Adapting PINN Models of Physical Entities to Dynamical Data

IF 1.9 Q2 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS
Dmitriy Tarkhov, T. Lazovskaya, V. Antonov
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引用次数: 0

Abstract

This article examines the possibilities of adapting approximate solutions of boundary value problems for differential equations using physics-informed neural networks (PINNs) to changes in data about the physical entity being modelled. Two types of models are considered: PINN and parametric PINN (PPINN). The former is constructed for a fixed parameter of the problem, while the latter includes the parameter for the number of input variables. The models are tested on three problems. The first problem involves modelling the bending of a cantilever rod under varying loads. The second task is a non-stationary problem of a thermal explosion in the plane-parallel case. The initial model is constructed based on an ordinary differential equation, while the modelling object satisfies a partial differential equation. The third task is to solve a partial differential equation of mixed type depending on time. In all cases, the initial models are adapted to the corresponding pseudo-measurements generated based on changing equations. A series of experiments are carried out for each problem with different functions of a parameter that reflects the character of changes in the object. A comparative analysis of the quality of the PINN and PPINN models and their resistance to data changes has been conducted for the first time in this study.
物理实体的PINN模型对动态数据的适应性
本文研究了使用物理信息神经网络(PINN)使微分方程边值问题的近似解适应被建模物理实体数据变化的可能性。考虑了两种类型的模型:PINN和参数PINN(PPINN)。前者是为问题的固定参数构造的,而后者包括输入变量数量的参数。模型在三个问题上进行了测试。第一个问题涉及对悬臂杆在不同载荷下的弯曲进行建模。第二个任务是平面平行情况下热爆炸的非平稳问题。初始模型是基于常微分方程构建的,而建模对象满足偏微分方程。第三个任务是求解一个依赖于时间的混合型偏微分方程。在所有情况下,初始模型都适用于基于变化方程生成的相应伪测量。针对每个问题,使用反映对象变化特征的参数的不同函数进行一系列实验。本研究首次对PINN和PPINN模型的质量及其对数据变化的抵抗力进行了比较分析。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Computation
Computation Mathematics-Applied Mathematics
CiteScore
3.50
自引率
4.50%
发文量
201
审稿时长
8 weeks
期刊介绍: Computation a journal of computational science and engineering. Topics: computational biology, including, but not limited to: bioinformatics mathematical modeling, simulation and prediction of nucleic acid (DNA/RNA) and protein sequences, structure and functions mathematical modeling of pathways and genetic interactions neuroscience computation including neural modeling, brain theory and neural networks computational chemistry, including, but not limited to: new theories and methodology including their applications in molecular dynamics computation of electronic structure density functional theory designing and characterization of materials with computation method computation in engineering, including, but not limited to: new theories, methodology and the application of computational fluid dynamics (CFD) optimisation techniques and/or application of optimisation to multidisciplinary systems system identification and reduced order modelling of engineering systems parallel algorithms and high performance computing in engineering.
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