Reproduce “Convex Equilibrium Potentials for Monge--Ampère: Curvature Bounds and A Posteriori Evaluation” on OpenResearch
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About this paper
Edison Vázquez, Yingdong Lu, Tomasz Nowicki
The authors introduce a convex equilibrium network for Monge–Ampère equations, using repeated positive softplus layers until a fixed point is reached. Its contraction and positivity preserve a unique state and convexity. They bound curvature and certify residual and boundary error across the unit disk and circle for six frozen trained models; all certified residuals are below 0.25, with boundary errors below 0.01.
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