Optimization and digital twin of chromatography purification process using physics-informed neural networks

1 . A system for optimization of a chromatography purification process using a physics-informed neural network, the system comprising:

a non-transitory memory storing instructions; and

a processor circuitry in communication with the non-transitory memory, wherein, the processor circuitry executes the instructions to cause the system to:

train the physics-informed neural network comprised in a digital twin model for providing process metrics and dynamic process control information to the chromatography purification process by:

inputting a plurality of process parameters into the physics-informed neural network to obtain a predicted output,

wherein the plurality of process parameters comprises a set of chromatography column process variables, or historic data from chromatogram sensors;

co-relating in an input layer, the process variables with operational and design variables in a parameterized form and the historic data from the chromatogram sensors;

predicting via an output layer of the physics-informed neural network, the predicted output guided by a set of governing equations, and a set of constraints of the chromatography purification process;

calculating a loss function via a loss layer of the physics-informed neural network based on the set of governing equations, the set of constraints of the chromatography purification process, and the predicted output,

wherein the set of governing equations includes at least one partial differential equation (PDE) or ordinary differential equation (ODE), at least one boundary condition (BC), or at least one initial condition (IC) and wherein the loss layer computes the loss function based on a weighted combination of the BCs/ICs and PDEs/ODEs that describes the chromatography purification process;

calculating a loss score based on the loss function;

determining whether the physics-informed neural network is convergent based on the calculated loss function;

in response to the physics-informed neural network being convergent, export the physics-informed neural network as a trained physics-informed neural network,

wherein the physics-informed neural network is convergent when the calculated loss score is smaller than a pre-defined threshold;

in response to the physics-informed neural network not being convergent:

update a plurality of weights via backpropagation in the physics-informed neural network, and

input the plurality of process parameters to the physics-informed neural network for a next convergence iteration to calculate the loss function and determine whether the physics-informed neural network is convergent;

exporting the trained physics-informed neural network includes:

iteratively inputting the predicted output into a Bayesian optimizer for optimizing the plurality of process parameters based on an optimization objective, wherein the optimization objective comprises maximizing a protein concentration, or minimizing a quantity of material consumption, and

wherein the iteration in the Bayesian optimizer continues for a number of times until the plurality of process parameters are optimized based on the optimization objective;

output the dynamic process control information from the digital twin model based on the process metrics; and

change the plurality of process parameters on the chromatography purification process based on the output dynamic process control information.

2 . The system according to claim 1 , wherein:

the plurality of process parameters comprises at least one of the following: one or more operation parameters, one or more process control parameters, one or more design parameters, or sensory data.

3 . The system according to claim 1 , wherein:

the set of governing equations comprises at least one of the following:

one or more interstitial mass balance partial differential equation (PDE),

one or more bead mass balance PDE, or

one or more sorption PDE.

4 . The system according to claim 3 , wherein:

the set of governing equations comprises the one or more sorption PDE, which comprises a quasi-stead-state approximation.

5 . The system according to claim 1 , wherein when the processor circuitry executes the instructions to cause the system to calculate the loss function based on the set of governing equations and the predicted output, the processor circuitry executes the instructions to cause the system to:

input the plurality of process parameters into the set of governing equations to obtain a result based on at least one boundary condition and/or at least one initial condition; and

calculate the loss function based on the predicted output and the result.

6 . The system according to claim 1 , wherein, after the physics-informed neural network is exported, the processor circuitry executes the instructions to cause the system to:

input the predicted output into the Bayesian optimizer for optimizing the plurality of process parameters based on the optimization objective;

generate a new plurality of process parameters by the Bayesian optimizer based on the optimization objective;

input the new plurality of process parameters into the physics-informed neural network to obtain a new predicted output; and

input the predicted output into the Bayesian optimizer for a next optimizer iteration.

7 . The system according to claim 6 , wherein:

the Bayesian optimizer comprises a constraint-aware Bayesian optimizer.

8 . The system according to claim 1 , wherein: the processor circuitry executes the instructions to further cause the system to:

obtain a reading by the sensor based on an output of the chromatography purification process; and

in response to a difference between the reading from the chromatography purification process and a corresponding prediction from the physics-informed neural network exceeding the pre-defined threshold:

update the loss function based on the difference, and

train the physics-informed neural network based on the updated loss function.

9 . A method for optimization of a chromatography purification process using a physics-informed neural network, the method comprising:

training, the physics-informed neural network comprised in a digital twin model for providing process metrics and dynamic process control information to the chromatography purification process by:

inputting, by a device comprising a memory storing instructions and a processor in communication with the memory, a plurality of process parameters into the physics-informed neural network to obtain a predicted output,

wherein the plurality of process parameters comprises a set of chromatography column process variables, or historic data from chromatogram sensors;

co-relating, in an input layer, the process variables with operational and design variables in a parameterized form and the historic data from the chromatogram sensors;

predicting, via an output layer of the physics-informed neural network, the predicted output guided by a set of governing equations, and a set of constraints of the chromatography purification process;

calculating, by the device, a loss function via a loss layer of the physics-informed neural network based on a set of governing equations, as set of constraints of the chromatography purification process, and the predicted output,

wherein the set of governing equations includes at least one partial differential equation (PDE) or ordinary differential equation (ODE), at least one boundary condition (BC), or at least one initial condition (IC) and wherein the loss layer computes the loss function based on a weighted combination of the BCs/ICs and PDEs/ODEs that describes the chromatography purification process;

calculating a loss score based on the loss function;

determining, by the device, whether the physics-informed neural network is convergent based on the calculated loss function;

in response to the physics-informed neural network being convergent, exporting, by the device, the physics-informed neural network as a trained physics-informed neural network,

wherein the physics-informed neural network is convergent when the calculated loss score is smaller than a pre-defined threshold;

in response to the physics-informed neural network not being convergent:

updating, by the device, a plurality of weights via backpropagation in the physics-informed neural network, and

inputting, by the device, the plurality of process parameters to the physics-informed neural network for a next convergence iteration to calculate the loss function and determine whether the physics-informed neural network is convergent;

exporting, the trained physics-informed neural network includes:

iteratively inputting the predicted output into a Bayesian optimizer for optimizing the plurality of process parameters based on an optimization objective, wherein the optimization objective comprises maximizing a protein concentration, or minimize a quantity of material consumption, and

wherein the iteration in the Bayesian optimizer continues for a number of time until the plurality of process parameters is optimized based on the optimization objective;

output the dynamic process control information from the digital twin model based on the process metrics; and

change the plurality of process parameters on the chromatography purification process based on the output dynamic process control information.

10 . The method according to claim 9 , wherein:

the plurality of process parameters comprises at least one of the following: one or more operation parameters, one or more process control parameters, one or more design parameters, or sensory data.

11 . The method according to claim 9 , wherein:

the set of governing equations comprises at least one of the following:

one or more interstitial mass balance partial differential equation (PDE),

one or more bead mass balance PDE, or

one or more sorption PDE.

12 . The method according to claim 9 , wherein when the calculating the loss function based on the set of governing equations and the predicted output comprises:

inputting the plurality of process parameters into the set of governing equations to obtain a result based on at least one boundary condition and/or at least one initial condition; and

calculating the loss function based on the predicted output and the result.

13 . The method according to claim 9 , wherein: after the exporting the physics-informed neural network, the method further comprises

inputting the predicted output into the Bayesian optimizer for optimizing the plurality of process parameters based on the optimization objective;

generating a new plurality of process parameters by the Bayesian optimizer based on the optimization objective;

inputting the new plurality of process parameters into the physics-informed neural network to obtain a new predicted output; and

inputting the predicted output into the Bayesian optimizer for a next optimizer iteration.

14 . The method according to claim 9 , further comprising:

obtaining a reading by the sensor based on an output of the chromatography purification process; and

in response to a difference between the reading from the chromatography purification process and a corresponding prediction from the physics-informed neural network exceeding the pre-defined threshold:

updating the loss function based on the difference, and

training the physics-informed neural network based on the updated loss function.

15 . A product comprising:

machine-readable media other than a transitory signal;

instructions stored on the machine-readable media; and

wherein when a processor circuitry executes the instructions, the product is configured to cause the processor circuitry to:

train the physics-informed neural network comprised in a digital twin model for providing process metrics and dynamic process control information to the chromatography purification process by:

inputting a plurality of process parameters into the physics-informed neural network to obtain a predicted output,

wherein the plurality of process parameters comprises a set of chromatography column process variables, or historic data from chromatogram sensors;

co-relating in an input layer, the process variables with operational and design variables in a parameterized form and the historic data from the chromatogram sensors;

predicting via an output layer of the physics-informed neural network, the predicted output guided by a set of governing equations, and a set of constraints of the chromatography purification process;

calculating a loss function via a loss layer of the physics-informed neural network based on the set of governing equations, the set of constraints of the chromatography purification process, and the predicted output,

wherein the set of governing equations includes at least one partial differential equation (PDE) or ordinary differential equation (ODE), at least one boundary condition (BC), or at least one initial condition (IC) and wherein the loss layer computes the loss function based on a superposition of the BCs/ICs and PDEs/ODEs that describes the chromatography purification process;

calculating a loss score based on the loss function;

determining whether the physics-informed neural network is convergent based on the calculated loss function;

in response to the physics-informed neural network being convergent, export the physics-informed neural network as a trained physics-informed neural network,

wherein the physics-informed neural network is convergent when the calculated loss score is smaller than a pre-defined threshold;

in response to the physics-informed neural network not being convergent:

update a plurality of weights via backpropagation in the physics-informed neural network, and

input the plurality of process parameters to the physics-informed neural network for a next convergence iteration to calculate the loss function and determine whether the physics-informed neural network is convergent;

exporting the trained physics-informed neural network includes:

iteratively inputting the predicted output into a Bayesian optimizer for optimizing the plurality of process parameters based on an optimization objective, wherein the optimization objective comprises maximizing a protein concentration, or minimize a quantity of material consumption, and

wherein the iteration in the Bayesian optimizer continues for a number of time until the plurality of process parameters is optimized based on the optimization objective;

output the dynamic process control information from the digital twin model based on the process metrics; and

change the plurality of process parameters on the chromatography purification process based on the output dynamic process control information.