Wolfram Technologies in
Physical Sciences

Represent the world for symbolic and numeric computation. Use powerful solvers, create stunning visualizations, leverage curated data and create models within an interactive notebook interface.

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Exact Symbolic Computation

Use built-in knowledge of special functions, differential equations, linear systems, asymptotics, geometry, statistical distributions and more to obtain exact symbolic results. Discover ground-truth results by building your own techniques on top of powerful and flexible functions.

Calculus and Algebra

Guide to Differential Equations

Guide to Special Functions

Numerical Computation

Evaluate expressions to specified numerical precision. Solve PDEs, find global and local extrema, and compute geometric meshes even when exact solution methods are unknown.

Optimization

Geometric Computation

Guide to Numerical Evaluation & Precision

Powerful Visualization

Simplify and automate the creation of publication-ready graphics. Visualize vector data, complex functions, volumetric data and geospatial data using functions tightly integrated with specialized functionality.

Visualization

Guide to Function Visualization

Guide to Data Visualization

PDE Numerical Solutions

Discover functions for easily specifying PDE components, generating meshes and computing over a mesh. Quantitatively analyze your designs and solve problems in domains from acoustics to nonlinear quantum mechanics. Experts can programmatically control every part of the solution process so that you can customize the algorithm you need.

Finite Element Methods

Finite Element Method User Guide

PDE Models Overview

Magnetic Potential inside an Electric Motor

Model Fitting and Statistical Analysis

Define quantitative models, process data and use built-in knowledge of statistical distributions to create and validate physical models. Use well-known models or define your own using the expressive syntax of Wolfram Language.

Fit and Analyze Models

Guide to Scientific Data Analysis

Functions for Diverse Model Types

Guide to Hypothesis Tests

Quantum Theory and Computation

Use built-in mathematical knowledge and special functions for studying continuum quantum systems. Adopt a streamlined framework for quantum circuits and other finite-dimensional quantum systems. Compare exact symbolic calculations to results from numerical simulations and real quantum hardware in a unified, functional style.

Wolfram Quantum Framework

Mathematical Functions for Quantum Mechanics

Query Quantum Processing Units

Support for Package Development

Functional programming design principles and easy context management allow you to build specialized functionality for your particular domain. From high-energy physics to quantitative MRI analysis, experts choose to build packages for their community and quickly prototype workflows using Wolfram Language.

xAct for Tensors

SmeftFR for Standard Model Effective Field Theory

QuESTlink for Quantum Computation

LieART for Lie Algebras and Representation Theory

QMRITools for Quantitative MRI

Stochastic Processes and Distributions

Wolfram Language has built-in knowledge of stochastic differential equations, matrix distributions, all common special classes of random processes and methods for spatial estimation. Processes and distributions can be quickly specified and derived properties computed automatically. You can also solve the inverse problem: estimating processes and distributions from data.

Guide to Stochastic Differential Equations

Guide to Matrix Distributions

Guide to Random Processes

Guide to Spatial Statistics

Dimensional Analysis and Units

Compute with data that has unit and uncertainty information. Real-world applications require converting between unit systems and propagating uncertainties through your computations. Use built-in knowledge of physical constants, units, uncertainty and dimensional analysis to easily connect mathematical models with the world.

Guide to Units and Quantities

Find Canonical Units

Nondimensional Form of Black Hole Surface Gravity

Graph Computations, Network Analysis and Clustering

Graphs, as purely mathematical objects or as representations of real-world networks, can be easily specified and graph properties efficiently computed. Algorithms for common problems like finding a shortest path, Hamiltonian cycles and postman tours are built in. Find communities and clusters within data. Specify method options like the distance metric from scratch or from common built-in options for your convenience.

Guide to Graphs & Networks

Guide to Cluster Analysis

Guide to Distance and Similarity Measures

Curated Data

From geospatial data to thousands of specific domains, use curated datasets as part of your next project. The the Wolfram Knowledgebase behind Wolfram|Alpha can be programmatically accessed and used by the entire Wolfram Language.

Guide to Knowledge Representation & Access

Guide to Engineering Data

Guide to Wolfram|Alpha Integration

Integrated Audio, Video and Machine Learning

Turn raw audio and video data into computed measurements. Machine learning models are integrated into many built-in functions. Use image processing techniques or train your own models to turn raw data into computable datasets.

Classification Example Gallery

Segment an Image to View Fluorescent Uptake of Cells

Use Image Processing to Identify Blood Cells

Control Systems

Use Wolfram Language from modeling to design to deployment. Work with PID controllers, LQ optimization methods and MPCs. Model systems with delays and important nonlinear dynamics. Deploy to physical microcontrollers or as an FMU.

Wolfram Control Systems

Guide to Control Systems

Guide to System Model Analytics & Design

Community of Researchers

Wolfram has been trusted by the research community for over 35 years. Share results, exchange programming tips and network. Resources such as Wolfram Community and Mathematica Stack Exchange give organized forums, while you can informally publish a notebook to the cloud for easy sharing.

Community Group for Publication Materials

Kerr Geodesics in Terms of Weierstrass Elliptic Functions

Quantitatively Visualizing Bipartite Datasets

Koopman Analysis of the Periodic Korteweg–De Vries Equation

Solar Temperature Variations Computed from SORCE SIM Irradiances Observed During 2003–2020

Machine Learning Regression Analysis for Hypothesis Generation in Physical Chemistry Lab

Wolfram Technologies in your industry

Key New Features

Connect to generative AI models for code assistance or content generation.
Built-in functions for line, surface and contour integrals.
Updates and improvements to numeric solvers.
Compute and solve over finite fields.

More functionality for specifying computations in astronomy, chemistry and biology.
Easily specify parameters in PDE components in domains from mechanics to electrostatics to quantum mechanics.
Streamlined support for integrating other languages.
Easy sharing of packages and functions with the wider community.

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Mathematica

Mathematica is the world's ultimate system for modern technical computing and the only platform fully integrating computation into complete workflows.

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Wolfram Language

Wolfram Language, the core technology underlying Mathematica, is unique in combining a symbolic paradigm, built-in algorithms and curated knowledge for scalable, highly automated computation and deployment.

Wolfram|Alpha

Use Wolfram's extensive, curated data in many fields—all ready to compute and accessible via linguistic interface.

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images and data

Wolfram Knowledgebase

The world's largest and broadest repository of curated data for computation, testing and analysis, powering Wolfram|Alpha and Wolfram Language.

Wolfram System Modeler

Bring Wolfram-powered integrated design optimization to modeling and simulation of large-scale engineering and other systems.

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Wolfram Resource System

Immediately search for and access user-contributed data, functions, packages and more for use in technical presentations and publications, or add your own resources for public or private sharing and collaboration.

Resources

Community

Join us! Wolfram Community is a platform for questions and answers, idea sharing and discussions about all of our technologies—including Mathematica, System Modeler, Wolfram|Alpha and all the rest!

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Learn With Our Experts

Wolfram U offers quick-start and in-depth courses on demand as well as scheduled live courses about Wolfram technologies, deep learning, image and signal processing, modeling and simulation and other computational topics. Or you can learn at your own pace with one of our acclaimed books.

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