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Physics-Informed Neural Networks (PINNs) have gained popularity in scientific computing in recent years. However, they often fail to achieve the same level of accuracy as classical methods in solving differential equations. In this paper,…
A physics informed neural network (PINN) incorporates the physics of a system by satisfying its boundary value problem through a neural network's loss function. The PINN approach has shown great success in approximating the map between the…
Physics-Informed Neural Networks (PINNs) often suffer from slow convergence, training instability, and reduced accuracy on challenging partial differential equations due to the anisotropic and rapidly varying geometry of their loss…
This paper introduces a framework based on physics-informed neural networks (PINNs) for addressing key challenges in nonlinear lattices, including solution approximation, bifurcation diagram construction, and linear stability analysis. We…
Physics informed neural networks (PINNs) represent a very popular class of neural solvers for partial differential equations. In practice, one often employs stochastic gradient descent type algorithms to train the neural network. Therefore,…
We propose the Physics-Informed Neural Network-driven Sparse Field Discretization method (PINN-SFD), a novel self-supervised, physics-informed deep learning approach for addressing the Near-Field Acoustic Holography (NAH) problem. Unlike…
Physics-informed neural networks (PINNs) have emerged as a flexible framework for solving partial differential equations, but their performance on interface problems remains challenging because continuity and flux conditions are typically…
Fourier ptychography (FP) is a newly developed computational imaging approach that achieves both high resolution and wide field of view by stitching a series of low-resolution images captured under angle-varied illumination. So far, many…
This paper explores the application of physics-informed neural networks (PINNs) to tackle forward problems in 3D contact mechanics, focusing on small deformation elasticity. We utilize a mixed-variable formulation, enhanced with output…
Engineering components must meet increasing technological demands in ever shorter development cycles. To face these challenges, a holistic approach is essential that allows for the concurrent development of part design, material system and…
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…
With the remarkable empirical success of neural networks across diverse scientific disciplines, rigorous error and convergence analysis are also being developed and enriched. However, there has been little theoretical work focusing on…
Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) have shown high potential in their ability to solve complex differential equations. One example is the use of PINNs to solve the gravity field modeling…
Physics-informed neural networks (PINNs) integrate fundamental physical principles with advanced data-driven techniques, driving significant advancements in scientific computing. However, PINNs face persistent challenges with stiffness in…
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…
We introduce a novel neural network structure called Strongly Constrained Theory-Guided Neural Network (SCTgNN), to investigate the behaviours of the localized solutions of the generalized nonlinear Schr\"{o}dinger (NLS) equation. This…
Neural networks have emerged as powerful tools for modeling complex physical systems, yet balancing high accuracy with computational efficiency remains a critical challenge in their convergence behavior. In this work, we propose the Hybrid…
This paper introduces a novel approach to solve inverse problems by leveraging deep learning techniques. The objective is to infer unknown parameters that govern a physical system based on observed data. We focus on scenarios where the…
Fresnel incoherent correlation holography (FINCH) is a well-established digital holography technique for 3D imaging of objects illuminated by spatially incoherent light. FINCH has a higher lateral resolution of 1.5 times that of direct…
Accurate solutions to inverse supersonic compressible flow problems are often required for designing specialized aerospace vehicles. In particular, we consider the problem where we have data available for density gradients from Schlieren…