A diffusion-enhanced version of the NSCH-Oldroyd system is locally well-posed, with PINN numerics confirming energy decay for representative thrombus models.
Auto-Adaptive PINNs with Applications to Phase Transitions
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abstract
We propose an adaptive sampling method for the training of Physics Informed Neural Networks (PINNs) which allows for sampling based on an arbitrary problem-specific heuristic which may depend on the network and its gradients. In particular we focus our analysis on the Allen-Cahn equations, attempting to accurately resolve the characteristic interfacial regions using a PINN without any post-hoc resampling. In experiments, we show the effectiveness of these methods over residual-adaptive frameworks.
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Local Well-Posedness of a Modified NSCH-Oldroyd System: PINN-Based Numerical Computation
A diffusion-enhanced version of the NSCH-Oldroyd system is locally well-posed, with PINN numerics confirming energy decay for representative thrombus models.