4.4. Parameter sensitivity analysis¶

4.4.2.1. Selecting parameters¶

Next we consider the parameters we would like to investigate.

This shows that all 12 parameters related to an H.O bond are active.

If we consider the parameter descriptions we see that 6 of them are associated with π-bonds which are not present in the training set, so they should have no influence on the optimization.

Instead of deactivating these parameters, we will leave these parameters active as a test of the sensitivity method.

4.4.2.2. Input options¶

We will now configure the sensitivity calculation.

Click to open the input panel

4.4.2.2.2. Loading/Generating Samples¶

The second set of options relate to producing or loading the samples of the loss function. If you have produced samples before, you can use them again for a different sensitivity calculation to save time because sampling takes longer than the sensitivity calculation.

In this tutorial you can choose to either

• Load samples from the sample directory (to get through the tutorial quicker), or

• Generate the samples yourself (if no samples had been generated previously, this would be a necessary step)

To load samplesTo generate samples

Deactivate Run Sampling

This enables the Samples Directory option

Click and select the samples directory in the example directory

The associated input keys for loading samples:

RunSampling No
SamplesDirectory path/to/samples

In general the Samples Directory must have the following structure:

samples_directory
├── training_set_results (or validation_set_results)
│   ├── running_active_parameters.txt
│   └── running_loss.txt
└── glompo_log.h5

• Only glompo_log.h5 or the running_*.txt files are needed.

• If glompo_log.h5 is present, it will take precedence.

• glompo_log.h5 is produced by saving residuals (see the To generate samples tab).

Tip

Sampling will produce a directory called sampling_results within the results directory. To load these samples point Samples Directory to: results/sampling_results/optimization.

4.4.2.2.3. Samples used in calculation¶

Our pool of samples contains 2000 samples. To take full advantage of these we can:

• Use all 2000 samples in a single calculation; or

• Take a subset of the samples, run a smaller calculation, and repeat this for different subsets.

It is always recommended to repeat the sensitivity calculation. The spread of results will tell you if you have enough samples. It is usually cheaper to repeat a calculation with subsets of samples than run it is to run it using all samples once.

We will repeat the calculation five times using subsets of 500 samples each time.

Set Repeat calculation n times to 5

Set Number of samples per repeat to 500

A new subset is drawn from the full pool for every calculation repeat.

If Sample with replacement is Yes then the subset can contain repeated samples from the full pool of samples. Otherwise, a sample can only appear once in a subset.

If Filter infinite values is Yes then any samples with an infinite loss function value will not be included in the full pool of samples.

Tip

If Run Reweight Calculation is Yes, then the sensitivity calculation is extended to provide suggested training set weights which should provide a better balance of sensitivities for the parameter set. This training set only has one item so we will not run the reweight calculation.

Data sets which are imbalanced can be harder to optimize. A reweight calculation

• suggests new training set weights,

• reveals dependencies within the training set,

• can help to guide training set design.

Unfortunately, a reweight calculation is much more computationally demanding than a regular sensitivity calculation.

4.4.2.2.4. Choosing Kernels¶

The key sensitivity calculation inputs are kernels. We need two kernels:

• a kernel to quantify the dis/similarity between parameter values;

• a kernel to classify the loss function values.

On the input panel, Details → Kernels

The default kernels should be sufficient in most scenarios.

The default parameter values kernel applies a Gaussian kernel to the parameter values. This measures the distance between parameter values and applies no underlying assumption on the shape of the distribution of parameter values.

The default loss values kernel is a conjunctive-Gaussian type kernel which places the bulk of its distribution on the lowest loss values. This helps identify small local sensitivities near the minima we are interested in which might otherwise be drowned out by large global sensitivities.

4.4.3.1. Graphical results¶

Once complete the GUI will show 2 summary plots:

The scatter plot shows:

• the sensitivity result for each parameter for each repeat (black dots);

• the mean sensitivity for each parameter (red line).

This does not identify particular parameters, but one can see:

• the number of parameters which dominate the sensitivity;

• if there is a large spread between repeats (means more samples are needed).

In this example:

• we detect significant sensitivity for only three parameters;

• the spread between repeats is robust and does not influence the ordering of parameters.

The pie chart shows the allocation of sensitivity to different groups. For ReaxFF, the groups are atoms and blocks combinations. Here we only analysed parameters in the H.O bond block, so all of the sensitivity is in that group.

4.4.3.2. Sensitivity values¶

Close the panel if it is open

Switch to the Parameters panel

Click the Active column header and deselect Show Non-Active

Click the Sensitivity column header and click Sort Decreasing

Each active parameter has been given the average sensitivity value from the repeats (seen as the red line on the plot).

In our results we see:

• negligible sensitivity was detected for the π-bond related parameters;

• H.O:p_be1, H.O:p_be2 and H.O:p_ovun1 are also found to be insensitive;

• Most of the sensitivity is divided between three σ-bond related parameters.

4.4.3.3. Results files¶

The results for a sensitivity calculation have the following structure:

jobname.results
├── sampling_results (if samples generated)
│   ├── settings_and_initial_data
│   └── optimization (directory to chose when loading samples)
├── settings_and_initial_data
│   └── data_sets
└── sensitivity
    ├── calculation_result.npz
    ├── parameter_interface_with_sensitivities.yaml
    ├── sensitivity_per_parameter.png
    ├── sensitivity_summary.png
    └── sensitivity_summary.txt

• calculation_result.npz contains the calculation results and the inputs which can be loaded in Python:

  from scm.glompo.analysis.hsic import HSICResult
  
  if __name__ == '__main__':
      result = HSICResult.load('path/to/calculation_result.npz')
  

  For more details see the API documentation

• parameter_interface_with_sensitivities.yaml is the normal parameter interface YAML file with a sensitivity metadata key for all the parameters. The key is blank if the parameter was not ‘active’ for the calculation.

  ---
  name: O.O:p_ij^xel1
  value: 0.0
  range:
  - -1.0
  - 1.0
  is_active: false
  atoms:
  - O
  - O
  block: BND
  block_index: 15
  category: Expert
  description: eReaxFF param for adjusting number of electrons available to host atom
  equation: '27'
  sensitivity: ''
  ---
  name: H.O:D_e^sigma
  value: 135.35101502052595
  range:
  - 133.76688000000001
  - 200.65031999999997
  is_active: true
  atoms:
  - H
  - O
  block: BND
  block_index: 0
  category: Standard
  description: Sigma-bond dissociation energy
  equation: 6,11a
  sensitivity: 0.2074254860483457
  ---
  

• sensitivity_per_parameter.png is a visual summary of sensitivity values for every parameter and every repeat.

  

• sensitivity_summary.png (and gui_sensitivity_summary.png) are discussed in Graphical results.

• sensitivity_summary.txt is a textual summary of the calculation inputs and sensitivity values for every parameter.

                     HSIC Result
  ==================================================
  Calculation Description:               TrainingSet
  --------------------------------------------------
  No. Factors                                     12
  No. Samples                                    500
  No. Bootstraps                                   5
  Sample with replacement                       True
  Includes reweight calc.                         No
  --------------------------------------------------
  Inputs Kernel                       GaussianKernel
     sigma                                       0.3
  Outputs Kernel           ConjunctiveGaussianKernel
     gamma                                       0.3
  --------------------------------------------------
  Factor Rankings:
       1.                      H.O:p_bo2 0.607±0.020
       2.                  H.O:D_e^sigma 0.207±0.021
       3.                      H.O:p_bo1 0.163±0.026
       4.                      H.O:p_be1 0.008±0.009
       5.                      H.O:p_bo3 0.003±0.005
       6.                      H.O:p_bo4 0.003±0.005
       7.                      H.O:p_be2 0.003±0.003
       8.                      H.O:p_bo5 0.002±0.003
       9.                    H.O:p_ovun1 0.001±0.001
      10.                     H.O:D_e^pi 0.001±0.002
      11.                   H.O:D_e^pipi 0.001±0.002
      12.                      H.O:p_bo6 0.001±0.001
  ==================================================
  

4.4.3.4. Using the results for optimization¶

The purpose of sensitivity analysis is guide parameter selection for optimization.

Our results suggest that only three parameters have an effect on the loss function.

We have run the optimization version of this tutorial 10 times:

We have also run the optimization with the exact same settings, but with only the three most sensitive parameters active; also repeated 10 times:

The optimizers working only with the most sensitive parameters clearly:

• converge much faster;

• all find same/better loss function values than the 12D optimizers.