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改进PINNs算法及其在非线性固结求解中的应用

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饱和软土非线性固结模型求解以数值方法为主,解析求解较为困难.以连续排水边界条件下的一维非线性固结问题为例,介绍了一种新的非传统数值方法——物理信息神经网络(PINNs)方法,并引入硬约束对原始PINNs算法进行修正,获得了具有较高计算精度的改进PINNs(PINNs-H)数值解.此外,基于孔隙水压力的时空测量数据,采用PINNs-H算法对固结模型中的非线性因子(Nσ)进行了反演.结果表明:在压缩指数Cc与渗透指数Ck比值等于1时,PINNs-H解与解析解吻合良好,而PINNs解误差较大;当Cc/Ck ≠ 1时,对比有限差分解,PINNs-H解是连续的,且基于较少的训练样本点,即可获得相似的平均固结度解答;PINNs-H算法能够获得准确的No反演结果,而PINNs算法则反演偏差较大.该方法为研究软土固结问题提供了一种新的求解思路.
Improved PINNs and Their Application in Nonlinear Consolidation Problems
The nonlinear consolidation models of saturated soft soils,generally difficult to resolve analytically,are mainly solved based on traditional numerical methods.Considering a one-dimensional nonlinear consolidation problem with continuous drainage boundary conditions,we introduce a new nontraditional numerical method,i.e.,physics-informed neural networks(PINNs),take the hard constraints into for modification,and obtain its high-precision PINNs-H solutions(PINNs-H denotes the PINNs with the hard constraints).The nonlinear factor(Na)in the consolidation model is correctly estimated via the PINNs-H method.It is found that when the ratio of compressibility index Cc to permeability index Ck is equal to 1,PINNs-H solutions agree well with the corresponding analytical solutions,while the PINNs solutions fail.When Cc/Ck ≠1,the PINNs-H solutions are revealed to be continuous compared with the discretization solutions of the finite difference,via the PINNs-H the same average degree of consolidation can be obtained based on fewer training sample points,which correspond to the grid points of the finite difference.In addition,we find that Na reflected by the PINNs-H is more accurate than that via the PINNs.PINNs-H provides a new strategy for studying soft soil consolidation problems.

nonlinear consolidationdeep learningnumerical methodphysics-informed neural networkparameter inversioncontinuous drainage boundaryhard constraints

兰鹏、张升、苏晶晶

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中南大学土木工程学院,湖南长沙 410075

非线性固结 深度学习 数值方法 物理信息神经网络 参数反演 连续排水边界 硬约束

国家重点研发计划项目湖湘高层次人才聚集工程项目中南大学研究生自主探索创新项目湖南省研究生科研创新项目湖南省自然科学青年基金项目国家自然科学基金青年基金项目

2017YFE01195002019RS10082022zzts0018CX202201092022JJ4056652208378

2024

10.16058/j.issn.1005-0930.2024.05.015

应用基础与工程科学学报
中国自然资源学会

应用基础与工程科学学报

CSTPCD北大核心
影响因子：0.895
ISSN：1005-0930
年,卷(期)：2024.32(5)