Ask Russ Rhinehart - What are the pros for first-principles models?

Russ' Response:

Earlier I shared that I typically classify models as empirical or phenomenological.

In phenomenological models, the mathematical functions are grounded in a mechanistic relation. These models could be termed rigorous, first-principles, mechanistic, or cause-and-effect. First-principles type of phenomenological models would be the same sort as those used in undergraduate instruction in process units, revealing basic principles, and not attempting to be rigorous about details of secondary importance.

Although empirical models have some advantages, I prefer phenomenological models for the following reasons:

1. Nonlinearity: The model naturally and efficiently represents the actual phenomena. Although the number of units in empirical models can be increased to better fit model to data, it might take many. And each rise in complexity has an associated increase in the number of model coefficients that need to be fit to data. This nonlinearity includes steady-state sensitivity changes as well as non-stationary behavior (how transport delays and mixing lags change with operating conditions).
2. Training: Phenomenological models preserve mechanistic understanding. This helps operational staff understand fundamental phenomena, and discard folklore from long ago. Mechanistic understanding is essential for rational process analysis, abnormal situation detection, process improvement, and such activities.
3. One-Model: The first-principles model is useful for design, operational optimization, control, training, maintenance forecasting, and other digital twin applications. Having “one model to rule them all” is efficient.
4. No diversion of staff: Staff are not diverted to learn irrelevant mathematical techniques such as back propagation, or parsimony (choosing the number of empirical model units to best fit data with minimum complexity), or time-matching input and response variables, or the concepts of Laplace, or FIR matrix transforms. The models use engineers’ mathematics.
5. Extrapolation: Empirical models are best fit to a data set, but since they do not capture the mechanistic phenomena, extrapolation might be doubtful. First-principles models should extrapolate to conditions for which they were designed (such as within turbulent flow).
6. Data acquisition: Very few process upsets are required to generate data for first-principles model calibration or validation. By contrast a significant amount of data is needed to confidently determine empirical model coefficient values. There may be much historical data that could be used for training empirical models. But because of inconsistencies (such as data from fouled or clean service, or prior to process upgrades) or incomplete data, or operating at new flow rates, new data would be needed to generate empirical models. The data generation could be costly, time consuming, and risky. And, in my experience, such extensive trials are often truncated by production overrides.
7. Insensitivity to data abnormalities: These include noise, or other data aberrations.
8. On-line monitoring: Process attributes, such as fouling, efficiency, or reactivity change in time. By observing how an adjustable coefficient of a first-principles model changes in time, one can have a useful forecast for maintenance scheduling, and ever-changing constraint conditions.
9. Simplicity of model calibration: There are only a few adjustable model coefficients, which means minimal process experimentation is required to calibrate and validate a first-principles model.

I prefer the use of first-principles models. But expediency might justify empirical modeling.

In subsequent Pods, I’ll introduce how to create your own first-principles models, how to simulate environmental vagaries, how to calibrate and validate models, and how to use the models to evaluate the various economic indicators of transient events.  I hope to visit with you later.  Meanwhile, visit my web site www.r3eda.com to access information about modeling, control, optimization, and statistical analysis.