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In this paper, we construct approximated solutions of Differential Equations (DEs) using the Deep Neural Network (DNN). Furthermore, we present an architecture that includes the process of finding model parameters through experimental data,…

In this paper, we propose a novel $hr$-adaptive finite element method, enhanced by neural networks, for parabolic equations. The main challenge of the conventional $h$-adaptive finite element method is interpolating the finite element…

This paper extends the finite element network analysis (FENA) to include a dynamic time-transient formulation. FENA was initially formulated in the context of the linear static analysis of 1D and 2D elastic structures. By introducing the…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. Data-driven networks like GNN, Neural Operators have…

A hybrid framework integrating the Virtual Element Method (VEM) with deep learning is presented as an initial step toward developing efficient and flexible numerical models for one-dimensional Euler-Bernoulli beams. The primary aim is to…

High-resolution simulation models are essential for representing complex physical systems, yet their substantial computational cost severely limits the number of feasible high-fidelity (HF) evaluations. This problem is often addressed…

Motivated by the drawbacks of cloud-based federated learning (FL), cooperative federated edge learning (CFEL) has been proposed to improve efficiency for FL over mobile edge networks, where multiple edge servers collaboratively coordinate…

Binary Neural Networks (BNNs), neural networks with weights and activations constrained to -1(0) and +1, are an alternative to deep neural networks which offer faster training, lower memory consumption and lightweight models, ideal for use…

Model fusion seeks to combine independently trained neural networks into a single model without retraining, but is complicated by representational divergence arising from permutation invariance, random initialization, and heterogeneous…

Deep neural networks (DNNs) have been widely applied in various domains in artificial intelligence including computer vision and natural language processing. A DNN is typically trained for many epochs and then a validation dataset is used…

In this study, we develop a novel multi-fidelity deep learning approach that transforms low-fidelity solution maps into high-fidelity ones by incorporating parametric space information into a standard autoencoder architecture. This method's…

The increasing use of deep neural networks (DNNs) in safety-critical systems has raised concerns about their potential for exhibiting ill-behaviors. While DNN verification and testing provide post hoc conclusions regarding unexpected…

One of the most challenging and consequential problems in climate modeling is to provide probabilistic projections of sea level rise. A large part of the uncertainty of sea level projections is due to uncertainty in ice sheet dynamics. At…

Simulating spatiotemporal turbulence with high fidelity remains a cornerstone challenge in computational fluid dynamics (CFD) due to its intricate multiscale nature and prohibitive computational demands. Traditional approaches typically…

In general, there is a mismatch between a finite element model {(FEM)} of a structure and its real behaviour. In aeronautics, this mismatch must be small because {FEM}s are a fundamental part of the development of an aircraft and of…

Storm surge and waves are responsible for a substantial portion of tropical and extratropical cyclones-related damages. While high-fidelity numerical models have significantly advanced the simulation accuracy of storm surge and waves, they…

In this paper, we present an Adaptive Ensemble Learning framework that aims to boost the performance of deep neural networks by intelligently fusing features through ensemble learning techniques. The proposed framework integrates ensemble…

Neural operators (NOs) struggle with high-contrast multiscale partial differential equations (PDEs), where fine-scale heterogeneities cause large errors. To address this, we use the Generalized Multiscale Finite Element Method (GMsFEM) that…

We propose a hybrid meta-learning framework for forecasting and anomaly detection in nonlinear dynamical systems characterized by nonstationary and stochastic behavior. The approach integrates a physics-inspired simulator that captures…

Deep neural networks (DNNs) have recently emerged as effective tools for approximating solution operators of partial differential equations (PDEs) including evolutionary problems. Classical numerical solvers for such PDEs often face…