中，偏微分方程被编码成一个损失函数，其中的偏导数可以通过自动微分（AD）得到。为了解决用AD计算Cahn-Hilliard方程四阶导数的难题，我们在主神经网络的基础上引入了一个辅助网络来近似能量势项的二阶导数。我们的模型可以同时预测未知的材料参数和速度、压力和变形梯度场，只需训练所有数据中的部分信息，即相场和压力测量，同时在时空域内保持高度灵活的采样以进行数据采集。我们通过光谱/hpelement方法（SEM）的数值解验证了我们的模型，并通过噪声测量训练证明了它的鲁棒性。我们的研究结果表明，pin - ns可以从有噪声的合成数据中推断出材料的性质，因此它们在从实验多模态和多保真度数据中推断这些性质方面具有很大的潜力。
We employ physics-informed neural networks (PINNs) to infer properties of biological materials using synthetic data. In particular, we successfully apply PINNs to extract the permeability and viscoelastic modulus from thrombus deformation data, which can be described by the fourth-order Cahn–Hilliard and Navier–Stokes Equations. In PINNs, the partial differential equations are encoded into a loss function, where partial derivatives can be obtained through automatic differentiation (AD). To tackle the challenge of calculating the fourth-order derivative in the Cahn–Hilliard equation with AD, we introduce an auxiliary network along with the main neural network to approximate the second-derivative of the energy potential term. Our model can simultaneously predict unknown material parameters and velocity, pressure, and deformation gradient fields by merely training with partial information among all data, i.e., phase field and pressure measurements, while remaining highly flexible in sampling within the spatio-temporal domain for data acquisition. We validate our model by numerical solutions from the spectral/hpelement method (SEM) and demonstrate its robustness by training it with noisy measurements. Our results show that PINNs can infer the material properties from noisy synthetic data ►and thus they have great potential for inferring these properties from experimental multi-modality and multi-fidelity data.