4 papers
Error Estimates in Physics-Informed Neural Networks to Heat-Wave Fluid-Structure Interactive System
Pelin G. Geredeli, Mohammad Mahabubur Rahman, Deepanshu Verma
We study a physics-informed neural network (PINN) approximation of a coupled PDE system that models the interaction between fluid and elastic dynamics. The canonical heat-wave mode…
Regularity and error estimates in physics-informed neural networks for the Kuramoto-Sivashinsky equation
Mohammad Mahabubur Rahman, Deepanshu Verma
Due to its nonlinearity, bi-harmonic dissipation, and backward heat-like term in the absence of a divergence-free condition, the -D/-D Kuramoto-Sivashinsky equation poses sig…
Latent Twins
Matthias Chung, Deepanshu Verma, Max Collins +3
Over the past decade, scientific machine learning has transformed the development of mathematical and computational frameworks for analyzing, modeling, and predicting complex syste…
Error estimates for viscous Burgers' equation using deep learning method
Wasim Akram, Sagar Gautam, Deepanshu Verma +1
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions…