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Spectral methods are an important part of scientific computing's arsenal for solving partial differential equations (PDEs). However, their applicability and effectiveness depend crucially on the choice of basis functions used to expand the…

Graph neural networks (GNNs) leverage message passing mechanisms to learn the topological features of graph data. Traditional GNNs learns node features in a spatial domain unrelated to the topology, which can hardly ensure topological…

Physics-informed deep learning often faces optimization challenges due to the complexity of solving partial differential equations (PDEs), which involve exploring large solution spaces, require numerous iterations, and can lead to unstable…

Physics-Informed Neural Network (PINN) is a novel multi-task learning framework useful for solving physical problems modeled using differential equations (DEs) by integrating the knowledge of physics and known constraints into the…

Recent years have witnessed a growth in mathematics for deep learning--which seeks a deeper understanding of the concepts of deep learning with mathematics and explores how to make it more robust--and deep learning for mathematics, where…

The prohibitive cost and low fidelity of experimental data in industry scale thermofluid systems limit the usefulness of pure data-driven machine learning methods. Physics-informed neural networks (PINN) strive to overcome this by embedding…

This research introduces an extended application of neural networks for solving nonlinear partial differential equations (PDEs). A neural network, combined with a pseudo-arclength continuation, is proposed to construct bifurcation diagrams…

We present a novel framework combining Deep Operator Networks (DeepONets) with Physics-Informed Neural Networks (PINNs) to solve partial differential equations (PDEs) and estimate their unknown parameters. By integrating data-driven…

Physics-informed neural networks (PINNs) have achieved notable success in modeling dynamical systems governed by partial differential equations (PDEs). To avoid computationally expensive retraining under new physical conditions,…

Physics-informed neural networks (PINNs) have shown promise in solving various partial differential equations (PDEs). However, training pathologies have negatively affected the convergence and prediction accuracy of PINNs, which further…

Mathematical models in neural networks are powerful tools for solving complex differential equations and optimizing their parameters; that is, solving the forward and inverse problems, respectively. A forward problem predicts the output of…

Partial differential equations (PDEs) with Dirichlet boundary conditions defined on boundaries with simple geometry have been succesfuly treated using sigmoidal multilayer perceptrons in previous works. This article deals with the case of…

Many successful methods to learn dynamical systems from data have recently been introduced. However, ensuring that the inferred dynamics preserve known constraints, such as conservation laws or restrictions on the allowed system states,…

This paper proposes a new framework using physics-informed neural networks (PINNs) to simulate complex structural systems that consist of single and double beams based on Euler-Bernoulli and Timoshenko theory, where the double beams are…

Successfully training Physics Informed Neural Networks (PINNs) for highly nonlinear PDEs on complex 3D domains remains a challenging task. In this paper, PINNs are employed to solve the 3D incompressible Navier-Stokes (NS) equations at…

Physics-informed neural networks (PINNs) have recently become a powerful tool for solving partial differential equations (PDEs). However, finding a set of neural network parameters that lead to fulfilling a PDE can be challenging and…

Thermal errors in machine tools significantly impact machining precision and productivity. Traditional thermal error correction/compensation methods rely on measured temperature-deformation fields or on transfer functions. Most existing…

Current physics-informed (standard or deep operator) neural networks still rely on accurately learning the initial and/or boundary conditions of the system of differential equations they are solving. In contrast, standard numerical methods…

Physics informed neural networks (PINNs) have emerged as a powerful tool to provide robust and accurate approximations of solutions to partial differential equations (PDEs). However, PINNs face serious difficulties and challenges when…

Physics-informed neural networks (PINNs) have recently emerged as a promising way to compute the solutions of partial differential equations (PDEs) using deep neural networks. However, despite their significant success in various fields, it…