EUTECNIQ Sciences

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Academy · Course 11 3 explorers Proposed approach

One ingredient decision weighs ten kinds of evidence at once, and only some of them can be learned from data

Choosing a botanical ingredient means passing legal gates and trading off strength, absorption, stability, evidence, supply and cost. This course teaches methods that make those trade-offs explicit, and what machine learning can and cannot add.

Level
Intermediate
Reading time
About 30 minutes
Builds on
Design space and optimization
Tools
3 explorers, 1 heat map
1,938FDA Form 483 citations under 21 CFR Part 111 in fiscal 2025; specifications led with 446
4legal gates a candidate must pass before any trade-off is weighed
18%of GPT-4 citations fabricated in 84 short reviews (55% for GPT-3.5)
294papers in 17 fields affected by data leakage in machine-learning studies

Status. EUTECNIQ has no laboratory, data or model. The engine described here is a proposal, and the candidates in the explorer are fictional.

At a glance

The objectives pull in different directions, so filtering on any one axis removes candidates that win on another

Brush any axis to filter 36 fictional candidates across five objectivesFictional, rule-generated

The same fictional candidate set used in this course's explorer, generated from the rules stated with the explorer below (src/modules/aceng/compute/make_candidates.py); not measurements of any ingredient. Color: passes all four gates, or fails at least one. Axes: marker strength (% w/w), bioaccessible fraction (%), marker retained at 12 months (%), cost of goods (US$/kg), supply risk (score); the evidence level is in the explorer below.

Drag along any axis to keep a range; click the axis to clear it.

You will learn

  1. To separate pass-or-fail gates from objectives and from uncertainty, and to say when each becomes measurable.
  2. To compute Derringer–Suich desirabilities and explain why a geometric mean lets one failure veto a candidate.
  3. To find a Pareto set and show why a weighted sum misses trade-offs on a nonconvex front.
  4. What Bayesian optimization, multi-fidelity models and active learning each need from the data.
  5. What AI and machine learning can and cannot do with sparse botanical data, and how a model is validated.
The problem

Four of the ten dimensions are legal gates, and the other six trade off against each other

Ten dimensions of one ingredient decision, each with what is measured and the governing sourceRegulation Schematic
Ten dimensions of one ingredient decision: four pass-or-fail gates set by law and six objectives that trade off, all carrying uncertaintyGates: pass or fail, set by regulation or lawA candidate that fails any gate leaves the setIdentityHPTLC or HPLC fingerprint,microscopy; DNA where suitable21 CFR 111.70(b)(1), 111.75(a)(1)(i)Contaminant limitsElements, pesticides, solvents,mycotoxins, microbes21 CFR 111.70(b)(3)Lawful regulatory routePre-1994 status, NDI notification ora food routeFD&C Act § 413; 21 CFR 190.6Lawful sourcingCITES permits; no goods of IranianoriginCITES Appendices I–II; 31 CFR560.201Objectives: ranked against each otherImproving one often costs anotherStrength andcompositionMarker content andconstituent ratios21 CFR 111.70(e)BioaccessibilityIn vitro digestion;human PK where itexistsINFOGEST protocol,Brodkorb 2019StabilityMarker retained overtime at stated storageMeasured per lot andconditionSynergy andinteractionsInteraction needs afactorial designAbout 4× theparticipants, Brookes2004Supply riskSupplier qualification,regions, history21 CFR111.75(a)(2)(ii)(A)Scale and cost ofgoodsYield, steps, solventand energy per kgProcess dataUncertainty on every valueEach number carries its lot, method, date and interval, and early values are estimates rather than measurementsTen dimensions of one ingredient decision: four gates and six objectives, all carrying uncertaintyGates: pass or fail, set by regulation or lawIdentityHPTLC or HPLC fingerprint, microscopy; DNA wheresuitable. 21 CFR 111.70(b)(1), 111.75(a)(1)(i)Contaminant limitsElements, pesticides, solvents, mycotoxins, microbes. 21CFR 111.70(b)(3)Lawful regulatory routePre-1994 status, NDI notification or a food route. FD&CAct § 413; 21 CFR 190.6Lawful sourcingCITES permits; no goods of Iranian origin. CITESAppendices I–II; 31 CFR 560.201Objectives: ranked against each otherStrength and compositionMarker content and constituent ratios. 21 CFR 111.70(e)BioaccessibilityIn vitro digestion; human PK where it exists. INFOGESTprotocol, Brodkorb 2019StabilityMarker retained over time at stated storage. Measuredper lot and conditionSynergy and interactionsInteraction needs a factorial design. About 4× theparticipants, Brookes 2004Supply riskSupplier qualification, regions, history. 21 CFR111.75(a)(2)(ii)(A)Scale and cost of goodsYield, steps, solvent and energy per kg. Process dataUncertainty on every valueEach number carries its lot, method, date and interval
21 CFR 111.70 and 111.75 (eCFR, current to October 21, 2026); FD&C Act § 413 and 21 CFR 190.6; CITES Appendices; 31 CFR 560.201; Brodkorb et al. 2019; Brookes et al. 2004.
Text version of the ten dimensions
  • Gates. Identity (21 CFR 111.70(b)(1) requires an identity specification; 111.75(a)(1)(i) requires at least one identity test for each dietary ingredient). Contaminant limits (111.70(b)(3)). A lawful regulatory route (pre-1994 status, an NDI notification under FD&C Act § 413 and 21 CFR 190.6, or a food route). Lawful sourcing (CITES permits for listed species; 31 CFR 560.201 prohibits importing goods of Iranian origin).
  • Objectives. Strength and composition (111.70(e)); bioaccessibility, measured for example by INFOGEST in vitro digestion; stability; synergy and interaction evidence; supply risk (supplier qualification under 111.75(a)(2)(ii)(A)); scale and cost of goods.
  • Uncertainty. Every value carries its lot, method, date and interval; early values are estimates.
Explanation, details and sources

Most are critical quality attributes: properties that "should be within an appropriate limit, range, or distribution to ensure the desired product quality" (ICH Q8(R2), written for drugs). For supplements, 21 CFR 111.70 requires identity, purity, strength, composition and contaminant specifications.

Structure

Gates remove candidates, objectives rank the rest, and uncertainty decides how far to trust the ranking

Multi-objective problem with gatesmaximize F(x) = (f1(x), …, fk(x))
subject to gj(x) = pass, j = 1 … m
Pareto dominance (Deb et al. 2002)a dominates b if fi(a) ≥ fi(b) for every i
and fi(a) > fi(b) for at least one i
The decision pipeline on the fictional candidate set, from 36 candidates to a recorded decisionFictional candidates
Decision pipeline on the fictional candidate set: 36 candidates, 21 pass the gates, 20 are Pareto-optimal, weighted desirability ranks C08 first, and the ranking survives the cautious boundCandidate pool36fictionalcandidates3 sources × 4routes × 3suppliersGates21pass all fourgatesIdentity −4,contaminant −1,regulatory −8,sourcing −2Pareto filter20arePareto-optimalIn six objectivesalmost nothing isdominatedWeighted rankingC08ranks first atD = 0.579Weighteddesirability, defaultweightsUncertainty checkC08still first atD = 0.528On one-sided 95%bounds; 18 passthe gatesDecisionRecordof the decisionWeights, gates,data versions andthe sign-offCounts from the illustrative candidate set used in the explorer below; they are not measurements.Decision pipeline on the fictional candidate setCandidate pool36 fictional candidates3 sources × 4 routes × 3 suppliersGates21 pass all four gatesIdentity −4, contaminant −1, regulatory −8, sourcing −2Pareto filter20 are Pareto-optimalIn six objectives almost nothing is dominatedWeighted rankingC08 ranks first at D = 0.579Weighted desirability, default weightsUncertainty checkC08 still first at D = 0.528On one-sided 95% bounds; 18 pass the gatesDecisionRecord of the decisionWeights, gates, data versions and the sign-offCounts from the illustrative candidate set; notmeasurements.
Counts computed with the explorer's model (src/modules/aceng/model.js) and checked by an independent Python reference.

The gates FDA cites most are specifications and identity

Form 483 citations under 21 CFR Part 111 by section, fiscal years 2022 to 2025FDA data
Heat map of FDA Form 483 citations under 21 CFR Part 111 by section and fiscal year 2022 to 2025; specifications are the largest single section and identity-test citations rose from 15 to 66 between 2023 and 2025FY2022FY2023FY2024FY2025111.70 specifications111.70 specifications · FY2022: 271271111.70 specifications · FY2023: 247247111.70 specifications · FY2024: 366366111.70 specifications · FY2025: 446446111.75 testing, all paragraphs111.75 testing, all paragraphs · FY2022: 129129111.75 testing, all paragraphs · FY2023: 104104111.75 testing, all paragraphs · FY2024: 173173111.75 testing, all paragraphs · FY2025: 265265of which identity test, (a)(1)(i)of which identity test, (a)(1)(i) · FY2022: 2222of which identity test, (a)(1)(i) · FY2023: 1515of which identity test, (a)(1)(i) · FY2024: 3939of which identity test, (a)(1)(i) · FY2025: 6666of which supplier qualification, (a)(2)(ii)(A)of which supplier qualification, (a)(2)(ii)(A) · FY2022: 2525of which supplier qualification, (a)(2)(ii)(A) · FY2023: 1818of which supplier qualification, (a)(2)(ii)(A) · FY2024: 2929of which supplier qualification, (a)(2)(ii)(A) · FY2025: 4545Other Part 111 sectionsOther Part 111 sections · FY2022: 818818Other Part 111 sections · FY2023: 822822Other Part 111 sections · FY2024: 1,0441,044Other Part 111 sections · FY2025: 1,2271,227All Part 111 citationsAll Part 111 citations · FY2022: 1,2181,218All Part 111 citations · FY2023: 1,1731,173All Part 111 citations · FY2024: 1,5831,583All Part 111 citations · FY2025: 1,9381,938FY2023 → FY2025× 1.8× 2.5× 4.4× 2.5× 1.5× 1.7Citations per fiscal year (log scale)102,000Counts are observations on Form 483, not rates: inspection numbers change from yearto year.
Counts summed over FDA citation IDs beginning "21 CFR 111" on the Foods tab; Form 483s prepared manually are not included. A citation records an investigator's observation; it does not establish harm.U.S. FDA, Inspection observations, FY2022–FY2025 data files, retrieved October 22, 2026, as tabulated on Competitive landscape.
Show data: Part 111 citations by section and fiscal year
SectionFY2022FY2023FY2024FY2025
111.70 specifications271247366446
111.75 testing, all paragraphs129104173265
of which identity test, 111.75(a)(1)(i)22153966
of which supplier qualification, 111.75(a)(2)(ii)(A)25182945
Other Part 111 sections8188221,0441,227
All Part 111 citations1,2181,1731,5831,938
Explanation, details and sources

Here x is a candidate (a botanical, a process route and a supplier), each fi is oriented so that larger is better, and a candidate no other candidate dominates is Pareto-optimal. In the fictional set below, gates remove 15 of 36 candidates, and 20 of the remaining 21 are Pareto-optimal in six objectives. The Pareto set narrows the choice; it rarely makes it. Uncertainty enters twice: a predicted value can cross a gate's limit, and two close scores may not differ at all.

Timing

Each criterion becomes measurable at a different stage, so early rankings rest on estimates

When each decision input is estimated, measured or decided across the eight proposed stagesProposed planning view
Proposed planning matrix: when each of ten decision inputs is estimated, first measured or decided across eight development stagesSourceIdentityCharacterizeSafetyDeliveryScale-upRegulatoryCommercialIdentityIdentity · Source: lowIdentity · Identity: highIdentity · Characterize: mediumIdentity · Scale-up: mediumIdentity · Regulatory: mediumIdentity · Commercial: highContaminant limitsContaminant limits · Source: lowContaminant limits · Identity: mediumContaminant limits · Characterize: mediumContaminant limits · Safety: highContaminant limits · Scale-up: mediumContaminant limits · Regulatory: mediumContaminant limits · Commercial: highLawful regulatory routeLawful regulatory route · Source: lowLawful regulatory route · Identity: lowLawful regulatory route · Characterize: lowLawful regulatory route · Safety: mediumLawful regulatory route · Delivery: mediumLawful regulatory route · Scale-up: mediumLawful regulatory route · Regulatory: highLawful regulatory route · Commercial: highLawful sourcingLawful sourcing · Source: highLawful sourcing · Identity: lowLawful sourcing · Scale-up: mediumLawful sourcing · Regulatory: mediumLawful sourcing · Commercial: highStrength and compositionStrength and composition · Source: lowStrength and composition · Identity: lowStrength and composition · Characterize: highStrength and composition · Safety: lowStrength and composition · Delivery: mediumStrength and composition · Scale-up: mediumStrength and composition · Regulatory: mediumStrength and composition · Commercial: highBioaccessibilityBioaccessibility · Source: lowBioaccessibility · Characterize: lowBioaccessibility · Safety: lowBioaccessibility · Delivery: highBioaccessibility · Scale-up: mediumBioaccessibility · Regulatory: lowBioaccessibility · Commercial: lowStabilityStability · Characterize: lowStability · Safety: lowStability · Delivery: mediumStability · Scale-up: highStability · Regulatory: mediumStability · Commercial: highSynergy and interactionsSynergy and interactions · Source: lowSynergy and interactions · Characterize: lowSynergy and interactions · Safety: mediumSynergy and interactions · Delivery: mediumSynergy and interactions · Regulatory: mediumSynergy and interactions · Commercial: mediumSupply riskSupply risk · Source: highSupply risk · Identity: lowSupply risk · Scale-up: mediumSupply risk · Regulatory: lowSupply risk · Commercial: highScale and cost of goodsScale and cost of goods · Source: lowScale and cost of goods · Delivery: lowScale and cost of goods · Scale-up: highScale and cost of goods · Regulatory: lowScale and cost of goods · Commercial: highGatesObjectivesDecided: a gate, or a measurement at decision scaleMeasured at bench or pilot scaleEstimated from literature, supplier data or a modelNot addressed at this stageStages follow the proposed EUTECNIQ pathway on the Platform page. A planning view; no schedule has been measured.
Stages from the proposed EUTECNIQ pathway. Interaction sample size: Brookes ST et al. J Clin Epidemiol. 2004;57(3):229–236, as summarized on Combination science.
Text version of the planning matrix

Decided (gate or decision-scale measurement): identity at the identity stage and per commercial lot; contaminants at safety and per lot; regulatory route at the regulatory stage; sourcing at intake and per lot; strength at characterization; bioaccessibility at delivery; stability and cost at scale-up; supply risk at intake and in commercial supply. Interaction evidence stays at bench measurement or estimate throughout, because decisive human evidence comes from dedicated studies.

Explanation, details and sources

Identity and sourcing can be decided at intake. Stability and cost are known only at scale. Interaction evidence is the most expensive: testing an interaction as large as a main effect needs about four times the participants (Brookes et al. 2004).

Method 1

Desirability functions put each criterion on a 0-to-1 scale, and a geometric mean lets one failure veto the rest

The exponent s decides how much partial credit a response earns between its limit and its targetComputed from the equations
Derringer–Suich desirability: for a larger-is-better response d rises from 0 at the lower limit to 1 at the target, and for a smaller-is-better response it falls; the exponent s bends the rampLarger is better00.51lower limittargets = 0.5s = 1s = 2s = 0.5s = 1s = 2dResponse ySmaller is better00.51targetupper limits = 0.5s = 1s = 2s = 0.5s = 1s = 2dResponse y
Derringer G, Suich R. J Qual Technol. 1980;12(4):214–219; NIST/SEMATECH e-Handbook of Statistical Methods, section 5.5.3.2.2.
Correlated responses leave no real trade-off: the Pareto set is replicate noise, and desirability ranks the replicates firstPublished data Our computation
Sixteen published extraction runs plotted by their two measured responses: the responses rise together, the non-dominated runs are three center-point replicates, and desirability ranks the four replicates firsta Measured responses of the 16 runs3545556520253035TPC, mg GAE/gDPPH scavenging, %Run 1: 60% ethanol, 25 °C, 45 min; TPC 28.4, DPPH 65.1Run 2: 30% ethanol, 25 °C, 30 min; TPC 25.7, DPPH 44.8Run 3: 60% ethanol, 75 °C, 15 min; TPC 21.8, DPPH 35.5Run 5: 30% ethanol, 50 °C, 45 min; TPC 24.3, DPPH 39.4Run 6: 90% ethanol, 25 °C, 30 min; TPC 24.5, DPPH 44.5Run 7: 30% ethanol, 50 °C, 15 min; TPC 24.3, DPPH 36.8Run 9: 60% ethanol, 75 °C, 45 min; TPC 21.1, DPPH 44.5Run 12: 60% ethanol, 25 °C, 15 min; TPC 22.2, DPPH 41.5Run 13: 90% ethanol, 75 °C, 30 min; TPC 19.2, DPPH 45.4Run 14: 90% ethanol, 50 °C, 45 min; TPC 22.6, DPPH 64.0Run 15: 30% ethanol, 75 °C, 30 min; TPC 20.4, DPPH 35.0Run 16: 90% ethanol, 50 °C, 15 min; TPC 19.3, DPPH 38.812356791213141516Run 4 (center point): TPC 35.1, DPPH 70.5Run 8 (center point): TPC 35.6, DPPH 68.0Run 10 (center point): TPC 35.2, DPPH 69.1Run 11 (center point): TPC 35.1, DPPH 69.0Center-point mean ± 2 replicate SD: TPC 35.25 ± 0.48 mg GAE/g, DPPH 69.15 ± 2.06%Run 4: TPC 35.1, DPPH 70.5; non-dominated4Run 8: TPC 35.6, DPPH 68.0; non-dominated8Run 10: TPC 35.2, DPPH 69.1; non-dominated10Run 11: TPC 35.1, DPPH 69.0; dominated by run 411Runs 4, 8 and 10 are non-dominated; all arereplicates of 60% ethanol, 50 °C, 30 minDashed box: mean ± 2 replicate SDr = 0.84 between the responsesb Overall desirability D, rankedRun 4 · 60%, 50 °C, 30 minRun 4: D = 0.9850.98Run 10 · 60%, 50 °C, 30 minRun 10: D = 0.9680.97Run 8 · 60%, 50 °C, 30 minRun 8: D = 0.9640.96Run 11 · 60%, 50 °C, 30 minRun 11: D = 0.9640.96Run 1 · 60%, 25 °C, 45 minRun 1: D = 0.6900.69Run 14 · 90%, 50 °C, 45 minRun 14: D = 0.4120.41Run 2 · 30%, 25 °C, 30 minRun 2: D = 0.3310.33Run 6 · 90%, 25 °C, 30 minRun 6: D = 0.2940.29Run 5 · 30%, 50 °C, 45 minRun 5: D = 0.1960.20Run 12 · 60%, 25 °C, 15 minRun 12: D = 0.1830.18Run 9 · 60%, 75 °C, 45 minRun 9: D = 0.1760.18Run 7 · 30%, 50 °C, 15 minRun 7: D = 0.1260.13Run 3 · 60%, 75 °C, 15 minRun 3: D = 0.0470.05Run 16 · 90%, 50 °C, 15 minRun 16: D = 0.0260.03Run 13 · 90%, 75 °C, 30 minRun 13: D = 0.0000.00Run 15 · 30%, 75 °C, 30 minRun 15: D = 0.0000.00d rises linearly from the lowest to the highest observed value of eachresponse; D = (dTPC​ · dDPPH​)1/2​. Teal marks the four center-point replicates.
The design-space page adds sonication time as a third objective, which creates a real trade-off and an NSGA-II front.Data: Gueffai A et al. Biomolecules. 2022;12(9):1311, Table 1, as reproduced on Design space and optimization. Correlation, replicate SD, dominance and D: EUTECNIQ computation.
Show data: the 16 runs, their desirabilities and dominance
RunEthanol, %Temperature, °CTime, minTPC, mg GAE/gDPPH, %d TPCd DPPHDNon-dominated
160254528.465.10.5610.8480.690No
230253025.744.80.3960.2760.331No
360751521.835.50.1590.0140.047No
460503035.170.50.9701.0000.985Yes
530504524.339.40.3110.1240.196No
690253024.544.50.3230.2680.294No
730501524.336.80.3110.0510.126No
860503035.668.01.0000.9300.964Yes
960754521.144.50.1160.2680.176No
1060503035.269.10.9760.9610.968Yes
1160503035.169.00.9700.9580.964No
1260251522.241.50.1830.1830.183No
1390753019.245.40.0000.2930.000No
1490504522.664.00.2070.8170.412No
1530753020.435.00.0730.0000.000No
1690501519.338.80.0060.1070.026No
Explanation, details and sources
Individual desirability, larger is better (Derringer & Suich 1980)d = 0 if y < L; d = (y − L)(T − L)s if L ≤ y ≤ T; d = 1 if y > T
smaller is better: d = ((U − y)/(U − T))s between T and U
Overall desirabilityD = (d1 d2 ⋯ dk)1/k
weighted form used below: Dw = ∏ diwi / Σw

y is a measured or predicted response, L and U are the unacceptable limits, T the target and s a shape exponent. If any d is 0, D is 0 (NIST/SEMATECH e-Handbook, 5.5.3.2.2). The weighted form is a modeling choice made on this page; with equal weights it is Derringer and Suich's D.

Worked example: sixteen published extraction runs

Gueffai et al. (2022) extracted black cumin seed in 16 designed runs and measured total phenolics (TPC, 19.2 to 35.6 mg GAE/g) and DPPH radical scavenging (35.0 to 70.5%). The two responses rise together (Pearson r = 0.84), so the measured runs do not trade off. The non-dominated runs are three replicates of one condition, separated by less than two replicate standard deviations (0.24 mg GAE/g and 1.0 points).

Method 2 · Explorer

A weighted sum can find only the Pareto points on the front's convex hull; an ε-constraint reaches the rest

ZDT fronts, g = 1 (Zitzler, Deb & Thiele 2000, Eq. 7–9)T1: f2 = 1 − √f1
T2: f2 = 1 − f12
T3: f2 = 1 − √f1 − f1 sin(10πf1)
Weighted sum: f10.250
Weighted sum: f20.500
ε-constraint: f10.360
ε-constraint: f20.400
Interior front points any weight can reach100%
Assumptions
  • Both objectives are minimized; each front is sampled at 1,001 values of f1, keeping only non-dominated points
  • A point is reachable when it lies on the lower convex hull of the front
Weighted-sum and ε-constraint optima on the selected frontPublished test functions
Teal: points some weight can reach. Copper: points no weight can reach. The dashed line is the weighted-sum iso-line through its optimum.
Method, assumptions and limits: weighted sum versus ε-constraint
What it calculates
The minimizer of w f1 + (1 − w) f2 over the front, the minimizer of f2 with f1 ≤ ε, and the share of interior front points that minimize the weighted sum for some w.
Equations
ZDT T1, T2 and T3 with g = 1 (Pareto-optimal), from Zitzler, Deb and Thiele (2000), Eq. 7–9. For T1 the weighted-sum optimum is f1* = ((1 − w)/(2w))2, capped at 1. For T2, w f1 + (1 − w)(1 − f12) is concave in f1, so its minimum is always an end point.
Variables and units
f1, f2: dimensionless objectives, both minimized. w: 0.01–0.99. ε: 0–1.
Assumptions
A discrete front of 1,001 samples; ties go to the smaller f1. If no point satisfies f1 ≤ ε, the point with the smallest f1 is shown.
Does not establish
Anything about a real ingredient. The fronts are mathematical test problems.
Verification
Readouts match an independent NumPy/SciPy reference (convex hull by Qhull) in six cases, including the analytic T1 optimum at w = 0.5 (f1 = 0.25, f2 = 0.5); unit tests in tests/unit/aceng.test.js.
References
Zitzler E, Deb K, Thiele L. Evol Comput. 2000;8(2):173–195. Das I, Dennis JE. Struct Optim. 1997;14(1):63–69. Haimes YY, Lasdon LS, Wismer DA. IEEE Trans Syst Man Cybern. 1971;SMC-1(3):296–297.
Explanation, details and sources

Minimizing w f1 + (1 − w) f2 slides a straight line against the front. Where the front bulges toward the worse corner, no line touches it (Das and Dennis 1997). The ε-constraint method (Haimes et al. 1971) minimizes f2 subject to f1 ≤ ε and reaches every point. The fronts are the published ZDT test problems. With more objectives, evolutionary algorithms such as NSGA-II (Deb et al. 2002) map a whole front in one run, as on the design-space page.

Explorer

Change weights and gates on 36 fictional candidates to see what the method decides and what it leaves to people

Weights (0 removes an objective)
Gates enforced
Pass the enforced gates21
Pareto-optimal, all six objectives20
Pareto-optimal, plotted pair4
Ranked firstC08
Its overall desirability0.579

Bioaccessible fraction against stability, gate-passing candidatesFictional candidates

Top ten by overall desirability

Top ten gate-passing candidates by overall desirability for the current settings
Rank and IDSource and routeSupplierDWeakest objective (d)Pareto, six objectives
1. C08Root spray-dried extract20.579Marker strength (0.31)Yes
2. C20Leaf spray-dried extract20.526Marker strength (0.19)Yes
3. C17Leaf purified fraction20.520Bioaccessible fraction (0.30)Yes
4. C07Root spray-dried extract10.512Marker strength (0.25)Yes
5. C11Root lipid matrix20.481Marker strength (0.23)Yes
6. C09Root spray-dried extract30.467Marker strength (0.25)Yes
7. C10Root lipid matrix10.438Marker strength (0.18)Yes
8. C06Root purified fraction30.435Bioaccessible fraction (0.16)Yes
9. C19Leaf spray-dried extract10.429Marker strength (0.17)Yes
10. C16Leaf purified fraction10.428Bioaccessible fraction (0.21)No

Excluded by gates: C12 (contaminant); C15 (identity); C18 (identity); C21 (identity); C22 (regulatory route); C23 (regulatory route); C24 (identity, regulatory route); C27 (sourcing); C28 (regulatory route); C29 (regulatory route); C30 (regulatory route, sourcing); C33 (sourcing); C34 (regulatory route); C35 (regulatory route); C36 (regulatory route, sourcing).

Show data: the 36 fictional candidates
IDSourceRouteSupplierStrength, % w/wBioaccessible, %Retained at 12 months, %Cost, US$/kgSupply riskEvidence, 0–3Contaminant ÷ limitValuesGates
C01RootHydroethanolic extract12.72291620.3620.67measuredpasses all four
C02RootHydroethanolic extract22.72691780.1520.59measuredpasses all four
C03RootHydroethanolic extract32.72591560.5820.90predictedpasses all four
C04RootPurified fraction116.412964050.4130.19measuredpasses all four
C05RootPurified fraction220.08964560.1130.26measuredpasses all four
C06RootPurified fraction316.114943700.5230.27predictedpasses all four
C07RootSpray-dried extract15.728951000.3820.38measuredpasses all four
C08RootSpray-dried extract26.92894970.1020.58measuredpasses all four
C09RootSpray-dried extract35.72690700.5020.93predictedpasses all four
C10RootLipid matrix14.454781600.4110.92measuredpasses all four
C11RootLipid matrix25.549781820.1310.86measuredpasses all four
C12RootLipid matrix35.549791350.6011.50predictedContaminants within limit
C13LeafHydroethanolic extract12.22688500.3610.24measuredpasses all four
C14LeafHydroethanolic extract22.53086670.1710.28measuredpasses all four
C15LeafHydroethanolic extract32.02984440.5810.48predictedIdentity confirmed
C16LeafPurified fraction111.617903780.3620.09measuredpasses all four
C17LeafPurified fraction211.722933540.1520.08measuredpasses all four
C18LeafPurified fraction312.413902730.5620.15predictedIdentity confirmed
C19LeafSpray-dried extract14.33088740.4410.18measuredpasses all four
C20LeafSpray-dried extract24.63991920.1110.26measuredpasses all four
C21LeafSpray-dried extract34.03486650.5710.41predictedIdentity confirmed
C22LeafLipid matrix13.561741310.3900.35measuredLawful regulatory route
C23LeafLipid matrix23.959741710.1400.39measuredLawful regulatory route
C24LeafLipid matrix34.157761200.5500.49predictedIdentity confirmed; Lawful regulatory route
C25SeedHydroethanolic extract13.31691740.5200.40measuredpasses all four
C26SeedHydroethanolic extract23.92292920.3100.32measuredpasses all four
C27SeedHydroethanolic extract33.61493700.7200.58predictedPermits and origin on file
C28SeedPurified fraction122.19945110.5810.15measuredLawful regulatory route
C29SeedPurified fraction222.512956340.2910.11measuredLawful regulatory route
C30SeedPurified fraction322.27993670.7110.21predictedLawful regulatory route; Permits and origin on file
C31SeedSpray-dried extract17.520941240.5200.24measuredpasses all four
C32SeedSpray-dried extract27.429911470.3000.26measuredpasses all four
C33SeedSpray-dried extract36.82694860.6800.60predictedPermits and origin on file
C34SeedLipid matrix16.147822410.5100.41measuredLawful regulatory route
C35SeedLipid matrix26.344782310.2900.55measuredLawful regulatory route
C36SeedLipid matrix35.444811890.7400.73predictedLawful regulatory route; Permits and origin on file
Method, assumptions and limits: candidate ranking
What it calculates
Which candidates pass the enforced gates, which are Pareto-optimal among those that pass (in all six objectives and in the plotted pair), and a ranking by weighted overall desirability.
Equations
d = ((y − lo)/(hi − lo)), clipped to 0–1, for larger-is-better objectives and ((hi − y)/(hi − lo)) for smaller-is-better ones, with s = 1. Limits (lo, hi): strength 1–20% w/w; bioaccessible fraction 5–60%; retained at 12 months 70–98%; cost 50–500 US$/kg; supply risk 0.10–0.80; evidence 0–3. D = ∏ diwi/Σw (0 if any weighted d is 0) or Σ wi di/Σw. Cautious values: mean − 1.645 SD (larger is better) or + 1.645 SD (smaller is better); contaminant ratio × (1 + 1.645 CV).
How the candidates were made
3 sources × 4 routes × 3 suppliers. Strength = route base {E 3, P 18, D 6, M 5} × source {R 1, L 0.75, S 1.25} × (1 + 0.3u). Bioaccessible fraction = {E 22, P 12, D 28, M 52} + {R 0, L +6, S −4} + 10u. Retained = {E 90, P 96, D 93, M 80} + {R 0, L −4, S +1} + 6u. Cost = {E 70, P 420, D 95, M 180} × supplier {1, 1.15, 0.8} × source {R 1, L 0.8, S 1.2} × (1 + 0.25u). Risk = supplier {0.40, 0.15, 0.55} + 0.15 for seed + 0.1u. Evidence = source {R 2, L 1, S 0} + route {E 0, P +1, D 0, M −1}, 0–3. Contaminant ratio = source {R 0.55, L 0.25, S 0.35} × route {E 1, P 0.4, D 0.9, M 1.4} × supplier {1, 1, 1.6} × (1 + 0.5u). u is uniform on −0.5 to 0.5 (NumPy default_rng, seed 11). Supplier 3 values are predicted (SD 20% of strength, bioaccessibility, cost and contaminant ratio; 4 points of retention; 0.10 of risk); others are measured (6%; 1 point; 0.05). Gates fail for leaf with supplier 3 (identity), a contaminant ratio above 1, lipid matrix of leaf or seed and purified fraction of seed (no filed notification), and seed with supplier 3 (permits).
Assumptions
Gates are independent pass-or-fail checks; objectives are independent of each other given the rules; ties in D go to the lower ID.
Does not establish
Any property of a real botanical, route or supplier, or a recommended weighting. Weights are a value judgment that the people accountable for the decision must make and record.
Verification
Readouts match an independent NumPy/SciPy reference in six cases (tests/numerics/ref/academy_multi-objective-ingredient-design.py); unit tests in tests/unit/aceng.test.js. Generator: src/modules/aceng/compute/make_candidates.py.
References
Derringer and Suich 1980; NIST/SEMATECH e-Handbook 5.5.3.2.2; Deb et al. 2002.
Explanation, details and sources

Each candidate combines a source (root, leaf or seed), a route (extract, purified fraction, spray-dried extract or lipid matrix) and a supplier. All values come from stated rules, not from any botanical.

  1. Switch to the arithmetic mean. Seed candidates with no evidence (d = 0) climb from D = 0 to the middle of the ranking.
  2. Turn on cautious bounds. Three more candidates fail the contaminant gate, because their upper bounds cross the limit.
  3. Plot strength against cost. The trade-off between purified fractions and extracts becomes visible.
Method 3

Bayesian optimization, multi-fidelity models and active learning decide which experiment to run next

Expected improvement, minimization (Jones, Schonlau & Welch 1998)EI(x) = (fmin − ŷ) Φ(z) + s φ(z), z = (fmin − ŷ)/s
Two fidelity levels (Kennedy & O'Hagan 2000)zt(x) = ρt−1 zt−1(x) + δt(x)
Cheap data are plentiful and expensive data decide; a published result differed about thirteen-fold between rats and peoplePublished example Schematic
Multi-fidelity ladder: cheaper predictions and in vitro data are plentiful, animal and human data are scarce and decisive; a published piperine–curcumin result differed about thirteen-fold between rats and peopleEvidence levelPublished example of a fidelity gapHumanPharmacokinetics and controlled trials under IRBoversightOne or two studies, the decisive evidenceIn vivo, animalPharmacokinetics and toxicology under protocolA few studiesIn vitroDissolution, INFOGEST digestion, cell modelsTens to hundreds of samplesIn silicoStructure-based predictions, read-across, processmodelsThousands of candidates; minutes eachCost per point and weight in the decision rise+2000% curcumin bioavailability in humans+154% in ratsPiperine 20 mg given with curcumin 2 g (Shoba et al. 1998). Theanimal result pointed the right way and was about 13 times smaller.A multi-fidelity model learns a scale ρ and a correction δ(x)between levels from paired data, so it needs some points at bothlevels.
Shoba G et al. Planta Med. 1998;64(4):353–356, as summarized on Combination science; Kennedy MC, O'Hagan A. Biometrika. 2000;87(1):1–13; Brodkorb A et al. Nat Protoc. 2019;14(4):991–1014.
Text version of the fidelity ladder

In silico predictions cover thousands of candidates; in vitro dissolution, digestion and cell data cover tens to hundreds of samples; animal studies are few; human studies are one or two and decide. In Shoba et al. (1998), piperine 20 mg with curcumin 2 g raised curcumin bioavailability by 154% in rats and by 2000% in humans. A multi-fidelity model needs paired points at both levels to learn the scale and correction between them.

One loop proposes, screens, measures and records, until a stop rule ends the campaignMethod schematic
Bayesian optimization and active learning loop: data train a surrogate with uncertainty, an acquisition rule proposes the next experiment, gates screen it, the laboratory measures it, and stop rules end the campaignLot recordsEach result with itsmethod, lot and intervalSurrogate modelPrediction anduncertainty for everyuntested optionAcquisition ruleExpected improvement,or the most uncertainpointGate checkRules remove unsafe orunlawful proposalsExperimentBench or partner study;the result is recordedRepeat until a stop rule firesStop rules•Expected improvement falls below replicate noise•Run budget spent•Prediction intervals miss their stated coveragePublished evidence•Shields et al. 2021: Bayesian optimization beat expert chemists on averagenumber of experiments and on consistency in a reaction-optimizationbenchmark•Settles 2009: an active learner asks for the labels that most improve themodel
Shields BJ et al. Nature. 2021;590(7844):89–96; Settles B. Active Learning Literature Survey. University of Wisconsin–Madison, Computer Sciences Technical Report 1648; 2009.
Text version of the loop

Lot records train a surrogate model; an acquisition rule (expected improvement, or the most uncertain point for active learning) proposes an experiment; deterministic gates remove unsafe or unlawful proposals; the laboratory or a partner runs the experiment and the result is recorded. The loop stops when expected improvement falls below replicate noise, the run budget is spent, or prediction intervals miss their stated coverage. Shields et al. (2021) found that Bayesian optimization beat expert chemists on average number of experiments and on consistency in a reaction-optimization benchmark.

Explanation, details and sources

A surrogate model predicts each untested option with an uncertainty. Expected improvement (Jones et al. 1998) then weighs a good prediction against a wide interval. A worked example on the Botanical Intelligence page shows it step by step.

ŷ and s are the predicted mean and standard deviation, fmin the lowest value measured so far, and Φ and φ the normal distribution and density functions. In the multi-fidelity model, zt is the more expensive level, ρ a scale and δ a learned correction.

The data

The data form a cube of lots, attributes, methods and time, and most of it is empty at the start

Lots × attributes × time, with the method and provenance carried by every cellSchematic
Data cube of lots by attributes by time: a certificate of analysis is one lot at release, a lot trend is one attribute across lots, a stability study is one attribute of one lot over time; most cells start empty, and every cell is a record with its method and provenanceCertificate of analysis: lot 1, attribute 1, at releaseCertificate of analysis: lot 1, attribute 2, at releaseCertificate of analysis: lot 1, attribute 3, at releaseCertificate of analysis: lot 1, attribute 4, at releaseCertificate of analysis: lot 1, attribute 5, at releaseLot 1, attribute 6, at releaseCertificate of analysis: lot 1, attribute 7, at releaseCertificate of analysis: lot 1, attribute 8, at releaseLot trend: lot 2, attribute 6, at releaseLot trend: lot 3, attribute 6, at releaseAn occasional measurementLot trend: lot 4, attribute 6, at releaseLot trend: lot 5, attribute 6, at releaseLot trend: lot 6, attribute 6, at releaseLot 1, attribute 1, at releaseLot 1, attribute 2, at releaseStability study: lot 1, attribute 3, time point 1Stability study: lot 1, attribute 3, time point 2Stability study: lot 1, attribute 3, time point 3Stability study: lot 1, attribute 3, time point 4Lot 1, attribute 4, at releaseLot 1, attribute 5, at releaseLot 1, attribute 6, at releaseLot 1, attribute 7, at releaseAn occasional measurementLot 1, attribute 8, at releaseLotssupplier, harvest, batchAttributesidentity, strength, contaminants …Time: release → 12 monthsLot-to-lot trendOne attribute across lots and suppliersCertificate of analysisOne lot, every attribute, at releaseEmpty cellsMost of the cube is unmeasured at the startStability studyOne lot, one attribute, over timeEach filled cell is a recordValue and unitUncertainty or intervalMethod and its validationInstrument and analystLot, supplier and dateReference materialLicense and provenanceThe method is a fourth dimension:one attribute measured two waysgives two records.
Record fields follow the proposed data policy on Computational science and AI.
Text version of the data cube

The three axes are lots (supplier, harvest, batch), attributes (identity, strength, contaminants and others) and time from release to 12 months. A certificate of analysis is one lot at release; a lot trend is one attribute across lots; a stability study is one attribute of one lot over time. Each filled cell is a record with its value and unit, uncertainty, method and validation, instrument and analyst, lot, supplier and date, reference material, and license and provenance. Measuring one attribute by two methods gives two records.

Explanation, details and sources

A certificate of analysis is one slice, a stability study another. A model is only as good as the provenance of each cell, and its tests must hold out whole lots and whole botanicals, because neighboring cells of one lot are not independent.

AI and its limits

Machine learning can rank and propose within its data; it cannot create evidence, replace an identity test or establish safety

What AI and machine learning can and cannot do for an ingredient programPublished evidence Regulation
What AI and machine learning can and cannot do for an ingredient programCan, given enough relevant data•Rank candidates for testing inside its applicability domain (OECDvalidation principle 3)•Propose the next experiment (Bayesian optimization; Shields et al.2021)•Flag a lot whose profile does not match earlier lots of the same material•Retrieve and summarize literature, with every citation checked by apersonCannot, whatever the data volume•Replace the identity test that 21 CFR 111.75(a)(1)(i) requires for eachdietary ingredient•Establish safety or efficacy; only studies of the ingredient can•Predict reliably for a botanical or process outside its training data•Survive leakage between training and test data (found in 17 fields, 294papers; Kapoor & Narayanan 2023)
OECD Principles for the Validation of (Q)SAR Models (2004); Shields et al. 2021; 21 CFR 111.75(a)(1)(i); Kapoor S, Narayanan A. Patterns. 2023;4(9):100804.
Text version of the can and cannot lists
  • Can, given enough relevant data: rank candidates for testing inside its applicability domain; propose the next experiment; flag a lot that does not match earlier lots; retrieve and summarize literature with every citation checked by a person.
  • Cannot: replace the identity test 21 CFR 111.75(a)(1)(i) requires; establish safety or efficacy; predict reliably outside its training data; survive leakage between training and test data, which Kapoor and Narayanan found in 17 fields and 294 papers.
Language models invent citations, so every reference a model proposes must be checkedPeer-reviewed study
Share of fabricated citations and of real citations with substantive errors in 84 short literature reviews written by ChatGPT-3.5 and ChatGPT-4 (Walters and Wilder 2023)Share of citations, %0204060Fabricated citationsFabricated citations, GPT-3.5: 55%55% GPT-3.5Fabricated citations, GPT-4: 18%18% GPT-4Real citations with substantive errorsReal citations with substantive errors, GPT-3.5: 43%43% GPT-3.5Real citations with substantive errors, GPT-4: 24%24% GPT-4636 citations in 84 reviews on 42 topics. Errors are counted among citations to works that exist.
Walters WH, Wilder EI. Fabrication and errors in the bibliographic citations generated by ChatGPT. Sci Rep. 2023;13:14045.
Show data: citation errors by model
MeasureChatGPT-3.5ChatGPT-4
Fabricated citations55%18%
Real citations with substantive errors43%24%

636 citations in 84 short literature reviews on 42 topics.

Explanation, details and sources

Structure collections are large (COCONUT's statistics page listed 738,795 unique molecules on October 24, 2026), but measurements paired across methods on the same authenticated lot are rare. A model must be tested on botanicals and lots it has never seen (time-split validation, Sheridan 2013) and must abstain outside its applicability domain.

Proposed engine

The proposed engine would keep rules, models and human sign-off in separate layers

Proposed architecture: sources, one lot-centered record, rules and models, optimizer, human decisionProposed architecture
Proposed engine architecture: sources feed one lot-centered record; a rules layer applies the gates, a model layer predicts with uncertainty, an optimizer ranks and proposes, and people decide; new experiments return to the recordSourcesRecordRules and modelsOptimizer and decisionLot records and certificatesof analysisSupplier documents andauditsStability and in vitrodigestion dataLiterature and regulatoryrecordsPartner study reports (GLP,clinical)One record per lot•Lot and supplier ID•Method, instrument,analyst•Result with uncertainty•License and provenance•Part 11 controls where Part111 requires the recordRules layerDeterministic gates: identity,limits, regulatory route,CITES and sanctions; neverlearnedModel layerProperty predictors andmulti-fidelity surrogates withintervals and an applicabilitydomainOptimizerDesirability ranking, Pareto set and thenext-experiment proposal (expectedimprovement)Human decisionQualified scientist and quality unit sign off; therecord keeps weights, gates and data versionsExperiment in the laboratory or at a partnerIts result returns to the record, with the decision that asked for itProposed design. EUTECNIQ has no data, model or laboratory yet; no component exists.Proposed engine architectureSourcesLot records, supplier documents, stability anddigestion data, literature, partner study reportsRecordOne record per lotLot, method, instrument, analyst, result with uncertainty,license and provenanceRules layerDeterministic gatesIdentity, limits, regulatory route, CITES and sanctions;never learnedModel layerPredictors and surrogatesWith intervals and an applicability domainOptimizerRanking, Pareto set, next experimentHuman decisionScientist and quality unit sign offExperiment; result returns to the recordProposed design. EUTECNIQ has no data, model orlaboratory yet.
Records under 21 CFR Part 11 controls where Part 111 requires the record (21 CFR 111.605(c)). EUTECNIQ has no data, model or laboratory yet.
Text version of the architecture

Sources (lot records and certificates, supplier documents, stability and digestion data, literature and regulatory records, partner study reports) would feed one record per lot holding the lot and supplier, method, instrument, analyst, result with uncertainty, and license and provenance. A rules layer would apply the gates; a model layer would predict with intervals and an applicability domain; an optimizer would rank, find the Pareto set and propose the next experiment. A qualified scientist and the quality unit would sign off, and each experiment's result would return to the record.

Explanation, details and sources

Gates would be written rules, never learned. Models would predict with intervals and feed an optimizer, and qualified people would decide. Each decision would be recorded with the weights, gates and data versions it used.

Limits

Six misreadings turn a sound method into a wrong decision

  • Pareto-optimal≠Good enough: every candidate may still miss a target
  • A weight≠A fact: it is a value judgment that must be recorded
  • Two correlated assays≠Two independent objectives
  • Bioaccessibility in vitro≠Systemic bioavailability in people
  • A model's prediction≠A measurement on the lot
  • Rank 1 on mean values≠Rank 1 once uncertainty is counted
Explanation, details and sources

For a product decision, write the gates, limits and weights before the data arrive, rank on cautious bounds when values are predicted, and send the top few candidates, not one, to the next experiment.

Key terms

Twelve terms used in this course

Show the 12 key terms
Critical quality attribute
A property kept within a limit to ensure quality (ICH Q8(R2)).
Gate
A pass-or-fail requirement that removes candidates.
Objective
A property to raise or lower, traded against others.
Desirability
A response rescaled to 0–1 between limit and target.
Pareto-optimal
No option is as good in every objective and better in one.
Supported point
A Pareto point on the convex hull; weighted sums find only these.
ε-constraint
Optimize one objective while bounding the others.
Surrogate model
A fast model predicting a costly measurement, with uncertainty.
Expected improvement
The average gain an untested option should give over the top result so far.
Multi-fidelity model
Links cheap, rough data with scarce, accurate data.
Applicability domain
The inputs for which a model has been shown to hold.
Bioaccessibility
The fraction released for absorption, often measured in vitro.
Check your understanding

Five questions

Why is identity a gate rather than an objective?

Because 21 CFR 111.75(a)(1)(i) requires an identity test for every dietary ingredient. A wrong identity cannot be offset by high strength or low cost, so it removes the candidate.

A candidate scores well everywhere except evidence, where d = 0. What does each aggregation do?

The geometric mean gives D = 0 and drops it to the bottom; the arithmetic mean keeps it high. Use the geometric mean only where a zero should truly veto.

In the published extraction runs, why are the three non-dominated runs not a real trade-off?

They are replicates of the same condition, and their differences are within two replicate standard deviations. The two responses are positively correlated (r = 0.84), so there is no conflict to trade.

Why can no weight make a weighted sum pick an interior point of the T2 front?

On T2, w f1 + (1 − w)(1 − f12) is concave in f1, so its minimum is always at an end of the front. The ε-constraint method reaches the interior.

A model trained on lots of one botanical is asked about a new botanical. What should it do?

Report that the input lies outside its applicability domain and abstain, or give a wide interval. Its validation should already have tested botanicals held out of training.

How this differs from suppliers and laboratories

Where the multi-objective approach would sit in the industry's value chain, and where EUTECNIQ would partner.

How EUTECNIQ differsDiscuss a program