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Supercritical CO2 Property Surrogate with ALAMO Surrogate Object - Training Surrogate (Part 1)#

Maintainer: Javal Vyas

Author: Javal Vyas

Updated: 2024-01-24

1. Introduction#

This notebook demonstrates leveraging of the ALAMO surrogate trainer and IDAES Python wrapper to produce an surrogate based on supercritical CO2 data from simulation using REFPROP package.

There are several reasons to build surrogate models for complex processes, even when higher fidelity models already exist (e.g., reduce model size, improve convergence reliability, replace models with externally compiled code and make them fully-equation oriented).

In this example, we intend to make a surrogate for the physical properties of S-CO2 to be embedded in the property package. This property package will be used to get the physical properties of S-CO2 in the flowsheet simulation. To learn more about property package, see the IDAES-PSE Github Page or IDAES Read-the-docs.

1.1 Need for ML Surrogate#

The properties predicted by the surrogate are enthalpy and entropy of the S-CO2 based on the pressure and temperature of the system. The analytical equation of getting the enthalpy and entropy from pressure and temperature are in the differential form and would make the problem a DAE system. To counter this problem and keep the problem algebric, we will use the surrogates and relate enthalpy and entropy with the pressure and temperature as an algebric equation.

1.2 Supercritical CO2 cycle process#

The following flowsheet will be used to optimize the design for the cooling of the fusion reactor using supercritical CO2 cycle. We shall focus on training the surrogate for this notebook and move to constructing the flowsheet and the properties package in the subsequent notebooks. The take away from this flowsheet is that, 3 variables can be measured in any given unit which are flow, pressure and temperature and other properties can be calculated using them. Thus, surrogate should have pressure and temperature as the inputs.

In this example, we will train a model using AlamoTrainer for our data and then demonstrate that we can solve an optimization problem with that surrogate model.

from IPython.display import Image
from pathlib import Path


def datafile_path(name):
    return Path("..") / name


Image(datafile_path("CO2_flowsheet.png"))
../../../../_images/d8050a37171e8e1c8ef9b92bd7f8a6b2f52abfff04d2faffafe235388ba5adee.png

2. Training and Validating Surrogate#

First, let’s import the required Python and IDAES modules:

# Import statements
import os
import numpy as np
import pandas as pd

# Import IDAES libraries
from idaes.core.surrogate.sampling.data_utils import split_training_validation
from idaes.core.surrogate.alamopy import AlamoTrainer, AlamoSurrogate, alamo
from idaes.core.surrogate.plotting.sm_plotter import (
    surrogate_scatter2D,
    surrogate_parity,
    surrogate_residual,
)

2.1 Importing Training and Validation Datasets#

In this section, we read the dataset from the CSV file located in this directory. 500 data points were simulated for S-CO2 physical properties using REFPROP package. This example is trained on the entire dataset to have cover different ranges of pressure and temperature. The data is separated using an 80/20 split into training and validation data using the IDAES split_training_validation() method.

We rename the column headers because they contained “.”, we change “.” to “_” as ALAMO accepts alphanumerical characters or underscores as the labels for input/output. Further, the input variables are pressure, temperature , while the output variables are enth_mol, entr_mol, hence we create two new dataframes for the input and output variables.

# Import training data
np.set_printoptions(precision=7, suppress=True)

csv_data = pd.read_csv(datafile_path('500_Points_DataSet.csv'))  

### ALAMO only accepts alphanumerical characters (A-Z, a-z, 0-9) or underscores as input/output labels
cols=csv_data.columns
cols=[item.replace(".", "_") for item in cols]
csv_data.columns=cols

data = csv_data.sample(n=500,random_state=0) 

input_data = data.iloc[:, :2]
output_data = data.iloc[:, 2:4]

# Define labels, and split training and validation data
input_labels = input_data.columns
output_labels = output_data.columns

n_data = data[input_labels[0]].size
data_training, data_validation = split_training_validation(
    data, 0.8, seed=n_data
) 

2.2 Training Surrogate with ALAMO#

IDAES provides a Python wrapper for the ALAMO machine learning tool via an imported AlamoTrainer class. Regression settings can be directly set as config attributes, as shown below. In this example, allowed basis terms include constant and linear functions, monomial power order 2 and 3, variable product power order 1 and 2, and variable ratio power order 1 and 2. ALAMO seeks to minimize the number of basis terms; here, we restrict each surrogate expression to a maximum of 10 basis terms.

Finally, after training the model we save the results and model expressions to a JSON file. Serializing the model in this fashion enables importing a previously trained set of surrogate models into external flowsheets. This feature will be used later.

# Create ALAMO trainer object
has_alamo=alamo.available()
if has_alamo:
    trainer = AlamoTrainer(
        input_labels=input_labels,
        output_labels=output_labels,
        training_dataframe=data_training,
    )

    # Set ALAMO options
    trainer.config.constant = True
    trainer.config.linfcns = True
    trainer.config.multi2power = [1, 2]
    trainer.config.monomialpower = [2, 3]
    trainer.config.ratiopower = [1]
    trainer.config.maxterms = [10] * len(output_labels)  # max terms for each surrogate
    trainer.config.filename = os.path.join(os.getcwd(), "alamo_run.alm")
    trainer.config.overwrite_files = True

    # Train surrogate (calls ALAMO through IDAES ALAMOPy wrapper)
    success, alm_surr, msg = trainer.train_surrogate()

    # save model to JSON
    model = alm_surr.save_to_file("alamo_surrogate.json", overwrite=True)

    # create callable surrogate object
    surrogate_expressions = trainer._results["Model"]
    input_labels = trainer._input_labels
    output_labels = trainer._output_labels
    xmin, xmax = [7,306], [40,1000]
    input_bounds = {
        input_labels[i]: (xmin[i], xmax[i]) for i in range(len(input_labels))
    }

    alm_surr = AlamoSurrogate(
        surrogate_expressions, input_labels, output_labels, input_bounds
    )
else:
    print('Alamo not found.')
Alamo not found.

2.3 Visualizing Surrogates#

Now that the surrogate models have been trained, the models can be visualized through scatter, parity and residual plots to confirm their validity in the chosen domain. The training data will be visualized first to confirm the surrogates are fit the data, and then the validation data will be visualized to confirm the surrogates accurately predict new output values.

# visualize with IDAES surrogate plotting tools
surrogate_scatter2D(alm_surr, data_training)
surrogate_parity(alm_surr, data_training)
surrogate_residual(alm_surr, data_training)
---------------------------------------------------------------------------
NameError                                 Traceback (most recent call last)
Cell In[6], line 2
      1 # visualize with IDAES surrogate plotting tools
----> 2 surrogate_scatter2D(alm_surr, data_training)
      3 surrogate_parity(alm_surr, data_training)
      4 surrogate_residual(alm_surr, data_training)

NameError: name 'alm_surr' is not defined

2.4 Model Validation#

# visualize with IDAES surrogate plotting tools
surrogate_scatter2D(alm_surr, data_validation)
surrogate_parity(alm_surr, data_validation)
surrogate_residual(alm_surr, data_validation)
../../../../_images/7607e0ba5fbcec58890d4455f82e939baceab87e16157813f96c5148e0672156.png ../../../../_images/e2d52fac4f8a79b5fdd76fd2da3de12543cb37f2b72a9008961db0ddf7aad309.png ../../../../_images/682dbda2ea854a290b506f6eba23bb985f9d2ed0d1e9db26d2c5e8dff190cd15.png ../../../../_images/d51d16e483c01eecd1a80cb55818c4616817c3b0314027065cbb50761de84d5a.png ../../../../_images/3e66fcdc2bd96f4cc06b079f68eee37fb32f594ab3e18d9808f6857f2f2314af.png ../../../../_images/4df5ca3235e95359fe25133ae2d97fa873784c63c13617a577ab86435bdc8e24.png ../../../../_images/53d571c30019e7a04b914f9f98d70d49e41ebb0354692dcf209284e090efd680.png ../../../../_images/29c005169d80ba47d871deb4d15c0247cd3373f4e21010e9bd284334eb152c2e.png ../../../../_images/7bb076d770688446278f20f827ae695666588cfab01f3ca81ff3ac3e223a1fc2.png ../../../../_images/d87fa8ce23f802ff0f98ad61e6570a5afda3ab39e038ec415c0b93f793c691ba.png

Now, the surrogate is trained and validated, we shall embed it in the property package, which is demonstrated in the surrogate_embedding file.