Physics-Informed Neural Networks for Dynamic Process Operations with Limited Physical Knowledge and Data

TL;DR

It is shown that PINNs are capable of modeling processes when relatively few experimental data and only partially known mechanistic descriptions are available, and this work concludes that they constitute a promising avenue that warrants further investigation.

Abstract

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 modeling 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 immeasurable states with reasonable accuracy, even if respective constitutive equations are unknown. 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.

Figures (10)

• Figure 1: Relationship between PINN time $t$ and process time $\tau$: The PINN time domain $[0,T]$ corresponds to the length of a step-wise constant control input. In general, PINN time $t$ differs from process time $\tau$ and chaining of model predictions is required to simulate longer periods of time. Only if the control input is constant over the entire process duration, $t$ and $\tau$ coincide. Measurements can come from an irregular grid.
• Figure 2: PINN-based dynamic process model with semi-explicit DAE physics model
• Figure 3: Schematic representation of the van de Vusse CSTR
• Figure 4: Test set error for the measured states for all models and data regimes. Boxplots show the results of 25 models (5 runs each for 5 data sets), averaged over the test set of each model. The error metric is the mean absolute percentage error (MAPE).
• Figure 5: Test set errors for the unmeasured differential states of PINN-C with $\mathbf{x}^u = [c_A]^T$, $\mathbf{x}^u = [T]^T$ and $\mathbf{x}^u = [T_K]^T$ for the Van de Vusse reactor example. All error values correspond to the respective unmeasured differential state, e.g., the value for the model with $\mathbf{x}^u = [c_A]^T$ shows the error of $c_A$. Boxplots show the results of 25 models (5 runs each for 5 data sets), averaged over the test set of each model. The error metric is the mean absolute percentage error (MAPE).