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math.NA2025
A finite element framework for simulating residential burglary in realistic urban geometries
Baoli Hao, Kamrun Mily, Annalisa Quaini +1
We consider a partial differential equation (PDE) model to predict residential burglary derived from a probabilistic agent-based model through a mean-field limit operation. The PDE…
math.NA2024
Stability in Training PINNs for Stiff PDEs: Why Initial Conditions Matter
Baoli Hao, Chun Liu, Ulisses Braga-Neto +2
Training physics-informed neural networks (PINNs) on stiff, time-dependent PDEs remains a fundamental challenge due to optimization instabilities and gradient pathologies. Through…