I-FENN with Temporal Convolutional Networks: expediting the load-history analysis of non-local gradient damage propagation

TL;DR

The paper addresses the high computational cost of simulating history-dependent non-local gradient damage by coupling Finite Element Method (FEM) with a Temporal Convolutional Network (TCN) within an Integrated Finite Element Neural Network (I-FENN) framework. It demonstrates a three-step workflow—coarse data generation, neural network training to map local to non-local strains, and refined FEM analysis using NN surrogates—to enable load-history analysis while preserving convergence and accuracy. Key contributions include validating I-FENN across single and double notch and shear damage scenarios, proving strict per-increment convergence, and achieving substantial computational savings (up to ~80% in some cases) compared to monolithic and staggered FEM solvers; it also explores data-driven vs physics-informed training, normalization strategies, and a hyperparameter optimization case. The approach offers a scalable, robust pathway to accelerate non-local damage simulations on refined meshes, with public data/code to support reproducibility and further research.

Abstract

In this paper, we demonstrate for the first time how the Integrated Finite Element Neural Network (I-FENN) framework, previously proposed by the authors, can efficiently simulate the entire loading history of non-local gradient damage propagation. To achieve this goal, we first adopt a Temporal Convolutional Network (TCN) as the neural network of choice to capture the history-dependent evolution of the non-local strain in a coarsely meshed domain. The quality of the network predictions governs the computational performance of I-FENN, and therefore we perform an extended investigation aimed at enhancing them. We explore a data-driven vs. physics-informed TCN setup to arrive at an optimum network training, evaluating the network based on a coherent set of relevant performance metrics. We address the crucial issue of training a physics-informed network with input data that span vastly different length scales by proposing a systematic way of input normalization and output un-normalization. We then integrate the trained TCN within the nonlinear iterative FEM solver and apply I-FENN to simulate the damage propagation analysis. I-FENN is always applied in mesh idealizations different from the one used for the TCN training, showcasing the framework's ability to be used at progressively refined mesh resolutions. We illustrate several cases that I-FENN completes the simulation using either a modified or a full Newton-Raphson scheme, and we showcase its computational savings compared to both the classical monolithic and staggered FEM solvers. We underline that we satisfy very strict convergence criteria for every increment across the entire simulation, providing clear evidence of the robustness and accuracy of I-FENN. All the code and data used in this work will be made publicly available upon publication of the article.

Figures (22)

• Figure 1: Schematic of an elastic domain with a sample damage contour
• Figure 2: Schematic overview of the overarching IFENN framework.
• Figure 3: Architecture of the TCN: a. Stack of dilated causal convolutions with dilation factors $dil = 1, 2$ and kernel size $ker = 3$. b. TCN residual block with added layers of weight normalization, activation function and dropout in the main path, and an additional residual connection.
• Figure 4: Schematic overview of the Data Generation stage of I-FENN.
• Figure 5: Schematic overview of the Network Training stage of I-FENN.