## 1 Introduction
Meanwhile, with the current development of artificial intelligence (AI), various types of artificial neural networks (ANNs) are being adopted to model complex nonlinear relationships that cannot be solved deterministically using traditional mathematical models. ANNs are a type of mathematical model that resembles the biological characteristics of the human brain. Numerous researchers have attempted to apply various types of neural networks to evaluate extremely complex systems and to predict the target values of the systems in various research fields, including structural engineering. [PERSON] et al. [12] developed a deep neural network (DNN) with high-order neurons, namely a second-order artificial neural network (SO-ANN), and used it to predict foamed concrete strength. [PERSON] et al. [13] investigated a vision-based method for crack detection in gusset plate welded joints of steel bridges using deep convolutional neural networks. [PERSON] [14] sought to predict the shear strength of CFS channels with slotted webs based on an ANN. [PERSON] et al. [15] developed a DNN model to predict the compressive strength of rubber concrete. [PERSON] et al. [16] suggested a machine learning-based formulation for predicting the shear capacity of squat flanged RC walls. [PERSON] and [PERSON] [17] developed a structural design method for reinforced concrete buildings based on DNNs. [PERSON] et al. [18] developed a prediction model for the compressive strength of CO2 concrete using regression analysis and ANNs. [PERSON] et al. [19] investigated the prediction of the stress-strain behavior of normal-weight and lightweight aggregate concrete exposed to high temperatures using an LSTM recurrent neural network. [PERSON] et al. [20] developed damage detection models for tethers of submerged floating tunnels based on CNNs. Based on the literature, it was indicated that applying neural networks can be effective for analyzing complex problems and predicting the target values that cannot be solved using traditional mathematical models. Furthermore, the bracing moments and forces induced by LTB in steel I-girder bracing systems are a type of complex structural system due to the secondary effects. To more accurately predict the bracing forces in the steel I-girder bracing systems, thus, this study aims to evaluate the structural behavior of the torsional bracing systems in steel I-girder bridges and more accurately estimate the internal forces compared with the current design methodology based on DNNs. The internal forces in the beam bracing systems comprise bracing moments and bracing forces, acting on torsional bracing in steel I-girder bridges when the applied loading reaches the LTB limit states. In this study, a comparative study was conducted based on geometric nonlinear FEA to determine the accurate internal forces at strength limit states. Furthermore, it explores the possibility of applying AI to estimate internal forces in the bracing system, which is one of the most complex structural systems due to the secondary effects. From the FEA results, estimates of internal forces in the torsional braced bridge system were implemented based on a DNN with respect to various design parameters to simplify the preliminary design phase. Based on statistical performance indices (i.e., root mean square error (RMSE), mean square error (MSE), mean absolute error (MAE), coefficient of determination (R\({}^{2}\))), the estimated values using DNN models were evaluated to determine the best prediction models. Finally, deep neural network (DNN) models, which can be tuned by adjusting hyperparameters such as the hidden layers, neurons, and epochs to accurately estimate internal forces (\(M_{br}\), \(F_{br}\)) in bracing elements, have been proposed and have been shown to produce the best prediction results.