This notebook is used to use KIM to perform inverse modeling for the Advanced Terrestrial Simulator (ATS).

# Libraries
from pathlib import Path
import pandas as pd
import numpy as np

from kim.map import KIM
from kim.data import Data
from kim.mapping_model import MLP

import jax

%load_ext autoreload
%autoreload 2

Read the data

• The Output_para.csv file includes the ensemble of the seven parameters to be estimated, represented by \(\mathbf{Y}\).

• The Input_logq.csv file includes the ensemble of the streamflow simulations generated by ATS, represented by \(\mathbf{X}\).

# File and folder paths
f_para = Path("./data/Output_para.csv")
f_state = Path("./data/Input_logq.csv")

df_para, df_state = pd.read_csv(f_para, index_col=0),pd.read_csv(f_state, index_col=0)

y_keys, x_keys = df_para.keys(), df_state.keys()
y, x = df_para.values, df_state.values
x.shape, y.shape

((396, 1461), (396, 8))

Configurations

Preliminary analysis configuration

seed_shuffle = 1234
f_data_save = Path("./results/data")

# Data configuration
data_params = {
    "xscaler_type": "minmax",
    "yscaler_type": "minmax",
}

# Sensitivity analysis configuration
sensitivity_params = {
    "method": "pc", "metric": "it-knn",
    "sst": True, "ntest": 100, "alpha": 0.05, "k": 3,
    "n_jobs": 100, "seed_shuffle": seed_shuffle,
    "verbose": 1
}

Ensemble learning configuration

Ns_train = 300
Ns_val = 50
hidden_activation = 'sigmoid'
final_activation = 'leaky_relu'
seed_ens = 1024
seed_predict = 3636
seed_dl = 10
seed_model = 100
training_verbose = 1
n_models = 100
n_jobs = 20

f_kim_save1 = Path("./results/map_many2many")
f_kim_save2 = Path("./results/map_many2one")
f_kim_save3 = Path("./results/map_many2one_cond")

# Mapping parameters for each test below
map_configs = {
    "model_type": MLP,
    'n_model': n_models,
    'ensemble_type': 'ens_random',
    'model_hp_choices': {
        "depth": [1,3,5,6],
        "width_size": [3,6,10]
    },
    'model_hp_fixed': {
        "hidden_activation": hidden_activation,
        "final_activation": final_activation,
        "model_seed": seed_model
    },
    'optax_hp_choices': {
        'learning_rate': [0.01, 0.005, 0.003],
    },
    'optax_hp_fixed': {
        'nsteps': 300,
        'optimizer_type': 'adam',
    },
    'dl_hp_choices': {
    },
    'dl_hp_fixed': {
        'dl_seed': seed_dl,
        'num_train_sample': Ns_train,
        'num_val_sample': Ns_val,
        'batch_size': 64
    },
    'ens_seed': seed_ens,
    'training_parallel': True,
    'parallel_config': {
        'n_jobs': n_jobs, 
        'backend': 'loky',
        'verbose': 1
    },
    'device': None,
}

Exploratory data analysis

# # Load the exploratory analysis result if available
# data = Data(x, y)
# data.load(f_data_save)

# Perform the sensitivity analysis if not done
data = Data(x, y, **data_params)
data.calculate_sensitivity(**sensitivity_params)

Using the kNN-based information theoretic metrics ...
Performing pairwise analysis to remove insensitive inputs ...

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Performing conditional independence testing to remove redundant inputs ...

# data.sensitivity_mask
data.cond_sensitivity_mask

array([[False, False, False, ..., False,  True, False],
       [False, False, False, ..., False,  True, False],
       [False, False, False, ..., False,  True, False],
       ...,
       [False, False, False, ..., False, False, False],
       [False, False, False, ..., False, False, False],
       [False,  True, False, ..., False, False, False]])

Train the inverse mapping

Now, let’s train the inverse mappings via ensemble learning. We are training three types of inverse mappings:

• kim1: The naive inverse mapping from all \(\mathbf{Y}\) to all \(\mathbf{X}\)

• kim2: The knowledge-informed inverse mapping from sensitive \(\mathbf{Y}\) to each of \(\mathbf{X}\) using global sensitivity analysis

• kim3: The knowledge-informed inverse mapping from sensitive \(\mathbf{Y}\) to each of \(\mathbf{X}\) using global sensitivity analysis + redundancy filtering check

# Initialize three diffferent KIMs
kim1 = KIM(data, map_configs, map_option='many2many')
kim2 = KIM(data, map_configs, mask_option="sensitivity", map_option='many2one')
kim3 = KIM(data, map_configs, mask_option="cond_sensitivity", map_option='many2one')

# Train the mappings
kim1.train()
kim2.train()
kim3.train()

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
/global/cfs/cdirs/m1800/peishi/.conda/envs/kim/lib/python3.12/site-packages/joblib/externals/loky/backend/fork_exec.py:38: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  pid = os.fork()
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 86%|████████▌ | 258/300 [00:03<00:00, 95.70it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:   37.3s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   53.2s finished

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   17.2s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 89%|████████▉ | 268/300 [00:03<00:00, 118.55it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.3s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   17.6s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 74%|███████▎  | 221/300 [00:02<00:00, 120.60it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.0s
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  5%|▍         | 14/300 [00:00<00:14, 19.53it/s]/global/cfs/cdirs/m1800/peishi/.conda/envs/kim/lib/python3.12/site-packages/joblib/externals/loky/process_executor.py:752: UserWarning: A worker stopped while some jobs were given to the executor. This can be caused by a too short worker timeout or by a memory leak.
  warnings.warn(
 51%|█████     | 152/300 [00:02<00:01, 114.45it/s]/global/cfs/cdirs/m1800/peishi/.conda/envs/kim/lib/python3.12/site-packages/joblib/externals/loky/backend/fork_exec.py:38: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  pid = os.fork()
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   38.0s finished

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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[Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    6.3s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   45.2s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 82%|████████▏ | 247/300 [00:03<00:00, 122.77it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.3s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   18.2s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 78%|███████▊  | 235/300 [00:02<00:00, 119.26it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.0s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   17.8s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 88%|████████▊ | 265/300 [00:03<00:00, 118.07it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.4s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   24.3s finished

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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[Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    4.9s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   46.4s finished

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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[Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.3s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   16.9s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 87%|████████▋ | 261/300 [00:02<00:00, 126.33it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.1s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   16.7s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 12%|█▏        | 35/300 [00:00<00:03, 83.37it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.2s
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 13%|█▎        | 40/300 [00:01<00:04, 55.93it/s]/global/cfs/cdirs/m1800/peishi/.conda/envs/kim/lib/python3.12/site-packages/joblib/externals/loky/process_executor.py:752: UserWarning: A worker stopped while some jobs were given to the executor. This can be caused by a too short worker timeout or by a memory leak.
  warnings.warn(
/global/cfs/cdirs/m1800/peishi/.conda/envs/kim/lib/python3.12/site-packages/joblib/externals/loky/backend/fork_exec.py:38: RuntimeWarning: os.fork() was called. os.fork() is incompatible with multithreaded code, and JAX is multithreaded, so this will likely lead to a deadlock.
  pid = os.fork()
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   30.1s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 84%|████████▍ | 252/300 [00:02<00:00, 126.31it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.0s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   54.8s finished

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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[Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.5s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   18.0s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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 78%|███████▊  | 235/300 [00:02<00:00, 120.70it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.2s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   16.8s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.

Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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  0%|          | 0/300 [00:00<?, ?it/s][Parallel(n_jobs=20)]: Done  10 tasks      | elapsed:    3.1s
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[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   29.4s finished
[Parallel(n_jobs=20)]: Using backend LokyBackend with 20 concurrent workers.
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Training completes.

 Performing ensemble training in parallel with 100 model configurations...

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Training completes.

[Parallel(n_jobs=20)]: Done 100 out of 100 | elapsed:   37.9s finished

Save all the results to disk

# Preliminary analysis results
data.save(f_data_save)

# Inverse mapping results
kim1.save(f_kim_save1)
kim2.save(f_kim_save2)
kim3.save(f_kim_save3)