相关论文: FE-PINNs: finite-element-based physics-informed ne…

This work presents a physics-informed neural network (PINN) based framework to model the strain-rate and temperature dependence of the deformation fields in elastic-viscoplastic solids. To avoid unbalanced back-propagated gradients during…

Neural Networks (NN) has been used in many areas with great success. When a NN's structure (Model) is given, during the training steps, the parameters of the model are determined using an appropriate criterion and an optimization algorithm…

Concurrent multiscale finite element analysis (FE2) is a powerful approach for high-fidelity modeling of materials for which a suitable macroscopic constitutive model is not available. However, the extreme computational effort associated…

Accurate computational modeling of damage and fracture remains a central challenge in solid mechanics. The finite element method (FEM) is widely used for numerical modeling of fracture problems; however, classical damage models without…

Physics-informed neural networks (PINNs) have emerged as a promising approach to solving partial differential equations (PDEs) using neural networks, particularly in data-scarce scenarios, due to their unsupervised training capability.…

Partial differential equations (PDEs) play a fundamental role in modeling and simulating problems across a wide range of disciplines. Recent advances in deep learning have shown the great potential of physics-informed neural networks…

This work presents a novel graph neural network (GNN) architecture, the Feature-specific Interpretable Graph Neural Network (FIGNN), designed to enhance the interpretability of deep learning surrogate models defined on unstructured grids in…

Physics-informed neural networks (PINNs) have emerged as an effective technique for solving PDEs in a wide range of domains. It is noticed, however, the performance of PINNs can vary dramatically with different sampling procedures. For…

In this contribution we propose a data-driven surrogate model for the prediction of magnetic stray fields in two-dimensional random micro-heterogeneous materials. Since data driven models require thousands of training data sets, FEM…

Physics-informed neural networks (PINNs) are a simple surrogate-modelling paradigm for partial differential equations, but their standard strong-form residual formulation is ill suited to the shallow water equations (SWE). It cannot enforce…

In this work, we present a deep neural network architecture that can efficiently approximate classical elasto-plastic constitutive relations. The network is enriched with crucial physics aspects of classical elasto-plasticity, including…

The great success of Physics-Informed Neural Networks (PINN) in solving partial differential equations (PDEs) has significantly advanced our simulation and understanding of complex physical systems in science and engineering. However, many…

The finite element methods (FEM) are important techniques in engineering for solving partial differential equations, but they depend heavily on element shape quality for stability and good performance. In this paper, we introduce the…

In complex engineering systems such as electro-thermal-fluid coupling, rapid and accurate prediction of multi-physics fields is essential for advanced applications like digital twins and real-time condition monitoring. Traditional numerical…

There has been rapid progress recently on the application of deep networks to the solution of partial differential equations, collectively labelled as Physics Informed Neural Networks (PINNs). In this paper, we develop Physics Informed…

We study a family of $H^m$-conforming piecewise polynomials based on artificial neural network, named as the finite neuron method (FNM), for numerical solution of $2m$-th order partial differential equations in $\mathbb{R}^d$ for any $m,d…

Physics-informed neural networks (PINNs) have gained prominence in recent years and are now effectively used in a number of applications. However, their performance remains unstable due to the complex landscape of the loss function. To…

Numerical solutions of partial differential equations (PDEs) require expensive simulations, limiting their application in design optimization, model-based control, and large-scale inverse problems. Surrogate modeling techniques seek to…

Operator-based neural network architectures such as DeepONets have emerged as a promising tool for the surrogate modeling of physical systems. In general, towards operator surrogate modeling, the training data is generated by solving the…

To solve high-dimensional parameter-dependent partial differential equations (pPDEs), a neural network architecture is presented. It is constructed to map parameters of the model data to corresponding finite element solutions. To improve…