Related papers: I-FENN with DeepONets: accelerating simulations in…

Multiscale modeling is an effective approach for investigating multiphysics systems with largely disparate size features, where models with different resolutions or heterogeneous descriptions are coupled together for predicting the system's…

We present a novel formulation for modeling phase-field fracture propagation based on the Integrated Finite Element Neural Network (IFENN) framework. IFENN is a hybrid solver scheme that utilizes neural networks as PDE solvers within FEM,…

Neural operators aim to learn mappings between infinite-dimensional function spaces, but their performance often degrades on complex or irregular geometries due to the lack of geometry-aware representations. We propose the Finite Element…

Most currently available methods for modeling multiphysics, including thermoelasticity, using machine learning approaches, are focused on solving complete multiphysics problems using data-driven or physics-informed multi-layer perceptron…

The finite element method (FEM) is among the most commonly used numerical methods for solving engineering problems. Due to its computational cost, various ideas have been introduced to reduce computation times, such as domain decomposition,…

Numerical solvers for PDEs often struggle to balance computational cost with accuracy, especially in multiscale and time-dependent systems. Neural operators offer a promising way to accelerate simulations, but their practical deployment is…

Unlike classical artificial neural networks, which require retraining for each new set of parametric inputs, the Deep Operator Network (DeepONet), a lately introduced deep learning framework, approximates linear and nonlinear solution…

We present a new Integrated Finite Element Neural Network framework (I-FENN), with the objective to accelerate the numerical solution of nonlinear computational mechanics problems. We leverage the swift predictive capability of neural…

We propose a Pretrained Finite Element Method (PFEM),a physics driven framework that bridges the efficiency of neural operator learning with the accuracy and robustness of classical finite element methods (FEM). PFEM consists of a physics…

We present an efficient hybrid Neural Network-Finite Element Method (NN-FEM) for solving the viscous-plastic (VP) sea-ice model. The VP model is widely used in climate simulations to represent large-scale sea-ice dynamics. However, the…

We introduce a novel hybrid methodology combining classical finite element methods (FEM) with neural networks to create a well-performing and generalizable surrogate model for forward and inverse problems. The residual from finite element…

Traditional numerical schemes for simulating fluid flow and transport in porous media can be computationally expensive. Advances in machine learning for scientific computing have the potential to help speed up the simulation time in many…

This study introduces the concept of finite element network analysis (FENA) which is a physics-informed, machine-learning-based, computational framework for the simulation of complex physical systems. The framework leverages the extreme…

We present a methodology combining neural networks with physical principle constraints in the form of partial differential equations (PDEs). The approach allows to train neural networks while respecting the PDEs as a strong constraint in…

The deep operator network (DeepONet) is a popular neural operator architecture that has shown promise in solving partial differential equations (PDEs) by using deep neural networks to map between infinite-dimensional function spaces. In the…

One of the major issues in the computational mechanics is to take into account the geometrical complexity. To overcome this difficulty and to avoid the expensive mesh generation, geometrically unfitted methods, i.e. the numerical methods…

Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…

The finite element method (FEM) is a well-established numerical method for solving partial differential equations (PDEs). However, its mesh-based nature gives rise to substantial computational costs, especially for complex multiscale…

Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…

Finite element modeling is a well-established tool for structural analysis, yet modeling complex structures often requires extensive pre-processing, significant analysis effort, and considerable time. This study addresses this challenge by…