A novel hybrid neural network for modeling dynamic systems using physics-informed regularization
Bibliographic record
Abstract
Physics-Informed Neural Networks (PINNs) are very popular due to their ability to incorporate first-principles knowledge in traditional neural network models. However, many applications of traditional PINNs in chemical process modeling treat time as an explicit input, rendering them incompatible with a process control framework. In contrast, more advanced approaches for modeling dynamic systems with process control in mind, such as Physics-Informed Recurrent Neural Networks (PI-RNNs), demand high computational resources for both training and implementation. As a solution, we propose a hybrid Physics-Informed Nonlinear Auto-Regressive with eXogenous inputs (PI-NARX) model that is accurate, computationally efficient, and inherits the desired properties of hybrid models. We demonstrate the effectiveness of this approach with a case study based on a Continuous Stirred Tank Reactor. The proposed hybrid model reduces the Mean Absolute Error by 17% for interpolation and 19.5% for extrapolation over the traditional data-driven NARX model. Additionally, we demonstrate the enhanced performance of PI-NARX over NARX in cases of practical importance, such as when limited data or limited process knowledge is available, and in the presence of noisy measurements, indicating the practicality and effectiveness of hybrid machine learning for real-world systems. We also benchmark the performance of the PI-NARX model against that of a PI-RNN, and demonstrate that the PI-NARX model outperforms the PI-RNN in terms of computational efficiency and prediction accuracy.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".