PHYSICS-INFORMED MODELING · 2024
Learning process dynamics while preserving physical structure
A CHO modeling study combines physical constraints, metabolic kinetics and machine learning to identify process dynamics.
THE SCIENTIFIC QUESTION
How can a learned model retain the physical relationships of a process?
How the study approaches it
The authors investigate black-box and gray-box identification, incorporating mass balances, kinetic expressions and differentiable optimization into model architectures.
REPORTED FINDING
The work demonstrates approaches for learning CHO dynamics while integrating partial physical knowledge and metabolic constraints.
What the evidence supports
The studied architectures and data determine the scope of the conclusions. A physically structured model still requires intended-use evaluation.
CONNECTION TO BIOMEDANA
BioMedAna uses mechanistic structure alongside data-driven modeling. Our worked example below illustrates mass-balance preservation through a reduced conversion model, not the paper's full CHO architecture.
Explore BioMedAna Twin ↗ANALYSIS PROTOCOL
Decision, data and execution method
Distinguish satisfying a physical balance from accurately predicting the time evolution of a process.
Input data and units
| Input | Value / range | Role in the calculation |
|---|---|---|
| System | A → B | Normalized total A + B = 1 |
| Initial state | A = 1; B = 0 | No other reaction or flow |
| Observations | Days 0–14 | Synthetic; deterministic 1% modulation |
| Reference rate | 0.15 day⁻¹ | Assumed comparator |
| Generator rate | 0.25 day⁻¹ | Used to construct the example |
Analysis sequence
- Select early observations for kinetic fitting.
- Fit the rate using log-linear least squares with fixed initial state.
- Calculate A and B from the analytic solution.
- Check conservation at every time point.
- Score predictions on later observations excluded from fitting.
Calibration and evaluation
Day zero contributes no slope information and is excluded from rate estimation. The analytic solution has no integration error. Conservation is exact by construction even when the rate is wrong; report held-out prediction error separately.
Reading the results
- A physically consistent curve can still be inaccurate.
- This conversion illustrates a structural principle; it is not the original paper’s full CHO network.
- Training size and held-out coverage affect the apparent reliability of the fitted rate.
Next experiments and deployment evidence
- Define measurement units and testable balances.
- Challenge additional reactions, unobserved states and varying conditions.
- Score prediction residuals and balance residuals independently.
ASK ASSIST · GUIDED EXAMPLE
Explore the question in BioMedAna's scientific workflow.
Choose a request to execute the educational model and inspect the results. This demonstration uses predefined requests and local calculations; it is not connected to the production Assist service.
Fit kinetics and check the physical balance
Fit kinetics and check the physical balance
BIOMEDANA WORKED EXAMPLE
Fit a kinetic rate while preserving a mass balance
This reduced A → B conversion example fits a reaction rate to early synthetic observations while enforcing A + B = 1. It illustrates a physical constraint, rather than CHO metabolism.
Product fraction: reference versus fitted kinetics Fraction of initial total
Model and fitting objective
A(t) = exp(−kt) B(t) = 1 − A(t) A + B = 1 kfit = −Σ[t · log(Aobserved)] / Σ[t²] Synthetic target k = 0.25 /day; reference k = 0.15 /day
Fitting uses the first 4 observations; 11 later observations are held out. Noise is deterministic at 1% of the remaining fraction. Conservation is built into the two-state structure, not learned from data.
The initial amounts are A = 1 and B = 0. This analytical solution has no numerical integration error. The construction excludes other reactions, unknown kinetics and measurement uncertainty.
Complete calculated values
| Day | Remaining A | Observed B | Reference B | Fitted B | Split |
|---|---|---|---|---|---|
| 0 | 1.0000 | 0.0000 | 0.0000 | 0.0000 | Fitting |
| 1 | 0.7805 | 0.2146 | 0.1393 | 0.2195 | Fitting |
| 2 | 0.6092 | 0.3880 | 0.2592 | 0.3908 | Fitting |
| 3 | 0.4755 | 0.5270 | 0.3624 | 0.5245 | Fitting |
| 4 | 0.3711 | 0.6349 | 0.4512 | 0.6289 | Held out |
| 5 | 0.2897 | 0.7162 | 0.5276 | 0.7103 | Held out |
| 6 | 0.2261 | 0.7775 | 0.5934 | 0.7739 | Held out |
| 7 | 0.1765 | 0.8251 | 0.6501 | 0.8235 | Held out |
| 8 | 0.1377 | 0.8633 | 0.6988 | 0.8623 | Held out |
| 9 | 0.1075 | 0.8942 | 0.7408 | 0.8925 | Held out |
| 10 | 0.0839 | 0.9184 | 0.7769 | 0.9161 | Held out |
| 11 | 0.0655 | 0.9367 | 0.8080 | 0.9345 | Held out |
| 12 | 0.0511 | 0.9505 | 0.8347 | 0.9489 | Held out |
| 13 | 0.0399 | 0.9611 | 0.8577 | 0.9601 | Held out |
| 14 | 0.0311 | 0.9695 | 0.8775 | 0.9689 | Held out |
Interpretation and limits
A physical balance can hold exactly even when the fitted rate is wrong. Inspect held-out prediction error as well as conservation. This example does not implement the original paper’s metabolic network or differentiable optimization.
Inspect the full implementation
Download executable JavaScript ↗Inspect the conservation function for the synthetic generator, fitting split and evaluation.
Before applying it to your process
Define the intended decision and acceptance criteria. Evaluate the method on representative held-out runs, inspect assumptions and uncertainty, and confirm performance prospectively before relying on its recommendations.
Editorial review: October 13, 2026. This report combines a publication summary with a BioMedAna educational implementation. The simulated results belong to the worked example; they do not reproduce the published experiments or establish a product benchmark.
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