Neural networks are increasingly used to construct numerical solution methods for partial
differential equations. In this expository review, we introduce and contrast three important …

Recent breakthroughs in computing power have made it feasible to use machine learning
and deep learning to advance scientific computing in many fields, including fluid mechanics …

Data scarcity is a major challenge when training deep learning (DL) models. DL demands a
large amount of data to achieve exceptional performance. Unfortunately, many applications …

Recently, a class of machine learning methods called physics-informed neural networks
(PINNs) has been proposed and gained prevalence in solving various scientific computing …

In this work, we present a Parametric Deep Energy Method (P-DEM) for elasticity problems
accounting for strain gradient effects. The approach is based on physics-informed neural …

Recently, physics informed neural networks have successfully been applied to a broad
variety of problems in applied mathematics and engineering. The principle idea is the usage …

Near-wall blood flow and wall shear stress (WSS) regulate major forms of cardiovascular
disease, yet they are challenging to quantify with high fidelity. Patient-specific computational …

Despite its rapid development, Physics-Informed Neural Network (PINN)-based
computational solid mechanics is still in its infancy. In PINN, the loss function plays a critical …

Partial differential equations (PDEs) play a fundamental role in modeling and simulating
problems across a wide range of disciplines. Recent advances in deep learning have shown …

Transformers are widely used in natural language processing due to their ability to model
longer-term dependencies in text. Although these models achieve state-of-the-art …