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Entropy-Enhanced Physics-Informed Neural Networks for Parametric Conservation Laws

A nonlinear model-order-reduction strategy that solves families of nonlinear hyperbolic conservation laws with a tiny meta-network whose activation functions are pre-trained physics-informed neural networks. Students learn how rewriting the PDE in characteristic form, weighting the loss near discontinuities, enforcing the Rankine-Hugoniot condition, and training a parameter-dependent transform layer let one to five neurons capture parameter-dependent shock formation, interaction, and merging in Burgers and Euler problems, including inverse problems.