In many real‐world applications, mathematical models are highly complex, and numerical simulations in high‐dimensional systems are challenging. Model order reduction is a useful method to obtain a reasonable approximation by significantly reducing the computational cost of such problems. Deep learning technology is a recent improvement in artificial neural networks that can find more hidden information from the data. Deep learning has the advantage of processing data in its raw form and trains the nonlinear system with different levels of representation and predicts the data. In this article, a reduced order model framework based on a combination of deep learning [long short‐term memory (LSTM)] and proper orthogonal decomposition/dynamic mode decomposition (POD/DMD) modes is presented. Due to the robustness and stability of the LSTM recurrent neural network in predicting chaotic dynamical systems, we consider LSTM architecture to develop our data‐driven reduced order modeling (ROM). We investigate the proposed method performance by solving two well‐known canonical cases: a steady shear flow exhibiting the Kelvin‐Helmholtz instability, and two‐dimensional and unsteady mass diffusion equation. The focus of this article is to use LSTM deep recursive neural network to learn the time dynamics and POD/DMD to generate the order reduction model. The results show that the proposed method is very accurate in predicting time dynamics and input reconstruction.

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When a user connects to the Internet to fulfill his needs, he often encounters a huge amount of related information.Recommender systems are the techniques for massively filtering information and offering the items that users find them satisfying and interesting. The advances in machine learning methods, especially deep learning, have led to great achievements in recommender systems, although these systems still suffer from challenges such as cold-start and sparsity problems. To solve these problems, context information such as user communication network is usually used. In this article, we have proposed a novel recommendation method based on matrix factorization and graph analysis methods, namely Louvain for community detection and HITS for finding the most important node within the trust network. In addition, we leverage deep autoencoders to initialize users and items latent factors, and the Node2vec deep embedding method gathers users' latent factors from the user trust graph. The proposed method is implemented on Ciao and Epinions standard datasets. The experimental results and comparisons demonstrate that the proposed approach is superior to the existing state-of-the-art recommendation methods. Our approach outperforms other comparative methods and achieves great improvements, that is, 15.56% RMSE improvement for Epinions and 18.41% RMSE improvement for Ciao.

This paper proposes the Trasfugen method for traffic assignment aimed at solving the user equilibrium problem. To this end, the method makes use of a genetic algorithm. A fuzzy system is proposed for controlling the mutation and crossover rates of the genetic algorithm, and the corrective strategy is exploited for handling the equilibrium problem constraints. In the model, an approximation algorithm is proposed for obtaining the paths between the origin–destination pairs in the demand matrix. Unlike the traditional deterministic algorithm that has exponential time complexity, this approximation algorithm has polynomial time complexity and is executed much faster. Afterward, the Trasfugen method is applied to the urban network of Tehran metropolitan and the efficiency is investigated. Upon comparing the results obtained from the proposed model with those obtained from the conventional traffic assignment method, namely, the Frank–Wolfe method; it is shown that the proposed algorithm, while acting worse during the initial iterations, achieves better results in the subsequent iterations. Moreover, it prevents the occurrence of local optimal points as well as early/premature convergence, thus producing better results than the Frank–Wolfe algorithm.

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