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The modern platform for technical computing

SciML: Scientific Computing + Machine Learning = Industrial Modeling for Engineers 

Understand how robust MPC takes parameter uncertainty into account ensuring that the controller achieves good performance and constraint satisfaction despite uncertainty in the model

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Julia collaboration has taken a revolutionary leap forward with JuliaHub Projects.

Thursday, December 7th | 1:00 PM ET (US)

Introduction to ModelingToolkit for Industrial Modelers

In this hands-on webinar, our expert team will walk you through getting started with using ModelingToolkit.jl to solve real-life problems. To start we’ll show the fundamentals of defining variables, parameters, and equations to solve a steady-state nonlinear problem. Then we’ll add time to the problem to show how we can also solve a set of differential equations. ModelingToolkit.jl can be used in this way to solve a flat system of equations, however, this quickly becomes cumbersome for more complex real-life systems. Acausal Modeling is then introduced to show how complex models can be constructed by assembly of components. Components are defined using the fundamentals previously covered. Finally, with the understanding of how to build components and connect them to create systems, we’ll cover a couple of fundamental industrial examples, such as a DC motor and Mass-Spring-Damper.

ModelingToolkit.jl is an open-source symbolic-numeric modeling Julia package. It combines some of the features from symbolic computing packages like SymPy or Mathematica with the ideas of equation-based modeling systems like the causal Simulink and the acausal Modelica. It bridges the gap between many different kinds of equations, allowing one to quickly and easily transform systems of DAEs into optimization problems, or vice-versa, and then simplify and parallelize the resulting expressions before generating code.

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Meet Your Speaker

MIke Tiller

Michael Tiller

Senior Director of Product Management for JuliaSim
Michael Tiller holds a PhD in Mechanical Engineering from the University of Illinois at Urbana-Champaign.  He is currently the Senior Director of Product Management for JuliaHub's JuliaSim product.  Before joining JuliaHub, Dr. Tiller worked for Ford Motor Company, LMS and Dassault Systèmes.  He was the Founder at Xogeny (later acquired by Ricardo) and was most recently the CTO of Realis Simulation.  He is the author of two textbooks on modeling of physical systems.
Brad Carman

Brad Carman

Director of Consulting 
Brad Carman served as a Mechanical Engineer at Instron specializing in System Modeling with focus on model and software development for the Crash Simulation system.  Recently Carman has joined JuliaHub to lead the Consulting team.


JuliaSim Control 

  • Model-predictive control (MPC) for linear and nonlinear systems

  • Robust MPC for uncertain systems

  • GUI apps for autotuning and model reduction

  • PID autotuning to automate workflows and quickly tune PID controllers

Model Discovery

Combine models with tools like DiffEqFlux and NeuralPDE to discover missing physics and generate digital twins.

Combine with Pre-Built Models and Digital Twins

Grab complete models from the JuliaSim Model Store and compose the pieces to accelerate the design process.

Specialized Numerical Environments

Use the latest numerical tools, like discontinuity-aware differential equation solvers, high-performance steady state solvers, and domain-specific environments.

Blending classical physical modeling with modern Scientific Machine Learning techniques.


JuliaSim is a next generation cloud-based simulation platform, combining the latest techniques in Scientific Machine Learning with equation-based digital twin modeling and simulation. Our modern ML-based techniques accelerate simulation by up to 500x, changing the paradigm of what is possible with computational design. The premise of the software is to facilitate the design and accelerate challenging real-life models of considerable complexity.


JuliaSim allows the user to import models directly from the Model Store (more information below) into the Julia environment, making it easy to build large complex simulations. The user-friendly GUI facilitates the process and makes simulation more accessible to a wider audience.


JuliaSim produces surrogates of blackbox (and regular) dynamical systems using Continuous Time Echo State Networks (CTESNs). This novel technique allows, amongst other features, for implicit training in parameter space to stabilize the ill-conditioning present in stiff systems.

Learn more about the JuliaSim Ecosystem

Julia Computing delivers JuliaSim as an answer to accelerating simulations through digital-twin (or surrogate) modeling. By blending classical, physical modeling with advanced scientific machine learning (SciML) techniques, JuliaSim provides a next-generation platform for building, accelerating, and analyzing models.