Related papers: Physics Constrained Learning for Data-driven Inver…

We propose the physics-constrained convolutional neural network (PC-CNN) to infer the high-resolution solution from sparse observations of spatiotemporal and nonlinear partial differential equations. Results are shown for a chaotic and…

A physics-informed neural network (PINN) uses physics-augmented loss functions, e.g., incorporating the residual term from governing partial differential equations (PDEs), to ensure its output is consistent with fundamental physics laws.…

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…

Data sparsity is a common issue to train machine learning tools such as neural networks for engineering and scientific applications, where experiments and simulations are expensive. Recently physics-constrained neural networks (PCNNs) were…

Partial differential equations (PDEs) are an essential computational kernel in physics and engineering. With the advance of deep learning, physics-informed neural networks (PINNs), as a mesh-free method, have shown great potential for fast…

Many scientific and industrial applications require solving Partial Differential Equations (PDEs) to describe the physical phenomena of interest. Some examples can be found in the fields of aerodynamics, astrodynamics, combustion and many…

This short note describes the concept of guided training of deep neural networks (DNNs) to learn physically reasonable solutions. DNNs are being widely used to predict phenomena in physics and mechanics. One of the issues of DNNs is that…

Physics-informed neural networks (PINNs) are a newly emerging research frontier in machine learning, which incorporate certain physical laws that govern a given data set, e.g., those described by partial differential equations (PDEs), into…

Inverse problems in partial differential equations (PDEs) involve estimating the physical parameters of a system from observed spatiotemporal solution fields. Neural networks are well-suited for PDE parameter estimation due to their…

We consider the approximation of a class of dynamic partial differential equations (PDE) of second order in time by the physics-informed neural network (PINN) approach, and provide an error analysis of PINN for the wave equation, the…

I will demonstrate the effectiveness of Physics-Informed Neural Networks (PINNs) in solving partial differential equations (PDEs) when training data are scarce or noisy. The training data can be located either at the boundaries or within…

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…

This paper proposes a meshless deep learning algorithm, enriched physics-informed neural networks (EPINNs), to solve dynamic Poisson-Nernst-Planck (PNP) equations with strong coupling and nonlinear characteristics. The EPINNs takes the…

Physics Informed Neural Networks (PINNs) are shown to be a promising method for the approximation of Partial Differential Equations (PDEs). PINNs approximate the PDE solution by minimizing physics-based loss functions over a given domain.…

The notion of an Evolutional Deep Neural Network (EDNN) is introduced for the solution of partial differential equations (PDE). The parameters of the network are trained to represent the initial state of the system only, and are…

Deriving governing equations in Electromagnetic (EM) environment based on first principles can be quite tough when there are some unknown sources of noise and other uncertainties in the system. For nonlinear multiple-physics electromagnetic…

Physics-informed neural networks (PINNs), rooted in deep learning, have emerged as a promising approach for solving partial differential equations (PDEs). By embedding the physical information described by PDEs into feedforward neural…

Physics-informed neural networks (PINNs) have emerged as a new learning paradigm for solving partial differential equations (PDEs) by enforcing the constraints of physical equations, boundary conditions (BCs), and initial conditions (ICs)…

In recent years, the researches about solving partial differential equations (PDEs) based on artificial neural network have attracted considerable attention. In these researches, the neural network models are usually designed depend on…

Deep learning approaches for partial differential equations (PDEs) have received much attention in recent years due to their mesh-freeness and computational efficiency. However, most of the works so far have concentrated on time-dependent…