Dyad SciML Tutorial: Model Discovery with Universal Differential Equations
Learn how to leverage Dyad's model discovery capabilities to automatically identify and complete missing physics in your engineering models using Scientific Machine Learning (SciML) and Universal Differential Equations (UDEs).
In this tutorial, you'll discover how to:
• Create a simple thermal pot model with basic physics
• Incorporate neural network components into physical models
• Train universal differential equations against experimental data
• Use symbolic regression to discover candidate physics equations
• Validate trained models against real-world measurements
This hands-on demonstration shows the complete workflow from initial model creation to physics discovery, showcasing how Dyad combines traditional physical modeling with machine learning to capture complex dynamics that are difficult to model from first principles alone.
Whether you're working on thermal systems, mechanical dynamics, or any domain where some physics may be unknown or too complex to model explicitly, this tutorial demonstrates how UDEs can help you build more accurate, data-informed models.
## Timeline
00:00 - Introduction to Model Discovery
00:29 - Setting Up the Component Library
00:42 - Installing Required Packages
01:21 - Creating the Simple Pot Model
01:43 - Understanding Model Components
02:08 - Heat Sources and Thermal Connections
03:05 - Running Initial Analysis
03:47 - Setting Up Julia Environment
04:16 - Comparing Simulation vs Experimental Data
05:57 - Identifying Missing Physics
06:29 - Creating the Thermal Neural Network Component
07:18 - Understanding Neural Network Parameters
08:01 - Defining UDE Inputs and Outputs
09:17 - Creating the Neural Pot Model
10:29 - Incorporating the Neural Network
11:44 - Setting Up Training Analysis
13:33 - Training the UDE Model
14:03 - Training Results and Convergence
14:28 - Analyzing Convergence Plots
14:52 - Evaluating Calibrated Simulation Results
15:50 - Validation Against Experimental Data
16:06 - Symbolic Regression for Physics Discovery
17:07 - Understanding UDE Analysis Results
17:31 - Interpreting Candidate Models
18:31 - Selecting Physically Meaningful Models
19:26 - Summary and Key Takeaways
## Resources
Learn more about Dyad: https://juliahub.com/products/dyad/
Dyad Documentation: https://help.juliahub.com/dyad/stable/
ModelingToolkit.jl: https://docs.sciml.ai/ModelingToolkit/stable/
DifferentialEquations.jl: https://docs.sciml.ai/DiffEqDocs/stable/
Scientific Machine Learning: https://sciml.ai/
## About JuliaHub
JuliaHub provides enterprise-grade tools for technical computing, modeling, and simulation in Julia. Dyad is our model-based systems engineering platform that combines traditional physical modeling with AI-powered workflows to accelerate engineering design and analysis.
#Dyad #JuliaLang #ScientificMachineLearning #SciML #UniversalDifferentialEquations #ModelDiscovery #PhysicsInformedML #SystemsEngineering #MBSE #NeuralODE #SymbolicRegression #JuliaHub
Learn how to leverage Dyad’s model discovery capabilities to automatically identify and complete missing physics in your engineering models using Scientific Machine Learning (SciML) and Universal Differential Equations (UDEs).
In this tutorial, you’ll discover how to:
• Create a simple thermal pot model with basic physics
• Incorporate neural network components into physical models
• Train universal differential equations against experimental data
• Use symbolic regression to discover candidate physics equations
• Validate trained models against real-world measurements
This hands-on demonstration shows the complete workflow from initial model creation to physics discovery, showcasing how Dyad combines traditional physical modeling with machine learning to capture complex dynamics that are difficult to model from first principles alone.
Whether you’re working on thermal systems, mechanical dynamics, or any domain where some physics may be unknown or too complex to model explicitly, this tutorial demonstrates how UDEs can help you build more accurate, data-informed models.
## Timeline
00:00 – Introduction to Model Discovery
00:29 – Setting Up the Component Library
00:42 – Installing Required Packages
01:21 – Creating the Simple Pot Model
01:43 – Understanding Model Components
02:08 – Heat Sources and Thermal Connections
03:05 – Running Initial Analysis
03:47 – Setting Up Julia Environment
04:16 – Comparing Simulation vs Experimental Data
05:57 – Identifying Missing Physics
06:29 – Creating the Thermal Neural Network Component
07:18 – Understanding Neural Network Parameters
08:01 – Defining UDE Inputs and Outputs
09:17 – Creating the Neural Pot Model
10:29 – Incorporating the Neural Network
11:44 – Setting Up Training Analysis
13:33 – Training the UDE Model
14:03 – Training Results and Convergence
14:28 – Analyzing Convergence Plots
14:52 – Evaluating Calibrated Simulation Results
15:50 – Validation Against Experimental Data
16:06 – Symbolic Regression for Physics Discovery
17:07 – Understanding UDE Analysis Results
17:31 – Interpreting Candidate Models
18:31 – Selecting Physically Meaningful Models
19:26 – Summary and Key Takeaways
## Resources
Learn more about Dyad: https://juliahub.com/products/dyad/
Dyad Documentation: https://help.juliahub.com/dyad/stable/
ModelingToolkit.jl: https://docs.sciml.ai/ModelingToolkit/stable/
DifferentialEquations.jl: https://docs.sciml.ai/DiffEqDocs/stable/
Scientific Machine Learning: https://sciml.ai/
## About JuliaHub
JuliaHub provides enterprise-grade tools for technical computing, modeling, and simulation in Julia. Dyad is our model-based systems engineering platform that combines traditional physical modeling with AI-powered workflows to accelerate engineering design and analysis.
#Dyad #JuliaLang #ScientificMachineLearning #SciML #UniversalDifferentialEquations #ModelDiscovery #PhysicsInformedML #SystemsEngineering #MBSE #NeuralODE #SymbolicRegression #JuliaHub
