Botanical Intelligence Proposed program Methods peer-reviewed Synthetic demonstration
The first model would predict extraction yield, and its funding stops at month 24 unless it beats physics and classical design
The model is defined here before any data exist: what it predicts, which simpler methods it must beat, how its uncertainty is checked and when the program stops.
15–30runs a classical response-surface design needs for three or four factors (NIST)
70–90%coverage band a well-calibrated 80% interval needs on 60 test runs (binomial)
250test runs needed before the band narrows to about 75–85%
5peer-reviewed papers by the founder on these methods, 2011–2016 (DOIs below)
Status. A proposed program: no laboratory, extraction data or trained model exist. Targets are thresholds, not results.
Academy fundamentals: Course 11, Multi-objective ingredient design · Related: targeted and non-targeted analysis · large botanical model
A narrow objective, defined in advance
- One target. Marker-compound yield in milligrams per gram of dry plant material, predicted from four process settings.
- Tested against simpler methods. It must beat the mass-transfer model alone and classical design of experiments, on a botanical it has never seen.
- Stops on schedule. Without both measured gains by month 24, machine-learning spending stops; the structured dataset is kept.
Architecture
A mass-transfer model carries the physics; machine learning corrects what the physics misses
Hybrid model: a physics core plus a learned residual, with calibrated uncertainty, closing the loop with the laboratoryProposed architecture
Hybrid neural-network and first-principles modeling: Psichogios & Ungar 1992, AIChE J. Bayesian optimization benchmarked against human chemists: Shields et al. 2021, Nature. Diffusion from a sphere: Crank 1975. Applying these methods to botanical extraction is a hypothesis to test.
Explanation, details and sources
- Target improvement≠an achieved result
- Synthetic demonstration≠botanical data
- Model prediction≠a product specification or a release test
Each designed experiment produces a measured yield. A physics core predicts the yield curve from diffusion out of plant particles; a learned residual corrects it; the combined prediction, with calibrated uncertainty, chooses the next experiment.
What it predicts
The target is the yield of one quantified marker compound, in milligrams per gram of dry plant material
Marker yield is one of three ratios, and the physics core predicts how it rises with timeProposed definitions Illustrative model
Physics core: diffusion out of a spherical particle of radius R (Crank 1975)Ym(t) = Y∞ [1 − (6/π²) Σn≥1 n⁻² exp(−n²π²Defft/R²)]
Text version: quantities, inputs, and the two model parts
| Quantity | Definition | Units | Role |
|---|---|---|---|
| Marker yield, Ym(t) | Mass of the marker compound recovered in the extract per mass of dry plant material, at extraction time t; 4 to 6 sampling times per run give the kinetic curve | mg/g dry weight | Primary target |
| Total extract yield | Dry extract mass per dry plant mass, gravimetric | g/100 g | Secondary target |
| Marker purity | Marker mass per dry extract mass | mg/g extract | Secondary target, reported with yield |
| Controlled inputs | Temperature; time; ethanol fraction of an ethanol–water solvent and solvent-to-solid ratio; particle size (sieve fraction) | °C; min; % v/v and mL/g; µm (d50) | Model inputs set by the design |
| Measured covariates | Raw-material lot, plant part, moisture content, harvest and drying records | various | Recorded; used to group data and to detect drift |
Physics core
Diffusion out of a spherical particle
Ym(t) = Y∞ [1 − (6/π²) Σn≥1 n⁻² exp(−n²π²Defft/R²)]
Two parameters per condition: the equilibrium-limited yield Y∞ and the effective diffusivity Deff (Arrhenius in temperature); R is the particle radius. Valid for a well-mixed solvent in excess (Crank 1975, sphere with constant surface concentration). For supercritical CO₂ extraction the broken-and-intact-cells model (Sovová 1994) would take its place.
Learned part
A Gaussian process on the residual
The machine-learning part learns the difference between measured and physics-predicted yield as a function of the four inputs. A Gaussian process (Rasmussen & Williams 2006) gives a mean and a standard deviation at every untested condition, which the optimizer needs.
Testing plan Proposal
Data are split by raw-material lot and by botanical, so the test always contains material the model has not seen
Lots and a whole botanical are held out, and the hybrid must beat three simpler baselinesProposed testing plan
Text version of the data sets and baselines
| Data set | Content | Used for |
|---|---|---|
| Training | Three development botanicals, about 60 designed runs each, two or more raw-material lots per botanical | Fitting the physics parameters and the residual model |
| Validation | One lot per botanical, held out as a group | Choosing kernels and hyperparameters; checking calibration |
| Internal test | A further held-out lot per botanical, opened once | Accuracy on new material of known botanicals |
| External test | A fourth botanical, never used for fitting or tuning | The success criteria below |
| Prospective check | New runs chosen by the optimizer and performed afterwards | Runs-to-target against classical design, measured, not simulated |
Baseline 1
Physics alone
The diffusion model with Y∞ and Deff fitted per botanical, no learned residual. Target: the hybrid's root-mean-square error on the external botanical is at least 20% lower.
Baseline 2
Classical design of experiments
A response-surface design (central composite or Box–Behnken) with a quadratic model (Box & Wilson 1951). Target: the optimizer reaches the target yield in at least 30% fewer runs.
Baseline 3
No model
The mean yield of the training data. Any model that cannot beat it on the external botanical is not reported as predictive.
Thresholds are proposals to be fixed before data collection starts and approved by the board; once fixed, they are not changed after results are seen.
Uncertainty and stopping
A stated 80% interval should contain the measured yield about 80% of the time, and the program stops on preset rules
Coverage must land inside a preset band, and three rules stop a campaign, a prediction or the programProposed acceptance criteria
Text version of calibration and stopping rules
Calibration
- Report coverage of the 80% and 95% prediction intervals on the validation and test sets, with the mean interval width (sharpness), as recommended by Gneiting et al. 2007.
- Acceptance band, proposed: the range in which a perfectly calibrated model's observed coverage falls for 95% of test sets of the size actually run (binomial). At 60 test runs: 70–90% for the 80% interval and 88–100% for the 95% interval; at about 250 runs: 75–85% and 92–98%.
- If coverage falls outside the band, intervals are recalibrated by split conformal prediction (Angelopoulos & Bates 2023) on the validation set, and the recalibrated intervals are checked on the test set.
- Predictions outside the range of training inputs are flagged and not used to stop experiments.
Stopping rules
- Each optimization campaign stops when the largest expected improvement falls below the run-to-run repeatability (estimated from center-point replicates) for three consecutive proposals, or when the run budget is spent.
- The model abstains for a botanical whose inputs or covariates fall outside the training range.
- The program stops machine-learning spending at month 24 if either success criterion is missed on the external botanical. The structured dataset, the physics model and the classical designs remain in use.
Coverage when true errors are k times the stated spreadc = 2 Φ(z/k) − 1, z = Φ−1((1 + p)/2); covered runs ~ Binomial(n, c)
Expected coverage80.0 %
Observed coverage, 95% of test sets: from70.0 %
to90.0 %
Chance of passing the band 70.0–90.0 %96.6 %
Expected coverage against miscalibration, with the spread of what a finite test set would showModel output
Gaussian errors assumed; binomial sampling of n independent test runs. Gneiting T, et al. 2007; Angelopoulos AN, Bates S. 2023.
Method, assumptions and limits
- What it calculates
- The share of measured yields expected inside a model's stated central interval at nominal level p when the true prediction errors have k times the spread the model states; the central 95% range of the share observed on n independent test runs; the acceptance band for n runs (the same range for a perfectly calibrated model, k = 1); and the probability that the observed share falls inside that band. At k = 1 passing is the correct outcome (at least 95% by construction); at any other k, passing means the miscalibration goes undetected.
- Equations
- z = Φ−1((1 + p)/2) (1.2816 for 80%, 1.9600 for 95%); c = 2Φ(z/k) − 1; X ~ Binomial(n, c); range = [q0.025, q0.975]/n with q the smallest x whose cumulative probability reaches the level; band = [q0.025, q0.975]/n of Binomial(n, p/100); P(band) = Σ P(X = x) for band low ≤ x/n ≤ band high.
- Variables and units
- p nominal level (%); k dimensionless (k > 1: intervals too narrow, overconfident; k < 1: too wide); n number of test runs; outputs in percent.
- Assumptions
- Normally distributed, unbiased, independent errors; constant k across runs. Repeated runs on one lot are correlated, which widens the real spread further.
- Valid range
- k 0.5–2; n 10–300; p 80% or 95% (the two intervals the page proposes to report).
- What it does not establish
- Any property of a real model; the yield data do not exist. It shows how wide the acceptance band must be for a given test-set size, and how large a miscalibration that band can detect.
- References
- Gneiting, Balabdaoui and Raftery 2007 (calibration and sharpness); Angelopoulos and Bates 2023 (split conformal prediction).
- Verification
- An independent SciPy implementation (tests/numerics/ref/digi_coverage.py) reproduces every readout for seven cases.
On 60 test runs the band must be 70–90% to pass a calibrated model 95% of the time, so it would flag intervals about 40% too narrow 80% of the time; about 250 runs narrow it to 75–85%.
Classical baseline NIST design tables
The classical baseline fixes its runs in advance: 15 to 27 runs for three factors, 27 to 30 for four
Three-factor response-surface designs in coded units: choose a design and drag to rotateNIST e-Handbook coordinates
Runs20
Distinct settings15
Levels per factor5
Data table: coded settings
| Design | Corner points | Axial or edge points | Centre runs | Total runs |
|---|---|---|---|---|
| CCC | 8 at (±1, ±1, ±1) | 6 at ±1.682 on each axis | 6 | 20 |
| CCF | 8 at (±1, ±1, ±1) | 6 at ±1 on each axis (face centres) | 6 | 20 |
| Box–Behnken | none | 12 edge midpoints, e.g. (±1, ±1, 0) | 3 | 15 |
| Three-level full factorial | 26 grid points of {−1, 0, +1}³ | (included in the grid) | 1 | 27 |
Runs required by central composite and Box–Behnken designs for two to six factorsNIST data
Data table: runs by number of factors
| Factors | Central composite | Box–Behnken |
|---|---|---|
| 2 | 13 (5 centre points) | not listed |
| 3 | 20 (6 centre runs) | 15 |
| 4 | 30 (6 centre runs) | 27 |
| 5 | 33 (fractional factorial) or 52 (full factorial) | 46 |
| 6 | 54 (fractional factorial) or 91 (full factorial) | 54 |
The adaptive optimizer below must reach the target yield in at least 30% fewer runs than such a design on the same botanical.
Live demonstration
Expected improvement picks the next experiment by weighing a high predicted yield against high uncertainty
A Gaussian process learns from the runs so far. Press "Run next experiment" to add the run it proposes; each press adds one synthetic measurement.
Expected improvement (after Jones et al. 1998; ξ is an added exploration margin)EI(x) = (μ − f* − ξ) Φ(Z)
+ σ φ(Z)
Z = μ − f* − ξσ
+ σ φ(Z)
Z = μ − f* − ξσ
Experiments run3
Best yield found
Gap to true optimum
Next suggested temperature
Expected improvement there
About this demo
- The response curve is a synthetic function of extraction temperature with measurement noise (standard deviation 0.6 yield points). It is not EUTECNIQ data and not a real botanical.
- Gaussian process with a squared-exponential kernel; hyperparameters fixed for clarity
- The proposed model would use four inputs and marker yields measured by a validated method
Posterior mean ± 2σ (top) and expected improvement (bottom)Synthetic demonstration
Jones DR, Schonlau M, Welch WJ. Efficient global optimization of expensive black-box functions. J Glob Optim. 1998;13:455–492. Rasmussen CE, Williams CKI. Gaussian Processes for Machine Learning. MIT Press; 2006.
Method, assumptions and limits
- What it calculates
- The Gaussian-process posterior mean μ(x) and standard deviation σ(x) of a synthetic yield curve on a 0.2 °C grid from 30 to 80 °C, the expected improvement EI(x) over the best measured yield, and the temperature that maximizes EI.
- Equations
- Kernel k(x, x′) = s² exp(−(x − x′)²/(2ℓ²)), s² = 64 (yield points)², ℓ = 6 °C; noise variance σn² = 0.36. Prior mean = mean of the measured yields. μ(x) = m + k*ᵀ(K + σn²I)⁻¹(y − m); σ²(x) = s² − k*ᵀ(K + σn²I)⁻¹k* (Rasmussen & Williams 2006, chapter 2). EI as shown above with f* = best measured yield and ξ = 0.01; EI is set to zero within 0.25 °C of an existing run.
- Variables and units
- x in °C; yield in percent (yield points); EI in yield points.
- Assumptions
- One input; fixed hyperparameters (not refitted as data arrive); Gaussian noise of known size; the synthetic truth is 62 + 17 exp(−((x − 64)/7.5)²) + 9 exp(−((x − 39)/5)²) − 0.0035 (x − 55)², with a second, lower peak near 39 °C that can trap a greedy search.
- Valid range
- 30–80 °C. The demo is deterministic: the same button presses give the same runs (fixed random seed).
- What it does not establish
- That Bayesian optimization outperforms classical design for any real botanical, or any yield value. Real campaigns have several inputs, refitted hyperparameters and batch effects.
- References
- Jones et al. 1998; Rasmussen & Williams 2006; Shields et al. 2021.
- Verification
- An independent NumPy/SciPy implementation (tests/numerics/ref/insights-botanical-intelligence.py) reproduces the proposed temperature, its expected improvement and the best yield after 0, 1, 3, 8 and 11 added runs.
Show data: runs so far
| Run | Temperature, °C | Measured yield, % |
|---|
Synthetic measurements: the hidden curve plus seeded random noise.
Data requirements Proposal
Every run would be recorded with its material, its method and its uncertainty, or it does not enter the dataset
Five records gate each run; each model version is rebuilt from a hashed snapshot and must pass the same testsProposed data policy
Text version: record contents, ownership and versioning
| Record | Minimum content |
|---|---|
| Material | Species and plant part with identity evidence, supplier lot, harvest and drying records, moisture content, particle-size fraction |
| Process | Extraction mode, temperature, time and sampling times, solvent composition and ratio, agitation; deviations from the plan |
| Measurement | Marker quantified against a reference standard by a validated method with stated limit of quantitation, recovery and precision; raw chromatograms retained |
| Replication | At least three center-point replicates per botanical to estimate pure error, which sets the stopping threshold |
| Integrity | Attributable, time-stamped entries in a laboratory information management system and electronic notebook from day one; corrections leave an audit trail |
Ownership
Who owns the data and the model
Data from EUTECNIQ's own programs would belong to EUTECNIQ. Data from a client project would belong to the client under the contract and would be used only for that client, unless the client agrees in writing to pooling. A model trained on pooled data would record which sources it used. The policy needs review by counsel before any client work.
Reproducibility and updates
Every model version can be rebuilt
Each version would record a frozen dataset snapshot (with a content hash), the code commit, the software environment, hyperparameters and random seeds. A new version replaces the old one only after passing the same external test and calibration checks; earlier versions and their model cards are kept. Retraining happens on a schedule or when drift is detected, never silently. Datasets would be kept findable, accessible, interoperable and reusable (the FAIR principles; Wilkinson et al. 2016).
Model card
The model card is written before the model exists, so its scope cannot drift after results arrive
Seven fields defined, two planned, results empty until measuredProposed model card
Show the table (10 rows)
| Field | Entry |
|---|---|
| Model | M1, hybrid extraction-yield model: diffusion physics core plus Gaussian-process residual, with an expected-improvement optimizer. Version: none yet (not trained). Owner: EUTECNIQ Sciences (in formation). |
| Intended use | Ranking extraction conditions and choosing the next laboratory run for botanicals inside the training scope, with the four inputs above. |
| Out of scope | Safety, efficacy or potency claims; product specifications or release decisions; botanicals, solvents or extraction modes outside the training data; scale-up without pilot verification. |
| Factors | Botanical, plant part, raw-material lot, moisture, particle size, extraction mode. |
| Metrics | Root-mean-square and mean absolute error of marker yield (mg/g); interval coverage and width; runs to reach the target yield. |
| Training data | Three botanicals, about 60 designed runs each (planned; not collected). |
| Evaluation data | Held-out lots, a fourth held-out botanical and prospective runs (planned). |
| Quantitative results | None yet. |
| Human oversight | A scientist approves every proposed run; the model never releases a lot or sets a specification. |
| Caveats | Small datasets; strong lot-to-lot variation in botanicals; marker yield may not track the full chemical profile of an extract. |
Computational molecular engineering Publications verified
The toolbox reaches well beyond machine learning, and the founder has published in its core
Five peer-reviewed papers, 2011–2016, and the botanical uses proposed for the same methodsPublications verified · applications proposed
Explanation, details and sources
The founder's peer-reviewed work includes neural-network modeling of an industrial solvent extraction (Chemical Engineering & Technology, 2011), mechanistic simulation of a rotating-disk extraction column (Industrial & Engineering Chemistry Research, 2013), computer-aided design of ionic liquids (AIChE Journal, 2013), optimal ionic-liquid design for thermal energy storage (Computers & Chemical Engineering, 2016) and quantum-chemistry descriptors for property prediction (Fluid Phase Equilibria, 2016). Those studies concern petroleum lubricant extraction, solvents and process fluids; applying the methods to botanical extraction and formulation is a proposal, not a demonstrated result.
| Method | Possible EUTECNIQ use |
|---|---|
| CAMD / CAILD | Select or design solvents, excipients and separation media against target properties |
| COSMO-RS / COSMO-SAC | Rank solvents from quantum-chemical surface charges (see Quantum chemistry) |
| QSPR / QSAR | Predict properties, and toxicological endpoints only inside a validated applicability domain |
| Mechanistic mass transfer | Predict extraction and purification performance (see the Science lab) |
| PBPK and population PK | Explore exposure and interaction scenarios; models need human data to be credible |
| DoE, RSM, Bayesian optimization | Choose the most informative next formulation or process experiment |
| Chemometrics (PCA, PLS-DA) | Fingerprint comparison, adulteration screening, batch-to-batch equivalence |
| Monte Carlo, sensitivity analysis | Quantify uncertainty in scientific and financial predictions |
Not every method warrants investment at once. The first model must show a measured performance and cost advantage before new computational programs are approved. The wider computational program is described under Computational science and AI.
Roadmap Proposal
Each later model must earn its start on measured data
Six models in sequence, each behind a gate measured on dataProposed roadmap
Text version of the roadmap
- M1 · Extraction yield and next experiment2027–28 in the plan; stops at month 24 without both measured gains.
- M2 · Formulation stabilityFrom 2029 in the plan, after M1 passes and at least 200 formulations are tracked.
- M3 · Fingerprinting and adulteration detectionAfter validation on blinded samples.
- M4 · Process and batch controlOnce the Phase II pilot plant runs.
- M5 · Evidence retrieval for dossiersAlways with human review and quality sign-off.
- M6 · Licensed modules on customer dataUnder contract only; from 2032 in the plan.
Each step starts only when the previous model passes its gate on measured data. Customer data are used only under contract terms.
Working on extraction data or experiment design?
EUTECNIQ is in formation and welcomes research partners with real botanical extraction data.