PINNs算法及其在岩土工程中的应用研究

物理信息神经网络(PINNs)算法采用自动微分方法将偏微分方程直接嵌入神经网络中,从而实现对偏微分方程的智能求解,属于一种新型的无网格算法,具有收敛速度快和计算精度高等优点。PINNs不仅能够实现对偏微分方程求解,还能够对偏微分方程未知参数进行反演,因此对岩土工程复杂问题具有广泛的应用前景。为了验证PINNs算法在岩土工程领域的可行性,对连续排水边界条件下的一维固结理论进行求解和界面参数反演。计算结果表明,PINNs数值结果与解析解具有高度一致性,且界面参数反演结果准确,说明PINNs算法能够为岩土工程相关问题提供新的求解思路。

PINNs algorithm and its application in geotechnical engineering

The physical information neural networks(PINNs) algorithm, a new mesh-free algorithm, uses the automatic differential method to embed the partial differential equation directly into the neural networks so as to realize the intelligent solution of the partial differential equation, which has the advantages of fast convergence speed and high computational accuracy. The PINNs algorithm has a promising application in geotechnical engineering because it can solve the complex partial differential equations(PDEs) and inverse the unknown parameters of the PDEs. In order to verify the feasibility of the PINNs algorithm in geotechnical engineering, the one-dimensional consolidation process with the continuous drainage boundary condition is taken as an example to illustrate the procedures of the PINNs algorithm in terms of both the forward and inverse problems. The results show that the PINNs solution is highly consistent with the analytical one, indicating that the PINNs algorithm can provide an alternative approach for solving the related problems in geotechnical engineering.