Related papers: Physics-Driven Neural Network for Solving Electrom…

We present a novel class of Physics-Informed Neural Networks that is formulated based on the principles of Evidential Deep Learning, where the model incorporates uncertainty quantification by learning parameters of a higher-order…

The solution of partial differential equations (PDES) on irregular domains has long been a subject of significant research interest. In this work, we present an approach utilizing physics-informed neural networks (PINNs) to achieve…

Solving inverse problems is a fundamental component of science, engineering and mathematics. With the advent of deep learning, deep neural networks have significant potential to outperform existing state-of-the-art, model-based methods for…

Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…

Deep learning is a powerful tool for solving data driven differential problems and has come out to have successful applications in solving direct and inverse problems described by PDEs, even in presence of integral terms. In this paper, we…

This paper proposes a novel neural network framework, denoted as spectral integrated neural networks (SINNs), for resolving three-dimensional forward and inverse dynamic problems. In the SINNs, the spectral integration method is applied to…

In this work, we consider an inverse potential problem in the parabolic equation, where the unknown potential is a space-dependent function and the used measurement is the final time data. The unknown potential in this inverse problem is…

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 networks (PINNs) have proven to be a promising method for the rapid solving of partial differential equations (PDEs) in both forward and inverse problems. However, due to the smoothness assumption of functions…

Physics-based differentiable rendering (PBDR) has become an efficient method in computer vision, graphics, and machine learning for addressing an array of inverse problems. PBDR allows patterns to be generated from perceptions which can be…

Physics-informed neural networks have gained growing interest. Specifically, they are used to solve partial differential equations governing several physical phenomena. However, physics-informed neural network models suffer from several…

In this work, we propose a deep learning-based imaging method for addressing the multi-frequency electromagnetic (EM) inverse scattering problem (ISP). By combining deep learning technology with EM physical laws, we have successfully…

Parameter Estimation (PE) and State Estimation (SE) are the most wide-spread tasks in the system engineering. They need to be done automatically, fast and frequently, as measurements arrive. Deep Learning (DL) holds the promise of tackling…

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) solve physical systems by incorporating governing partial differential equations directly into neural network training. In electromagnetism, where well-established methodologies such as FDTD and FEM…

Fault detection in rotating machinery is a complex task, particularly in small and heterogeneous dataset scenarios. Variability in sensor placement, machinery configurations, and structural differences further increase the complexity of the…

Why rely on dense neural networks and then blindly sparsify them when prior knowledge about the problem structure is already available? Many inverse problems admit algorithm-unrolled networks that naturally encode physics and sparsity. In…

We revisit the original approach of using deep learning and neural networks to solve differential equations by incorporating the knowledge of the equation. This is done by adding a dedicated term to the loss function during the optimization…

Physics-informed Neural Networks (PINNs) have been shown as a promising approach for solving both forward and inverse problems of partial differential equations (PDEs). Meanwhile, the neural operator approach, including methods such as Deep…

We propose physics-informed holomorphic neural networks (PIHNNs) as a method to solve boundary value problems where the solution can be represented via holomorphic functions. Specifically, we consider the case of plane linear elasticity…