  For a Koszul Artin-Schelter regular algebra (also called twisted Calabi-Yau
algebra), we show that it has a "twisted" bi-symplectic structure, which may be
viewed as a noncommutative and twisted analogue of the shifted symplectic
structure introduced by Pantev, To\"en, Vaqui\'e and Vezzosi. This structure
gives a quasi-isomorphism between the tangent complex and the twisted cotangent
complex of the algebra, and may be viewed as a DG enhancement of Van den
Bergh's noncommutative Poincar\'e duality; it also induces a twisted symplectic
structure on its derived representation schemes.
