Predictive Modeling

Predictive Modeling Toolkit

The Predictive Modeling Toolkit in pSeven is a set of tools building and managing approximation models. All of its components can work both with data gathered from a pSeven workflow and data sets imported from CSV or Excel files. Models can be evaluated to get predictions or integrated into a workflow.

Using the Predictive Modeling Toolkit, you can:

  • Build fast and robust models with automatic choosing of approximation technique.
  • Validate quality, test against reference data and compare models to find the best approximation using error plots and statistics.
  • Explore behavior of multidimensional model with studying input-output dependencies on a series of two-dimensional slices, each showing an input-output pair.
  • Export models to C source code, Matlab/Octave, Excel and FMI (FMU for Co-Simulation) format.
Model Builder

Model Builder

Model Validator

Model Validator

Model Explorer

Model Explorer

Approximation

The approximation is used for predicting function’s response values or behavior of the product designs without running new simulations and full-scale experiments. At the basis, an approximation model is a complex polynomial that describes model’s response surface or, in other words, a substitution (“black box”) of existing data or simulation.

Data Arrow Approximation Arrow Analytics

Provide input data

 

Evaluate approximation model

 

Predict outputs

Approximation models also allow capturing essential knowledge from vast amounts of data in a convenient format, safely exchange models between partners preserving IP rights and accelerate the computation of complex simulation models by many orders of magnitude, for example, for fast parametric and optimization studies.

pSeven is a «Swiss Army Knife» for creating approximation models:

  • Easy-to-use graphical user interface
  • Perfectly handles samples of varied sizes: from tiny to huge datasets
  • Exact fit and smoothing
  • Handling of missing data and discontinuities
  • Accuracy and error assessment
  • Updating of existing models with new data and combining of models
  • Full control over building time

Approximation Techniques

pSeven provides a variety of industry-proven techniques for any type of data and approximation:

  • Piecewise Linear Approximation (PLA)
  • 1D Splines with Tension (SPLT)
  • Response Surface Model (RSM)
  • Tensor Approximation (TA)
  • Incomplete Tensor Approximation (iTA)
  • Gaussian Processes (GP)
  • Sparse Gaussian Process (SGP)
  • Tensored Gaussian Processes (TGP)
  • Gradient Boosted Regression Trees (GBRT)
  • High-Dimensional Approximation (HDA)
  • High-Dimensional Approximation Combined with Gaussian Processes (HDAGP)
  • Mixture of Approximators (MoA)
  • Table Function (TBL)
SmartSelection

For users with little experience in approximation pSeven offers a special technique called SmartSelection. It is a built-in decision tree with a hierarchical system of options for automatic choosing and tuning of the most effective approximation technique(s) for a given type of problem and data.

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Data Fusion

Data Fusion is a highly powerful tool in pSeven that contributes to approximation techniques and handles datasets of variable fidelities. As an input for building approximation models, it uses high- and low-fidelity data sets. It is supposed that these data sets are generated using high-fidelity and low-fidelity sources or models respectively, for example, experimental and simulation data. With Data Fusion, the number of expensive experiments and simulations can be reduced due to more accurate predictions made with approximation models.

Experiment Arrow Model Arrow Data Fusion Arrow Analytics

Provide high-fidelity data

 

Provide low-fidelity data

 

Build mixed approximation

 

Analyze outputs

Data Fusion allows users to meet their specific requirements for an approximation model using a wide range of powerful techniques:

  • Difference Approximation (DA)
  • Variable Fidelity Gaussian Processes (VFGP)
  • Multiple Fidelity Gaussian Process (MFGP)
  • Sparse Variable Fidelity Gaussian Processes (SVFGP)
  • High-Fidelity Approximation (HFA)

Automatic selection of techniques based on provided data and user requirements is also available.

Models for System Simulation

The more complicated the products become, the less modeling of single physics or a separate part helps to ensure overall product reliability and deliver customer the best product characteristics on the market. Simulation and optimization of the system behavior as a whole become more critical than ever. Connecting every simulation to a systems modeling software may be the way to go, but when the computation of a single model takes several hours, often there is no time left for system optimization, and thus the best characteristics may not be found at all.

Model Arrow Approximation Arrow Export Arrow System model

Create model

 

Build approximation

 

Export to external file

 

Import to system model

Fast and robust approximation models can answer this need and drastically speed up system simulation. Created from simulation, analytical and experimental data in an easy-to-use pSeven graphical user interface with automatic choosing of approximation technique they can be then exported in FMI (FMU for Co-Simulation) or other formats for use in any systems modeling software.

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