Related papers: A hybrid FEM-PINN method for time-dependent partia…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

Iterative methods are widely used for solving partial differential equations (PDEs). However, the difficulty in eliminating global low-frequency errors significantly limits their convergence speed. In recent years, neural networks have…

The data-driven discovery of partial differential equations (PDEs) consistent with spatiotemporal data is experiencing a rebirth in machine learning research. Training deep neural networks to learn such data-driven partial differential…

We propose machine learning methods for solving fully nonlinear partial differential equations (PDEs) with convex Hamiltonian. Our algorithms are conducted in two steps. First the PDE is rewritten in its dual stochastic control…

We introduce a class of Sparse, Physics-based, and partially Interpretable Neural Networks (SPINN) for solving ordinary and partial differential equations (PDEs). By reinterpreting a traditional meshless representation of solutions of PDEs…

This paper presents a comprehensive review of the design of experiments used in the surrogate models. In particular, this study demonstrates the necessity of the design of experiment schemes for the Physics-Informed Neural Network (PINN),…

We investigate the inverse problem for Partial Differential Equations (PDEs) in scenarios where the parameters of the given PDE dynamics may exhibit changepoints at random time. We employ Physics-Informed Neural Networks (PINNs) - universal…

In this paper, we introduce the Deep Finite Volume Method (DFVM), an innovative deep learning framework tailored for solving high-order (order \(\geq 2\)) partial differential equations (PDEs). Our approach centers on a novel loss function…

Physics-informed neural networks (PINNs) have been widely applied to solve partial differential equations (PDEs) by enforcing outputs and gradients of deep models to satisfy target equations. Due to the limitation of numerical computation,…

The numerical reconstruction of controls for nonlinear partial differential equations (PDEs) remains a challenging and relatively underdeveloped problem, despite the extensive literature on controllability theory. In this work, we introduce…

Partial differential equations play a fundamental role in the mathematical modelling of many processes and systems in physical, biological and other sciences. To simulate such processes and systems, the solutions of PDEs often need to be…

Physics-informed neural networks (PINNs) have shown remarkable prospects in solving forward and inverse problems involving partial differential equations (PDEs). However, PINNs still face the challenge of high computational cost in solving…

Physics-informed neural networks (PINNs) have been widely utilized for solving a range of partial differential equations (PDEs) in various scientific and engineering disciplines. This paper presents a Fourier heuristic-enhanced PINN (termed…

In this work, we present a machine learning approach for reducing the error when numerically solving time-dependent partial differential equations (PDE). We use a fully convolutional LSTM network to exploit the spatiotemporal dynamics of…

Physics-informed Neural Networks (PINNs) have recently emerged as a principled way to include prior physical knowledge in form of partial differential equations (PDEs) into neural networks. Although PINNs are generally viewed as mesh-free,…

With the recent study of deep learning in scientific computation, the Physics-Informed Neural Networks (PINNs) method has drawn widespread attention for solving Partial Differential Equations (PDEs). Compared to traditional methods, PINNs…

Approximating solutions to partial differential equations (PDEs) is fundamental for the modeling of dynamical systems in science and engineering. Physics-informed neural networks (PINNs) are a recent machine learning-based approach, for…

Physics-informed neural networks (PINNs) have been proposed to learn the solution of partial differential equations (PDE). In PINNs, the residual form of the PDE of interest and its boundary conditions are lumped into a composite objective…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Physics-Informed Neural Networks (PINNs) are a class of deep neural networks that are trained, using automatic differentiation, to compute the response of systems governed by partial differential equations (PDEs). The training of PINNs is…