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math.NA2025
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…
math.NA2025
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…