Building Models from Data and Scientific Principles

• Mathematical Modeling Overview
• Building Models from Data and Scientific Principles
• Evaluating and Optimizing Models

With the MATLAB and Simulink product families you can model virtually any type of system, including:

• Linear and nonlinear
• Static and dynamic
• Deterministic and stochastic
• Discrete and continuous

You can choose from several modeling environments, enabling you to describe your system programmatically, symbolically, or with block diagrams and state machines.

Develop Models from Data

Ensure model accuracy by choosing the modeling technique that is right for your experimental or historical data. If you know how various parameters affect the behavior of your system, use statistics and curve fitting tools to model your data with linear and nonlinear regression and other data-fitting techniques.  If you’re unsure of the factors determining your system output, you can use nonparametric techniques such as neural networks and system identification.

Develop Models Based on Mathematical, Engineering, and Scientific Principles

You can choose from multiple approaches for creating mathematical models based on first principles. For example, you can:

• Use symbolic computing to derive equations and analytical models that describe your system
• Create block diagrams of complex multidomain systems
• Use finite element methods for systems described using partial differential equations

Develop Models for Domain-Specific Applications

MathWorks application-specific products let you develop mathematical models for applications in the following areas:

• Computational finance — portfolio optimization, risk estimation, and economic forecasting
• Physical modeling — mechanical, electrical, hydraulic, and drive-line systems
• Automotive — powertrain modeling and calibration
• Computational biology — gene expression analysis, sequence analysis, and pathway modeling
• Aerospace systems — environmental and aerodynamic modeling