Predictive Modeling

What is Predictive Modeling?

Predictive modeling is an engineering approach that helps engineers answer the following questions:

  • How to predict product behavior in various conditions?
  • How to process data from experiments and simulations together?
  • How to use huge data samples and simulations faster?

Provide input data


Evaluate approximation model


Predict outputs

Predictive modeling is based on building, managing and evaluating approximation models (also called RSM models, surrogate models, metamodels etc.)

Approximation Models

Approximation models are 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.

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 includes a set of tools for building and managing approximation models that can work both with data gathered from pSeven workflows and data sets imported from CSV or Excel files. Models can be evaluated to get predictions or integrated into a workflow.

Model Builder

Model Builder

Model Validator

Model Validator

Model Explorer

Model Explorer

pSeven is a «Swiss Army Knife» for building, validating and evaluating approximation models:

  • Easy-to-use graphical user interface
  • Perfectly handles samples of varied sizes: from tiny to huge datasets
  • Handling of missing data and discontinuities
  • Full control over building time
  • Exact fit and smoothing
  • Validate quality, test against reference data and compare models to find the best approximation using error plots and statistics
  • Update existing models with new data and combine models
  • 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

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)

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.


Provide high-fidelity data


Provide low-fidelity data

Data Fusion

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.


Evaluate model responses


Build approximation


Export to external file

System model

Import to system model

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

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