Building Models from Data and Scientific Principles

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

When you have physical insight, you can create models from first principles using analytic or symbolic approaches. Data-driven modeling techniques are especially useful when you do not have sufficient information about your system. In this case, you can ensure model accuracy by choosing a modeling technique that is right for your experimental or historical data. Use statistics and curve fitting tools to explore relationships among your data. You can use linear and nonlinear regression models, classification, clustering, and surface fitting tools. Dynamic models that allow you to express the effect of a system’s past experiences on its current and future behavior can be modeled using neural networks and system identification techniques. Data-driven techniques can also be used to tune the coefficients of your first-principles model in order to fit experimental data using grey-box modeling and response optimization techniques.

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
• Control systems — plant modeling, controller design and verification, closed loop system simulation