Physics-Informed Neural Network Digital Twin for Dynamic Tray-Wise Modeling of Distillation Columns under Transient Operating Conditions

Debadutta Patra; Ayush Bardhan Tripathy; Soumya Ranjan Sahu; Sucheta Panda

cs.LGMar 25, 2026

Physics-Informed Neural Network Digital Twin for Dynamic Tray-Wise Modeling of Distillation Columns under Transient Operating Conditions

Authors: Debadutta Patra, Ayush Bardhan Tripathy, Soumya Ranjan Sahu, Sucheta Panda

Organizations: Department of Chemical Engineering, Veer Surendra Sai University of Technology, Burla 768018, India · Department of Computer Science & Engineering, Veer Surendra Sai University of Technology, Burla 768018, India

Abstract

Digital twin technology, when combined with physics-informed machine learning with simulation results of Aspen, offers transformative capabilities for industrial process monitoring, control, and optimization. In this work, the proposed model presents a Physics-Informed Neural Network (PINN) digital twin framework for the dynamic, tray-wise modeling of binary distillation columns operating under transient conditions. The architecture of the proposed model embeds fundamental thermodynamic constraints, including vapor-liquid equilibrium (VLE) described by modified Raoult's law, tray-level mass and energy balances, and the McCabe-Thiele graphical methodology directly into the neural network loss function via physics residual terms. The model is trained and evaluated on a high-fidelity synthetic dataset of 961 timestamped measurements spanning 8 hours of transient operation, generated in Aspen HYSYS for a binary HX/TX distillation system comprising 16 sensor streams. An adaptive loss-weighting scheme balances the data fidelity and physics consistency objectives during training. Compared to five data-driven baselines (LSTM, vanilla MLP, GRU, Transformer, DeepONet), the proposed PINN achieves an RMSE of 0.00143 for HX mole fraction prediction (R^2 = 0.9887), representing a 44.6% reduction over the best data-only baseline, while strictly satisfying thermodynamic constraints. Tray-wise temperature and composition profiles predicted under transient perturbations demonstrate that the digital twin accurately captures column dynamics including feed tray responses, reflux ratio variations, and pressure transients. These results establish the proposed PINN digital twin as a robust foundation for real-time soft sensing, model-predictive control, and anomaly detection in industrial distillation processes.

Figures & tables

Sensor	Description	Unit	Mean $\pm$ Std
Sensor 1	Liquid % in Condenser	%	50.00 $\pm$ 0.29
Sensor 2	Condenser Pressure	kPa	101.28 $\pm$ 0.45
Sensor 3	Liquid % in Reboiler	%	49.56 $\pm$ 6.12
Sensor 4	Mass Flow Rate — Feed	kg/h	3823 $\pm$ 511
Sensor 5	Mass Flow Rate — Top Outlet	kg/h	6866 $\pm$ 755
Sensor 6	Net Mass Flow — Main Tower	kg/h	2806 $\pm$ 260

Table 1: Distillation column dataset,sensor descriptions, units, and summary statistics (N = 961 timesteps, sampled at 30 s intervals, generated in Aspen HYSYS

Figure 1: Temporal evolution of eight key sensor channels across the 8-hour simulation horizon. The dataset captures rich transient dynamics including oscillations in reboiler hold-up and monotonic reflux ratio ramp.

Figure 2: Pearson correlation heatmap for all 18 sensor and target variables. Strong inter-pressure correlations ( $\rho>0.99$ ) and moderate composition–holdup couplings are evident.

Figure 3: Methodology workflow for PINN-based digital twin of a distillation column

Figure 4: Architecture of the proposed Physics-Informed Neural Network (PINN) for distillation column modeling , showing the column process (left), neural network with 16 sensor inputs and predicted outputs $x_{\mathrm{HX}}$ , $x_{\mathrm{TX}}$ , $T$ , and $P$ (middle), and the physics-informed loss combining data loss with governing thermodynamic and transport equations (right).

Figure 5: PINN architecture for the distillation column digital twin. The network combines four hidden layers (256–256–128–64, Swish activation) with physics residual constraints on VLE, mass balance, and energy balance embedded in the composite loss function $L_{\mathrm{total}}$ .

Figure 6: (Left) Semi-log training convergence curves for total, data, physics, and validation losses. (Right) Adaptive loss-weighting schedule,the physics weight $\lambda_{\mathrm{p}}$ decreases sigmoidally from 1.0 to $\sim 0.02$ after epoch 300.

Figure 7: PINN vs Baseline MLP prediction performance on the test set. (Top-left) Time-series comparison for HX mole fraction. (Top-right) Parity plot showing PINN $R^{2}=0.9887$ . (Bottom-left) TX mole fraction time-series. (Bottom-right) Residual distribution confirming tighter PINN error bounds.

Model	MSE	RMSE	MAE	$\mathbf{R^{2}}$	Phys. Cons.
LSTM [ 5 ]	$1.34\times 10^{-5}$	0.00366	0.00278	0.9482	No
Vanilla MLP [ 25 ]	$8.70\times 10^{-6}$	0.00295	0.00219	0.9645	No
GRU [ 6 ]	$7.90\times 10^{-6}$	0.00281	0.00207	0.9688	No
Transformer [ 14 ]	$6.66\times 10^{-6}$	0.00258	0.00195	0.9721	No
DeepONet [ 20 ]	$5.12\times 10^{-6}$	0.00226	0.00181	0.9796	Partial
PINN (Ours)	$\mathbf{2.05\times 10^{-6}}$	0.00143	0.00109	0.9887	Yes

Table 2: Quantitative comparison of PINN against five data-driven baselines on the held-out test set. Best results in bold. Physics Cons. = satisfaction of thermodynamic constraints (VLE + mass balance).

Figure 8: (Left) Predicted tray-wise temperature profiles at three simulation times. (Centre) Predicted HX composition profiles showing S-curve sharpening with increasing reflux. (Right) Comparative RMSE bar chart across all models, with per-bar $R^{2}$ annotations.

Figure 9: (Left) GBDT feature importance for HX mole fraction prediction, confirming Sensor 7 and Sensor 3 as dominant state variables. (Right) HX reboiler vs top-outlet composition scatter, colored by feed tray temperature, revealing thermal coupling in the separation.

Figure 10: Distillation column PINN performance—(A) Physical consistency regularization reduces RMSE compared to the transformer baseline. (B) PINN shows better accuracy in low-data conditions. (C) Sigmoid adaptive weighting achieves the lowest loss. (D) PINN accurately predicts transient startup dynamics.

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