Predictive Modeling

Predict response values for new designs, accelerate complex simulations and capture knowledge from vast amounts of data with automatic and adaptive technique choosing.

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?

Predictive Modeling is based on building, managing and evaluating predictive models that are also often called approximation models, response surface models (RSM), reduced oreder models (ROM), surrogate models, metamodels etc.

Predictive 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, a predictive model is a complex polynomial that describes model’s response surface or, in other words, a substitution (“black box”) of existing data or simulation.

Input parameters

Provide input parameters

Predictive model

Evaluate predictive model

Output parameters

Predict output parameters

Predictive models 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.

Building & Managing Models

pSeven includes a set of tools for building and managing predictive 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 and managing predictive 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
  • Validate quality, test against reference data and compare models to find the best approximation using error plots and statistics
  • Exact fit and smoothing
  • 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

Predictive Modeling Techniques

pSeven provides a variety of industry-proven techniques for building predictive models from any type of data:

  • 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 predictive modeling 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 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 predictive modeling techniques and handles datasets of variable fidelities. As an input for building predictive 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 such models.


Provide low-fidelity data


Provide high-fidelity data

Data Fusion

Build mixed predictive model

Model Explorer

Predict outputs for new designs

Data Fusion allows users to meet their specific requirements for a predictive 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.

Dimension Reduction

Complex geometries are described by a large number of parameters, and it is often desirable to reduce their dimensionality for easier parameterization, optimization or visualization. For example, if the geometry is represented as a set of multi-dimensional points, pSeven can approximate it with a smooth hypersurface and produce compression and decompression procedures which allow to:

  • Automatically re-parameterize geometry with a smaller number of parameters.
  • Quickly generate topologically similar geometries.

The number of parameters required to describe the geometry with the smallest error in pSeven is estimated automatically and may be manually changed.

Original profile

Provide input parameters for a set of profiles

Dimension Reduction

Run Dimension Reduction

Reconstructed profile

Reconstruct profiles with less input parameters

Model Export

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

Predictive model

Build predictive model


Export to external file

System model

Import to external software, e.g. for system modeling

Fast and robust predictive models can answer this need and drastically speed up system simulation. Models created in pSeven from simulation, analytical and experimental data can be exported for use in external software products, for example, in system modeling software. pSeven supports export of predictive models in following formats:

  • FMI (FMU for Co-Simulation)
  • MS Excel
  • Matlab/Octave
  • Executable
  • C source code

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