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Physics-Informed Neural Networks (PINNs) have recently emerged as a promising alternative for solving partial differential equations, offering a mesh-free framework that incorporates physical laws directly into the learning process. In this…

Vortex-induced vibration (VIV) exists widely in natural and industrial fields. The main approaches for solving VIV problems are numerical simulations and experimental methods. However, experiment methods are difficult to obtain the whole…

We present a new physics informed neural network (PINN) algorithm for solving brittle fracture problems. While most of the PINN algorithms available in the literature minimize the residual of the governing partial differential equation, the…

Direct observations of earthquake nucleation and propagation are few and yet the next decade will likely see an unprecedented increase in indirect, surface observations that must be integrated into modeling efforts. Machine learning (ML)…

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…

Dense granular flows exhibit nonlocal effects due to stress transmission in microplastic events, especially in quasi-static or slowly sheared regions. Hence, traditional local rheological models fail to capture spatial cooperativity effects…

We propose a supervised-machine-learning-based wall model for coarse-grid wall-resolved large-eddy simulation (LES). Our consideration is made on LES of turbulent channel flows with a first grid point set relatively far from the wall…

Rigorous error estimation is a fundamental topic in numerical analysis. With the increasing use of physics-informed neural networks (PINNs) for solving partial differential equations, several approaches have been developed to quantify the…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…

Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs. We provide rigorous upper bounds on the generalization error of PINNs approximating solutions of the forward problem for…

A machine learning method to predict steady external fluid flows using elliptic input features is introduced. Using data from as few as one high-fidelity simulation, the proposed method produces models generalizable under changes to…

Accurate prediction of rarefied gas dynamics is crucial for optimizing flows through microelectromechanical systems, air filtration devices, and shale gas extraction. Traditional methods, such as discrete velocity and direct simulation…

Two models based on convolutional neural networks are trained to predict the two-dimensional velocity-fluctuation fields at different wall-normal locations in a turbulent open channel flow, using the wall-shear-stress components and the…

Accurate reconstruction of magnetic fields in inaccessible regions is vital for many high-precision experiments in physics. Traditional methods, such as spherical harmonic expansion, often suffer from truncation errors that limit their…

This paper introduces scour physics-inspired neural networks (SPINNs), a hybrid physics-data-driven framework for bridge scour prediction using deep learning. SPINNs integrate physics-based, empirical equations into deep neural networks and…

Resolving the diffusion coefficient is a key element in many biological and engineering systems, including pharmacological drug transport and fluid mechanics analyses. Additionally, these systems often have spatial variation in the…

Deep learning techniques with neural networks have been used effectively in computational fluid dynamics (CFD) to obtain solutions to nonlinear differential equations. This paper presents a physics-informed neural network (PINN) approach to…

For decades, solutions to regional scale landslide prediction have mostly relied on data-driven models, by definition, disconnected from the physics of the failure mechanism. The success and spread of such tools came from the ability to…

Given the facts of the extensiveness of multi-material diffusion problems and the inability of the standard PINN(Physics-Informed Neural Networks) method for such problems, in this paper we present a novel PINN method that can accurately…

Modeling self-gravitating gas flows is essential to answering many fundamental questions in astrophysics. This spans many topics including planet-forming disks, star-forming clouds, galaxy formation, and the development of large-scale…