Using scientific machine learning to develop universal differential equation for multicomponent adsorption separation systems
Bibliographic record
Abstract
Abstract Universal differential equations are a concept in scientific machine learning that leverages the potential of the universal approximator theorem and the physical knowledge of a given system. Creating this level of hybridization within a stiff partial differential equation system is a challenge. On the other hand, adsorption phenomenological models have sink/source terms that describe the adsorption equilibrium through a well‐known simplified model (e.g., Langmuir; Sips; and Brunauer, Emmet, Teller [BET]). These suitable mechanistic assumptions are identified through experiments, providing the parameters of the sink/source model. However, these mechanistic assumptions are a simplification of the system phenomenology. Therefore, the resulting model is limited by its premises. In this scenario, the universal ordinary differential equations (UODE) is presented as an approach that conciliates the potential of artificial neural networks to learn given phenomena without conceptual simplifications. On the other hand, keeping into consideration the system physics. This work proposes a UODE system to solve the multicomponent separation by adsorption in a fixed bed column. Experimental data is used to identify the hybrid model. The required amount of data used in the model identification demonstrates that hybrid models can use a few data points to precisely describe the system. Furthermore, the obtained model can describe competitive adsorption with higher precision than the Langmuir model.
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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 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| 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".