Estimating and Assessing Differential Equation Models with Time-Course Data
Bibliographic record
Abstract
Ordinary differential equation (ODE) models are widely used to describe chemical or biological processes. This Article considers the estimation and assessment of such models on the basis of time-course data. Due to experimental limitations, time-course data are often noisy, and some components of the system may not be observed. Furthermore, the computational demands of numerical integration have hindered the widespread adoption of time-course analysis using ODEs. To address these challenges, we explore the efficacy of the recently developed MAGI (MAnifold-constrained Gaussian process Inference) method for ODE inference. First, via a range of examples we show that MAGI is capable of inferring the parameters and system trajectories, including unobserved components, with appropriate uncertainty quantification. Second, we illustrate how MAGI can be used to assess and select different ODE models with time-course data based on MAGI's efficient computation of model predictions. Overall, we believe MAGI is a useful method for the analysis of time-course data in the context of ODE models, which bypasses the need for any numerical integration.
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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 | 0.012 | 0.037 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| 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".