  Learning-based approaches to cloth simulation have started to show their
potential in recent years. However, handling collisions and intersections in
neural simulations remains a largely unsolved problem. In this work, we present
\moniker{}, a learning-based solution for handling intersections in neural
cloth simulations. Unlike conventional approaches that critically rely on
intersection-free inputs, \moniker{} robustly recovers from intersections
introduced through missed collisions, self-penetrating bodies, or errors in
manually designed multi-layer outfits. The technical core of \moniker{} is a
novel intersection contour loss that penalizes interpenetrations and encourages
rapid resolution thereof. We integrate our intersection loss with a
collision-avoiding repulsion objective into a neural cloth simulation method
based on graph neural networks (GNNs). We demonstrate our method's ability
across a challenging set of diverse multi-layer outfits under dynamic human
motions. Our extensive analysis indicates that \moniker{} significantly
improves collision handling for learned simulation and produces visually
compelling results.
