Stationary Stochastic Field Generator


NeurOK Software's Stationary Stochastic Field (SSF) generator is a high-performance, computational software library providing a complete set of functions necessary for the numerical simulation of realistic, multi-dimensional stationary random fields.  SSF was developed to meet the specific requirements of one of the world's leading design automation and engineering software companies.  The library serves as the basis of top-level, user-oriented applications devoted to the modeling of stochastic components in a broad class of analytical and prognostic problems.

In mechanical, chemical and electrical engineering stochastic fields describe uncertainties in initial and boundary conditions, material and geometric variations, and a lack of exact knowledge about external sources.  Economics, financial and business management applications may benefit from realistic treatment of uncertainties in market and consumer data which are spread structurally, temporally and geographically.  Climatology, ecology and geo-statistics data may also be treated as stochastic fields.


The SSF library has a flexible two-level architecture. The inner layer is a library kernel comprised of basic objects such as matrices and mesh functions with classical numerical math procedures for manipulating them. The outer layer contains basic algorithms of stochastic field theory such as:

  • Direct problems – Generates new samples of field trajectories with a given statistical properties
  • Inverse problems – Estimate statistical properties from a given set of sample trajectories (e.g. experimentally measured) and reuse them to generate new independent realizations
  • Testing of trajectories of stochastic fields
  • Pre- and post-processing of field trajectories - Fourier analysis, interpolation and extrapolation to new mesh, as well as approximations and more

The library’s methods are designed for extremely simple simulations of 1D, 2D or 3D trajectories of stochastic field with user-defined correlation structures, or with statistical properties automatically estimated from examples. Automated procedures are supplied for dealing with data presented in different digital formats.

The Stationary Stochastic Fields Generator library is implemented in pure standard ANSI C taking into account contemporary approaches of object-oriented software design.


Analysis and uncertainty assessments of a broad spectrum of modern complicated systems are typically based on computer models of real processes.  A key factor in the quality of numerical solutions is the correctness of model assumptions and their relation to the nature of a simulated system.  In most cases, realistic treatment should take into account stochastic components relevant to system uncertainties such as noise, geometry deviations, impurities and other perturbations.

Examples of the application of stochastic fields methods include:

  • Dynamic processes in real mechanical systems such as surface perturbations, uncertainties in stress tensor, and material fluctuations
  • Geological properties such as porosity, permeability
  • Chemical and bio-chemical reactions
  • Wave propagation through atmospheric turbulence
  • Other multi-dimensional static and dynamic processes

A simple, computationally efficient, but theoretically solid description of stochasticity can be achieved with Stationary Stochastic Fields Generator from NeurOK Software, LLC.

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2D Stochastic Fields



3D Stochastic Fields



2D Perturbations



3D Perturbations