  In chemical engineering, process data are expensive to acquire, and complex
phenomena are difficult to fully model. We explore the use of physics-informed
neural networks (PINNs) for dynamic processes with incomplete mechanistic
semi-explicit differential-algebraic equation systems and scarce process data.
In particular, we focus on estimating states for which neither direct
observational data nor constitutive equations are available. We propose an
easy-to-apply heuristic to assess whether estimation of such states may be
possible. As numerical examples, we consider a continuously stirred tank
reactor and a liquid-liquid separator. We find that PINNs can infer unmeasured
states with reasonable accuracy, and they generalize better in low-data
scenarios than purely data-driven models. We thus show that PINNs are capable
of modeling processes when relatively few experimental data and only partially
known mechanistic descriptions are available, and conclude that they constitute
a promising avenue that warrants further investigation.
