Finite Element Analysis (FEA) is a powerful but computationally intensive method for simulating physical phenomena. Recent advancements in machine learning have led to surrogate models capable of accelerating FEA. Yet there are still limitations in developing surrogates of transient FEA models that can simultaneously predict the solutions for both nodes and elements with applicability on both the 2D and 3D domains. Motivated by this research gap, this study proposes DeepFEA, a deep learning-based framework that leverages a multilayer Convolutional Long Short-Term Memory (ConvLSTM) network branching into two parallel convolutional neural networks to predict the solutions for both nodes and elements of FEA models. The proposed network is optimized using a novel adaptive learning algorithm, called Node-Element Loss Optimization (NELO). NELO minimizes the error occurring at both branches of the network enabling the prediction of solutions for transient FEA simulations. The experimental evaluation of DeepFEA is performed on three datasets in the context of structural mechanics, generated to serve as publicly available reference datasets. The results show that DeepFEA can achieve less than 3% normalized mean and root mean squared error for 2D and 3D simulation scenarios, and inference times that are two orders of magnitude faster than FEA. In contrast, relevant state-of-the-art methods face challenges with multi-dimensional output and dynamic input prediction. Furthermore, DeepFEA's robustness was demonstrated in a real-life biomedical scenario, confirming its suitability for accurate and efficient predictions of FEA simulations.

翻译：有限元分析（FEA）是一种功能强大但计算密集的物理现象模拟方法。机器学习的最新进展催生了能够加速FEA的代理模型。然而，在开发瞬态FEA模型的代理模型方面仍存在局限，这些模型需要能同时预测节点和单元的求解结果，并适用于二维和三维域。针对这一研究空白，本研究提出了DeepFEA，一种基于深度学习的框架。该框架利用多层卷积长短期记忆（ConvLSTM）网络，分支为两个并行的卷积神经网络，以预测FEA模型的节点和单元求解结果。所提出的网络采用一种新颖的自适应学习算法——节点-单元损失优化（NELO）进行优化。NELO最小化网络两个分支的误差，从而实现对瞬态FEA模拟求解的预测。DeepFEA的实验评估在结构力学领域的三个数据集上进行，这些数据集已公开作为参考基准。结果表明，在二维和三维模拟场景中，DeepFEA的归一化平均误差和均方根误差可低于3%，且推理速度比FEA快两个数量级。相比之下，相关的先进方法在多维输出和动态输入预测方面面临挑战。此外，DeepFEA在真实生物医学场景中展现了其鲁棒性，证实了其适用于FEA模拟的准确高效预测。