Hybrid process modelling: Blending physics and data

A model has a simple job: provide a useful representation of a real-life process. In practice, usefulness is defined by more than predictive accuracy: models must also be robust, interpretable, computationally efficient, and support real operational decisions.  

Process models are traditionally divided into two broad categories. First-principles models describe systems through explicit descriptions of the underlying physical, chemical and/or biological phenomena. This mechanistic structure provides insight into process behaviour and, in principle, supports extrapolation beyond normal operating conditions. The application of such models is, however, often constrained. They are typically time-consuming to develop, computationally expensive to solve, and depend on explicit descriptions of mechanisms that may only be partially understood. As a result, highly complex fundamental models can convey a sense of accuracy that is not always justified when applied to real-life systems. 

On the other hand, data-driven models have demonstrated significant value across many industries. Empirical models can capture complex input-output relationships and often have strong predictive performance within the operating range used to train them. They do, however, require the availability of large volumes of high-quality operational data. In many operations, critical variables cannot be measured continuously or with sufficient accuracy, and data are often collected within narrow control ranges. This limits the richness of the data and constrains the ability of purely empirical models to generalise, remain stable over time, and provide meaningful insight into process behaviour. 

Hybrid models address these limitations by blending first-principles physics with data-driven learning. The value of hybrid models becomes especially clear in three common scenarios: 

When extrapolation is required 

Data-driven models perform best within the range of operating conditions represented in their training data. In many industrial applications, however, available operational data represent only a limited snapshot of process behaviour, due to, for example, infrequent sampling or constrained operating envelopes. Hybrid models mitigate this limitation by embedding empirical components within a mechanistic structure, enabling more reliable extrapolation. 

When computational speed is important 

First-principles models can offer deep operational insight, but their computational demands often limit their usefulness in applications that require fast or repeated simulations. The hybrid approach reduces model complexity by replacing computationally expensive or unknown fundamental components with data-driven approximations, based on the real-life process. This balance enables faster simulation without sacrificing accuracy. 

When underlying phenomena are not fully understood 

Many real-life processes involve aspects that are not understood well enough or are too complex to model from first principles. This can lead to excessive simplifying assumptions. Hybrid models provide a pragmatic approach by allowing data-driven components to capture unresolved behaviour, uncertainties, and complexities. 

In conclusion, hybrid modelling represents a convergence of physical understanding and data-driven adaptability. By constraining data science components within a first-principles structure, it turns theory into practical tools that can be used to support confident, informed decision-making for industrial operations.