Partial differential equations (PDEs) are commonly employed to model complex industrial systems characterized by multivariable dependence. Existing physics-informed neural networks (PINNs) excel in solving PDEs in a homogeneous medium. However, their feasibility is diminished when PDE parameters are unknown due to a lack of physical attributions and time-varying interface is unavailable arising from heterogeneous media. To this end, we propose a data-physics-hybrid method, physically informed synchronic-adaptive learning (PISAL), to solve PDEs for industrial systems modeling in heterogeneous media. First, Net 1 , Net 2 , and Net I , are constructed to approximate the solutions satisfying PDEs and the interface. Net 1 and Net 2 are utilized to synchronously learn each solution satisfying PDEs with diverse parameters, while Net I is employed to adaptively learn the unavailable time-varying interface. Then, a criterion combined with Net I is introduced to adaptively distinguish the attributions of measurements and collocation points. Furthermore, Net I is integrated into a data-physics-hybrid loss function. Accordingly, a synchronic-adaptive learning (SAL) strategy is proposed to decompose and optimize each subdomain. Besides, we theoretically prove the approximation capability of PISAL. Extensive experimental results verify that the proposed PISAL can be used for industrial systems modeling in heterogeneous media, which faces the challenges of lack of physical attributions and unavailable time-varying interface.Note to Practitioners-The motivation behind this paper is to devise a method for industrial systems modeling, even in cases where unknown PDE parameters are caused by a lack of physical attributions and an unavailable time-varying interface is caused by heterogeneous media. Existing methods apply domain decomposition technique under the assumption that the interface is available. To this end, a data-physics-hybrid method, PISAL, in which Net 1 , Net 2 , and Net I with SAL strategy are proposed to solve PDEs for industrial system modeling in heterogeneous media. Net 1 , Net 2 , and Net I are first constructed to learn the solutions satisfying PDEs and the time-varying interface. Net 1 and Net 2 are for synchronously learning each solution satisfying PDEs with diverse parameters; Net I is for adaptively learning the unavailable time-varying interface. Subsequently, a criterion combined with Net I is introduced, which is to adaptively distinguish different physical attributions of measurements and collocation points. Additionally, Net I is integrated into a dataphysics-hybrid loss function. Accordingly, a SAL strategy is proposed to decompose and optimize each subdomain. Besides, we theoretically prove the approximation capability of PISAL. To validate the efficacy of the proposed PISAL, the classical two-phase Stefan problem and the mixed Navier-Stokes problem are employed. Results highlight the feasibility of our method in industrial systems modeling with the abovementioned challenges and demonstrate some com...