Mathematical Modeling

MATLAB and Simulink for
Mathematical Modeling

Develop and optimize mathematical models of complex systems

Mathematical models are critical to understanding and accurately predicting the behavior of complex systems. These models enable critical tasks, such as:

Forecasting and optimizing system behavior
Designing control systems
Characterizing system response

MathWorks products provide all the tools you need to develop mathematical models. MATLAB^® supports both numeric and symbolic modeling approaches and provides curve fitting, statistics, optimization, ODE and PDE solving, calculus, and other core mathematical tools. Simulink^® adds an environment for modeling and simulating the behavior of multidomain systems and for developing embedded systems.

“Unlike companies that rely on off-the-shelf quantitative analysis solutions, we can see our process improving all the time. We have the flexibility to continuously improve our algorithms and models in MATLAB—and that is a big advantage.”
Willem Jellema, Robeco

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. Creating data-driven or physics-based models enable many different benefits such as extracting insight from data, informing design processes through Model-Based Design, enabling Virtual Commissioning, or creating operational digital twins.

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 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.

Learn More

Code Examples

Classical Pendulum: Some Algorithm-Related Issues Classical Pendulum: Some Algorithm-Related Issues

Explore Products

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

Learn More

Explore Products

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
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

Evaluating and Optimizing Models

After developing your model, you can exercise it under different conditions, manage and visualize simulation results, and optimize its fidelity. You can also document your work and share the model with colleagues.

Simulate your Model

Simulation lets you predict the behavior of your system for different conditions or validate your model by comparing simulation results to test data. MathWorks tools make it easy to manage all aspects of model simulation. You can:

Define the simulation conditions using DoE, probability distributions, and other test vectors
Run the simulation using world-class numeric solvers and parallel computing
Post-process results using MATLAB data analysis, data management, and visualization capabilities

Learn More

Explore Products

Optimize your Model

Once you’ve built your model, you can optimize parameters and validate the model against actual system behavior. MathWorks optimization tools let you refine a model of an existing system or optimize a new system design, by adjusting design variables to meet specific performance criteria.

Learn More

Explore Products

Document and Share your Model

With MATLAB and Simulink reporting tools you can automatically document model derivation steps and simulation results, and keep these up to date with your design. You can use MathWorks desktop and Web deployment tools to share your optimized models and associated applications with colleagues.