In recent years, physics-informed neural networks (PINN) have been used to solve stiff-PDEs mostly in the 1D and 2D spatial domain. PINNs still experience issues solving 3D problems, especially, problems with conflicting boundary conditions at adjacent edges and corners. These problems have discontinuous solutions at edges and corners that are difficult to learn for neural networks with a continuous activation function. In this review paper, we have investigated various PINN frameworks that are designed to solve stiff-PDEs. We took two heat conduction problems (2D and 3D) with a discontinuous solution at corners as test cases. We investigated these problems with a number of PINN frameworks, discussed and analysed the results against the FEM solution. It appears that PINNs provide a more general platform for parameterisation compared to conventional solvers. Thus, we have investigated the 2D heat conduction problem with parametric conductivity and geometry separately. We also discuss the challenges associated with PINNs and identify areas for further investigation.

Prakhar Sharma

Llion Evans

Michelle Tindall

Perumal Nithiarasu

Archives of Computational Methods in Engineering

工程计算方法档案为传播计算工程研究和先进实践的成果提供了一个活跃的论坛，特别强调力学及其相关领域。该杂志在选定领域独家发表扩展的最先进的评论，这是该杂志的一个独特之处。发表在该期刊上的评论不仅提供了对当前文献的调查，而且还对该主题的全部复杂性进行了批判性阐述。主题的部分列表包括建模；求解技术和计算方法在各个领域的应用（例如，液体和气体动力学、固体和结构力学、生物力学等）；与实施有限元和边界元方法相关的变分公式和数值算法；有限差分法和有限体积法；和其他基本的计算方法。

The Archives of Computational Methods in Engineering provides a vibrant forum for disseminating the results of computational engineering research and advanced practices, with a particular emphasis on mechanics and related fields. This journal uniquely publishes extended state-of-the-art reviews, which not only survey the current literature but also critically elaborate on the complexities of the subject. Some of the topics covered include modeling, solution techniques, and the application of computational methods in various fields such as fluid and gas dynamics, solid and structural mechanics, and biomechanics; variational formulations and numerical algorithms related to the implementation of finite element and boundary element methods; finite difference methods and finite volume methods; and other fundamental computational methods.

《Archives of Computational Methods in Engineering》是一个活跃的论坛，致力于传播计算工程研究和先进实践的成果，特别强调力学及其相关领域。该期刊独家发表扩展的前沿评论，这是其独特之处。这些评论不仅对当前文献进行了全面的调查，还对主题的复杂性进行了深入的批判性阐述。部分主题包括建模、求解技术以及计算方法在液体和气体动力学、固体和结构力学、生物力学等各个领域的应用；与实施有限元和边界元方法相关的变分公式和数值算法；有限差分法和有限体积法；以及其他基本的计算方法。

Category	Quartile
工程技术	2
工程技术, 工程综合	1
工程技术, 数学跨学科应用	1
工程技术, 计算机跨学科应用	2

Stiff-PDEs and Physics-Informed Neural Networks

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Journal Info

Category	Quartile
MATHEMATICS, INTERDISCIPLINARY APPLICATIONS	1