Scaling up machine learning-based chemical plant simulation: A method for fine-tuning a model to induce stable fixed points

TL;DR

This work addresses the instability of ML-based, flowsheet-wide chemical plant simulations as plant size grows and cycles become nested. It introduces a two-stage training approach: first train per-unit neural surrogates, then fine-tune end-to-end by backpropagating through the cycle solver, aligning gradients to direct solvers toward the true stationary state. On a synthetic Cumene process, the authors show that naive training leads to divergence in cycle solving for large flowsheets, while the proposed fine-tuning yields near-perfect end-to-end predictions and robust cycle convergence, with only minor impacts on individual unit accuracy. The findings suggest a viable path to scalable, data-driven digital twins for industrial plants, including potential extensions to real plants via hybrid data and optimization applications.

Abstract

Idealized first-principles models of chemical plants can be inaccurate. An alternative is to fit a Machine Learning (ML) model directly to plant sensor data. We use a structured approach: Each unit within the plant gets represented by one ML model. After fitting the models to the data, the models are connected into a flowsheet-like directed graph. We find that for smaller plants, this approach works well, but for larger plants, the complex dynamics arising from large and nested cycles in the flowsheet lead to instabilities in the solver during model initialization. We show that a high accuracy of the single-unit models is not enough: The gradient can point in unexpected directions, which prevents the solver from converging to the correct stationary state. To address this problem, we present a way to fine-tune ML models such that initialization, even with very simple solvers, becomes robust.

Figures (10)

• Figure 1: Left: Flowsheet schematic. $u_1$, $u_2$ and $u_3$ are process units. The arrows indicate in which direction the chemicals flow. Right: In the present study, the first-principles-based simulation for each process unit is turned into an ML model, in this case, NNs.
• Figure 2: Cumene process flowsheet. For the type of each unit, refer to Table \ref{['table:single_unit_errors']}
• Figure 3: Flowsheet schematic with the tear stream indicated in red.
• Figure 4: Top left: Data are generated either from sensors in a real plant, or from a first-principles-based simulation. Top right: The ML models representing each flowsheet unit are fitted entirely isolated from each other, with each input/output set by the collected data. Bottom: The flowsheet is sequentially predicted from beginning to end, including the iterative cycle-solving (forward pass, black arrows). Afterward, the gradient is backpropagated through each node along the unrolled forward pass (blue arrows).
• Figure 5: Visualization of a flowsheet response function and corresponding solve iterations of two different solve methods. The intersections of the flowsheet response curve (solid line) and the diagonal line where $f(x)=x$ (dotted line) are the fixed points of the flowsheet response function. Left: Direct substitution method. Right: Newton method. The blue and orange lines represent iterations for different initial values. The initial values were chosen for illustrative purposes. Each solve iteration starts at the large circles.