Physics-Informed Neural Networks (PINNs)
in Chemical Process Control

The Failure Mode of Purely Data-Driven Models in Process Engineering

The case for machine learning in process optimization is clear: complex, non-linear process behaviour is difficult to model from first principles, and modern processes generate large amounts of sensor data that conventional analysis does not fully exploit. The promise is that ML models can identify patterns and correlations that human engineers miss.

The failure mode is equally clear to anyone who has tried to deploy data-driven process models in production: they work well within the envelope of their training data and fail — often catastrophically — when conditions change. A neural network trained on normal operating data cannot tell you what will happen if you increase aeration by 20% beyond the training range. It was never shown that condition; it will either interpolate incorrectly or produce physically impossible predictions.

This is not a problem that more data solves. It is a structural limitation of models that have no internal representation of the physical laws governing the system. Any model that can fit arbitrary data can also fit physically impossible data — and will, if that is what the training set implies.

What Physics-Informed Neural Networks Do Differently

Physics-Informed Neural Networks, introduced formally by Raissi, Perdikaris, and Karniadakis (2019), address this limitation by embedding physical equations as constraints in the training process. The loss function a PINN minimizes has two components:

• Data loss: the discrepancy between model predictions and observed measurements — the standard supervised learning objective.
• Physics residual loss: the extent to which the model's predictions violate known physical equations — such as the Navier-Stokes equations for fluid flow, mass conservation, or reaction kinetic expressions.

The result is a model that is simultaneously consistent with observations and with physics. It cannot predict a fluid flowing uphill without a driving force; it cannot produce a mass balance that violates conservation. In regions of the state space where no training data exists, the model's predictions are guided by physical principles rather than unconstrained extrapolation.

The Mathematical Foundation

Consider a PINN applied to a convection-diffusion problem governing concentration transport in a reactor. The network approximates the concentration field c(x,t) as a function of spatial coordinates and time. The total loss includes a boundary/initial condition term and a PDE residual term that penalizes deviations from the governing equation:

ℒ_total = ℒ_data + λ · ℒ_physics
where ℒ_physics = ||∂c/∂t + u·∇c − D·∇²c − R(c)||²

The weighting parameter λ controls the trade-off between fitting data and enforcing physics. In data-rich regions, the model fits observations closely; in data-sparse regions, physical consistency becomes the primary constraint. This is precisely the behaviour needed for industrial process models, where measurements are always incomplete relative to the dimensionality of the system.

Why PINNs Are Particularly Relevant for Process Engineering

Chemical and bioprocessing applications have several characteristics that make PINNs especially well-suited — and that distinguish them from domains where purely data-driven approaches are more adequate:

The Critical Data Requirement: Why Spatial Resolution Matters

PINNs trained on data from point sensors face a fundamental limitation that is often underappreciated: a model constrained by physics can resolve spatial structure that the sensors cannot see — but only if the training data carries enough information to distinguish spatial configurations.

Consider the problem of inferring mixing quality in a reactor from a dissolved oxygen probe. The probe reports one scalar value. A PINN trained on this data can learn how the probe responds to changes in agitation or aeration — a temporal model. But it cannot resolve where mixing dead zones are, because the training data contains no spatial information. The physics constraints do not help here: the Navier-Stokes equations constrain the possible spatial configurations, but they do not uniquely specify the configuration if only a single scalar measurement is available.

This is why spatially resolved, high-frequency sensor data is the enabling condition for Physical AI in process engineering — not a nice-to-have, but a fundamental requirement for the physics to fully inform the model.

Applications in Industrial Process Control

Reaction Kinetic Parameter Identification

PINNs can be used to identify reaction kinetic parameters — rate constants, activation energies, inhibition coefficients — from continuous process data, without requiring the dedicated batch experiments that conventional kinetic modelling demands. As the process operates, the model continuously updates its estimate of the kinetic parameters. This is particularly valuable in bioprocesses, where cell culture kinetics change over time and between batches.

Process State Estimation

Given a sparse set of measurements, a PINN constrained by process physics can reconstruct the full process state — including unmeasured quantities — more reliably than either interpolation or pure ML models. For a distillation column, this means inferring the full liquid and vapor composition profiles from a few temperature measurements and a holdup distribution at one cross-section.

What-If Simulation for Process Optimization

A calibrated PINN can be used as a surrogate simulator for process optimization: evaluating the predicted process response to changes in operating conditions (feed rate, temperature, agitation, gas flow) without requiring the change to be made physically. This is the foundation of model predictive control — and PINNs trained on spatially resolved data can support it with physically consistent predictions.

Anomaly Detection with Physical Interpretation

When a process deviates from its PINN-predicted state, the nature of the deviation — the specific physical equation that is being violated — provides diagnostic information about the cause. A mass balance deviation implies a measurement fault or process leak; a momentum balance deviation implies a change in fluid properties or flow regime. This physical interpretability distinguishes PINN-based anomaly detection from statistical process control.

Current State of Research and Industrial Deployment

PINN research has grown rapidly since the foundational 2019 paper, with applications across computational fluid dynamics, structural mechanics, and increasingly in chemical engineering. Key research groups active in process engineering applications include those at MIT (Barzilay group), ETH Zürich, and TU Munich, with publications appearing primarily in Computers & Chemical Engineering, the Industrial & Engineering Chemistry Research journal, and Chemical Engineering Journal.

Industrial deployment of PINNs in chemical process control remains in early stages as of 2026. The primary bottleneck is not the modelling methodology — it is the sensor data. Most operating plants still rely on point sensors that cannot provide the spatial information PINNs require to resolve the physics at the scale relevant to process performance. As spatially resolved inline sensors become available for industrial deployment, the conditions for physical AI become available alongside them.