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math.NA2026
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…
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…