Function analysis

Parameter optimization

Parameter optimization solves an inverse problem: finding the input conditions that lead to a specified output of the model. It computes inputs minimizing deviation measured by loss function.

Using Datagrok fitting feature, you can improve performance and accuracy of a model.

Usage

To run parameter optimization:

• Click the "Fit inputs" icon on the top panel. Fitting View opens.

• In the Fit block, use switchers to specify inputs to be found:

  • Set min and max values for each selected item. They define the variation range
  • Set values of all other inputs

• Set output constraints in the Target block:

  • Use switchers to specify target outputs
  • Set target value for each selected item

• Specify settings of fitting:

  • Choose numerical optimization method (in the method field). Click the gear icon to specify its settings
  • Set loss function type (in the loss field)
  • Specify number of points to be found (in the samples field)
  • Set the maximum scaled deviation between similar fitted points (in the similarity field): the higher the value, the fewer points will be found

• Click the "Run" icon on the top panel to perform fitting. You will get a grid containing

  • loss function values and fitted inputs
  • viewers visualizing the goodness of fit
  • line chart showing the loss function minimization

An inverse problem may have several solutions. Specify their expected number in the samples field. To filter fitted points, set similarity:

• it is the maximum scaled deviation between "similar" points
• the higher the value, the fewer points will be displayed

Table output

Apply the feature to models with table outputs as well:

• Specify the target dataframe in the table input
• Set dataframe column with values of independent variable (in the argument choice input)

Open Context Panel (F4). You will get the model run corresponding to the selected grid row:

Platform function annotaion

Apply parameter optimization to any function with the RichFunctionView editor. Add meta.features: {"fitting": true} to enable it:

//name: Test
//language: javascript
//input: double x
//output: double y
//editor: Compute:RichFunctionViewEditor
//meta.features: {"fitting": true}

let y = x * x;

See also

• Optimization
• Nelder-Mead method
• Scripting

Sensitivity analysis

Sensitivity Analysis runs the computation multiple times with varying inputs, and analyzes the relationship between inputs and outputs. Datagrok provides the following methods:

• Monte Carlo explores a function at randomly taken points
• Sobol decomposes output variance into fractions, which can be attributed to inputs
• Grid studies a function at the points of a grid with the specified step

To run the sensitivity analysis, click the Run sensitivity analysis () icon on the top panel, choose a method, specify inputs and outputs, and click RUN.

Monte Carlo

Once you've chosen it in Method

• Set in Samples the number of random points
• Use switchers to specify varied inputs and outputs to be analyzed
• Press RUN or on the top panel. You will get
  • Correlation plot for exploring correlations between varied inputs and the specified outputs
  • PC plot visualizing multivariate data and providing variations of the selected inputs & outputs
  • Line chart or Scatterplot (dependently on the varied inputs count) showing a behavior of each output separately
  • Grid containing inputs and outputs values of each function evaluation

Use the sliders in the PC plot to filter the model evaluations:

When exploring complex models, some evaluations may be of particular interest. To get them:

• Click on grid row with the required input and output values
• Open Context Panel (F4). You will get the function run corresponding to the selected row

Sobol

This method performs variance-based sensitivity analysis and decomposes the output variance into fractions, which can be attributed to inputs. It provides the same visualizations as Monte Carlo and bar charts showing Sobol' indices:

• First-order indices indicate the contribution to the output variance of varying each input alone
• Total-order indices measure the contribution to the output variance of each input, including all variance caused by its interactions with any other inputs

Grid

This method evaluates a function at the points of uniform grid within the specified ranges. It provides the same visualizations as Monte Carlo:

Sensitivity Analysis can be applied to any function with the RichFunctionView editor. Add meta.features: {"sens-analysis": true} to enable it:

//name: Test
//language: javascript
//input: double x
//output: double y
//editor: Compute:RichFunctionViewEditor
//meta.features: {"sens-analysis": true}

let y = x + 3;

Learn more

• Sensitivity analysis
• Variance-based sensitivity analysis