Related papers: Physics-constrained 3D Convolutional Neural Networ…

The semiconductor industry faces a computational crisis in extreme ultraviolet (EUV) lithography optimization, where traditional methods consume billions of CPU hours while failing to achieve sub-nanometer precision. We present a…

The integration of machine learning with domain-specific physics is transforming the design, monitoring, and control of electricity systems, where data scarcity, limited interpretability, and the need to enforce physical laws constrain…

In this article, we present an efficient deep learning method called coupled deep neural networks (CDNNs) for coupled physical problems. Our method compiles the interface conditions of the coupled PDEs into the networks properly and can be…

The neural network method of solving differential equations is used to approximate the electric potential and corresponding electric field in the slit-well microfluidic device. The device's geometry is non-convex, making this a challenging…

This study develops and validates neural network frameworks with physics-based constraints for surrogate modeling of rarefied gas dynamics across different levels of complexity. As a baseline, we first examine the BGK kinetic relaxation…

In this paper, we consider the problem of reconstructing a dense 3D model using images captured from different views. Recent methods based on convolutional neural networks (CNN) allow learning the entire task from data. However, they do not…

Recent research works for solving partial differential equations (PDEs) with deep neural networks (DNNs) have demonstrated that spatiotemporal function approximators defined by auto-differentiation are effective for approximating nonlinear…

Enhancing neural networks with knowledge of physical equations has become an efficient way of solving various physics problems, from fluid flow to electromagnetism. Graph neural networks show promise in accurately representing irregularly…

Soft- and hard-constrained Physics Informed Neural Networks (PINNs) have achieved great success in solving partial differential equations (PDEs). However, these methods still face great challenges when solving the Navier-Stokes equations…

Prostate cancer is one of the most common causes of cancer deaths in men. There is a growing demand for noninvasively and accurately diagnostic methods that facilitate the current standard prostate cancer risk assessment in clinical…

CoVariance Neural Networks (VNNs) perform convolutions on the graph determined by the covariance matrix of the data, which enables expressive and stable covariance-based learning. However, covariance matrices are typically dense, fail to…

Stress prediction in porous materials and structures is challenging due to the high computational cost associated with direct numerical simulations. Convolutional Neural Network (CNN) based architectures have recently been proposed as…

I provide an introduction to the application of deep learning and neural networks for solving partial differential equations (PDEs). The approach, known as physics-informed neural networks (PINNs), involves minimizing the residual of the…

Based on the analysis of biquaternion quadratic forms of field, it is shown that Maxwell equations arise as a consequence of the principle of conservation of the energy-momentum flow of field in space-time. It turns out that this principle…

Graph Neural Networks (GNNs) are a promising deep learning approach for circumventing many real-world problems on graph-structured data. However, these models usually have at least one of four fundamental limitations: over-smoothing,…

Physics-based deep learning frameworks have shown to be effective in accurately modeling the dynamics of complex physical systems with generalization capability across problem inputs. However, time-independent problems pose the challenge of…

Observing 3D magnetic fields, including orientation and strength, within the interstellar medium is vital but notoriously difficult. However, recent advances in our understanding of anisotropic magnetohydrodynamic (MHD) turbulence…

Recent work in deep learning focuses on solving physical systems in the Ordinary Differential Equation or Partial Differential Equation. This current work proposed a variant of Convolutional Neural Networks (CNNs) that can learn the hidden…

Despite their successes in the field of self-learning AI, Convolutional Neural Networks (CNNs) suffer from having too many trainable parameters, impacting computational performance. Several approaches have been proposed to reduce the number…

We investigate the use of Physics-Informed Neural Networks (PINNs) for solving the wave equation. Whilst PINNs have been successfully applied across many physical systems, the wave equation presents unique challenges due to the multi-scale,…