Skip to main content

Hybrid modelling in Novasign Studio

Novasign Studio builds every process model on hybrid modelling. What is known about the process, such as its mass balances, is given to the model, and machine learning learns only what is hard to write down from first principles. How much of each a model contains is yours to set, for a bioreactor as much as for a TFF step or a chromatography column. So every process you model needs less data, stays interpretable and can often predict beyond the conditions it was trained on.

Book a demo
Hybrid Model for a Bioreactor
next time stepInside the Mass Balancect+1 Vt+1 = ct Vt + Σ cin Vin − ct Σ VoutProcess ParametersTemperature, pHFeedGlucoseSamplesVolume removedMass BalanceGiven · mechanisticMachine LearningLearned · from dataRates of changeKineticsGiven · mechanisticNew statesPredictedVCDTiterGlucose
  • Inside the Mass Balance. c t+1 V t+1 = c t V t + Σ c in V in − c t Σ V out
  • Process Parameters. Temperature, pH
  • Feed. Glucose
  • Samples. Volume removed
  • Mass Balance. Given · mechanistic
  • Machine Learning. Learned · from data. Rates of change
  • Kinetics. Given · mechanistic. New states
  • Predicted. VCD. Titer. Glucose

What is hybrid modelling?

Hybrid modelling (physics-informed AI) combines a mechanistic description of a unit operation, its mass balances and stoichiometry, with machine learning that learns only how the states change. In a bioreactor that is the reaction kinetics, in TFF the flux through the membrane and in chromatography the binding in the column. The mechanistic structure is given and not learned, so the model needs less data, stays interpretable and often extrapolates further than a purely data-driven model.

Hybrid modelling is used in every process unit Novasign Studio models.

  • Reactor

    The reactor model predicts the productivity and product quality of an upstream process.

    The reactor in Studio

  • TFF

    The TFF model predicts the permeate flux and the protein and salt concentrations of an ultrafiltration and diafiltration step.

    TFF in Studio

  • Chromatography

    The chromatography model predicts how product and impurities leave the column, the basis for the yield and purity of the step.

    Chromatography in Studio

White box, black box, and the middle

The model structure in Novasign Studio allows a multitude of models, from fully mechanistic to purely data-driven. There is no free lunch: no single class of model is the best choice for every process and every dataset.

Three model structures

Mechanistic

White box

Inputs

  • x₁
  • x₂
  • x₃

Equations, fixed form

dydt=f(y, x; θ)\frac{dy}{dt} = f(y,\ x;\ \theta)

Outputs

  • y₁
  • y₂

Inputs and outputs fixed by the equations

Data needed
Low
Accuracy
Limited, often oversimplified
Extrapolation
If correct
Interpretability
Full
Effort to extend
High
Extra measurements
Often

Hybrid

Novasign’s approach

Inputs

  • x₁
  • x₂
  • x₃
  • and more, up to xₙ

Neural network

r=NN(x, y)r = \mathrm{NN}(x,\ y)

Known balance

dydt=fknown(y)+r\frac{dy}{dt} = f_{\mathrm{known}}(y) + r

Outputs

  • y₁
  • y₂
  • and more, up to yₘ

Add inputs and outputs from the data

Data needed
Limited
Accuracy
High
Extrapolation
Good
Interpretability
Partial
Effort to extend
Low
Extra measurements
Few

Data-driven

Black box

Inputs

  • x₁
  • x₂
  • x₃
  • and more, up to xₙ

Neural network

y=NN(x)y = \mathrm{NN}(x)

Outputs

  • y₁
  • y₂
  • and more, up to yₘ

Add inputs and outputs from the data

Data needed
High
Accuracy
High within its data
Extrapolation
Poor
Interpretability
Low
Effort to extend
Low
Extra measurements
Few

Novasign’s main approach to modelling is the hybrid model. It sits at the sweet spot of limited data requirements, high accuracy and flexibility, because what is known about the process is given as equations and machine learning learns only what is hard to write down, which is usually the part of the mechanism nobody knows well enough.

A hybrid model is a composition that allows for flexibility

Hybrid tells you two kinds of model are in the room. It does not tell you how they are joined, and how they are joined is most of the engineering. Studio composes a different model for each unit operation.

Reactor Model
previous time stepstates after the balancetiterglucose and volumeProcess ParametersTemperature, pHGlucose FeedLinear at 1 mL/h400 g/L glucoseSamplingEvery 24 h, 20 mLMass BalanceGiven · mechanisticFor the volume and everycomponentVt+1 = Vt + Σ Vin − Σ Voutct+1 Vt+1 = ct Vt + Σ cin Vin − ct Σ VoutMachine LearningLearned · from dataReads temperature, pH, VCD,titer, glucose and highmolecular weight species (HMW)Returns one rate per stateμVCDqPTiterrHMWHMWKineticsGiven · mechanisticEach state changes by its ratetimes the state that drives itVCDt+1 = VCDt (1 + μ Δt)Titert+1 = Titert + qP VCDt ΔtHMWt+1 = HMWt + rHMW Titert ΔtVolumetric ProductivityGiven · mechanisticmP = Titert VtPV = mP / (Vt t)PredictedVCDTiterGlucoseHMW speciesVolumeVolumetricproductivity
  • Process Parameters. Temperature, pH
  • Glucose Feed. Linear at 1 mL/h. 400 g/L glucose
  • Sampling. Every 24 h, 20 mL
  • Mass Balance. Given · mechanistic. For the volume and every component. V t+1 = V t + Σ V in − Σ V out. c t+1 V t+1 = c t V t. + Σ c in V in − c t Σ V out
  • Machine Learning. Learned · from data. Reads temperature, pH, VCD, titer, glucose and high molecular weight species (HMW). Returns one rate per state. μ VCD. q P Titer. r HMW HMW
  • Kinetics. Given · mechanistic. Each state changes by its rate times the state that drives it. VCD t+1 = VCD t (1 + μ Δt). Titer t+1 = Titer t + q P VCD t Δt. HMW t+1 = HMW t + r HMW Titer t Δt
  • Volumetric Productivity. Given · mechanistic. m P = Titer t V t. P V = m P / (V t t)
  • Predicted. VCD. Titer. Glucose. HMW species. Volume. Volumetric productivity
TFF Model
buffer volume and compositionprevious time stepProcess ParametersTMPFeed flowDiafiltration BufferReplaces the permeatewhile diafiltration runsMachine LearningLearned · from dataReads protein and saltconcentrations, TMP and feedflowReturns the fluxJPermeate fluxKineticsGiven · mechanisticIntegrates the flux over themembrane area AVperm = J A ΔtMass BalanceGiven · mechanisticR is the rejection of eachcomponentVt+1 = Vt + Vbuf − Vpermct+1 Vt+1 = ct Vt + cbuf Vbuf − (1 − R) ct VpermPredictedRetentate volumeProteinconcentrationSalt concentrationPermeate volume
  • Process Parameters. TMP. Feed flow
  • Diafiltration Buffer. Replaces the permeate while diafiltration runs
  • Machine Learning. Learned · from data. Reads protein and salt concentrations, TMP and feed flow. Returns the flux. J Permeate flux
  • Kinetics. Given · mechanistic. Integrates the flux over the membrane area A. V perm = J A Δt
  • Mass Balance. Given · mechanistic. R is the rejection of each component. V t+1 = V t + V buf − V perm. c t+1 V t+1 = c t V t + c buf V buf. − (1 − R) c t V perm
  • Predicted. Retentate volume. Protein concentration. Salt concentration. Permeate volume

A block also does not have to be machine learning. Blocks are logical units, each representing a set of mechanistic equations, a neural network or another machine learning model, a trainable equation, a control unit, or a full end-to-end process. The hybrid model can also take the outputs of other models as inputs, such as the kLa and shear that a computational fluid dynamics model gives for your vessel.

Combine models across the chain

If a block can be a whole model, a model of one unit operation can feed the next. In ECONTI four models were connected into one model of a continuous process.

ECONTI Process Chain

  1. Seed Reactor

    • Machine LearningGrowth rateMachine learning
    • KineticsMechanistic
    • Mass BalanceCells, glucoseMechanistic

  2. Production Reactor

    • Machine LearningGrowth and production ratesMachine learning
    • KineticsMechanistic
    • Mass BalanceCells, glucose, productMechanistic

    Trained on Intensified DoE runs

  3. Membrane Filtration

    • Machine LearningPermeate flowMachine learning
    • Mass BalanceProduct in the permeateMechanistic

    Trained on Recorded process data

  4. Chromatography

    • Binding IsothermCapacity set by conductivityMechanistic
    • Breakthrough CurveMechanistic

    Trained on Tuned mechanistic

From training to a digital twin

Every model in Novasign Studio takes the same four steps, from the first training run to the digital twin that simulates the runs you have not performed.

  1. 1

    Train

    The bioprocess structure, the mass balance and the kinetics, is given, and the machine learning part is fitted through the whole model against the measured runs. Where a kinetic law such as Monod is chosen, its parameters are fitted with it.

  2. 2

    Store checkpoints

    Training stores checkpoints as the model learns, the first and the last epoch and optionally every few epochs or the best by a validation metric. Each holds the fitted model with its configuration and data transformations, so it reloads exactly. The model you use is therefore chosen from checkpoints, not from wherever training happened to stop.

  3. 3

    Select the model

    The model selector narrows a tuning run down to the checkpoints that go on, by hand from the trials table or automatically by rules, such as the top trials and the best checkpoint of each by the validation metric.

  4. 4

    Simulate conditions

    The selected checkpoint runs as a digital twin. Conditions nobody has run are simulated over the ranges you set, so the promising ones can be compared before they are run in the lab.

Viral Vector Process Simulator

Simulation inputs

7.2
33 °C
0.003

pH 7.2; Temperature (°C) 33 °C; Multiplicity of infection 0.003; Cells on micro-carrier highest predicted 1.12 ×10⁶ cells/mL at 80 h; Virus titer highest predicted 6.923 log₁₀ TCID50/mL at 160 h

Highest predicted value

  • Cells on micro-carrier

    1.12 ×10⁶ cells/mL

    highest predicted · at 80 h

  • Virus titer

    6.923 log₁₀ TCID50/mL

    highest predicted · at 160 h

Hybrid modelling, written up

The method on this page, argued at length and applied to real campaigns.

All posts

See a hybrid model built on your own data

The demo is a working session. Bring a dataset from a recent campaign, and the conversation is about your components, your streams and your assay coverage.

Book a demoThe peer-reviewed papers
Related