Revisiting Conditional Whitney Forms: From Structure Preservation to Physics Recovery

Conditional Whitney forms have recently emerged as a promising framework at the intersection of scientific machine learning and finite element analysis. They offer a solid theoretical foundation for enforcing structure preservation in complex learning settings. However, their use so far has been restricted to tasks where structural constraints can be satisfied in a trivial manner. In this work, we analyze why existing formulations reduce to trivial reformulations, highlight the necessity of incorporating additive structure and validate experimentally our theoretical insights.