In many engineering systems, we understand part of the physics but not all of it. There may be an unknown friction term, an unmodeled actuator lag, or a hidden coupling between thermal and electrical subsystems. That’s where Dyad Model Discovery comes in.
Our new tutorial shows how by leveraging Universal Differential Equations (UDEs), Model Discovery lets you integrate neural networks directly into your physical models, train them on data, and then recover interpretable equations from what the neural net has learned.
What You’ll Learn:
How to insert a neural network component inside a Dyad model
How to train that network using experimental data
How to extract symbolic representations of the learned dynamics
Why component-level UDEs make acausal modeling uniquely powerful
The Problem: Partial Knowledge in Engineering Models
Traditional system identification treats the model as a black box. Pure physics modeling, on the other hand, assumes everything is known. But most real-world systems sit in the middle: we know the structure, but not every term. Dyad’s UDE framework bridges this gap by embedding a neural network as a learnable part of a physics-based model.
This means you can use neural networks to learn missing dynamics between your model and experimental data. And you can do this while keeping your mass and energy conservation laws intact.
Component-Level UDEs in Dyad
In acausal modeling, each component contributes its own differential–algebraic equations (DAEs). Dyad’s UDE implementation operates before structural simplification, meaning the neural component behaves like any other block in your system.
This makes UDEs:
Modular and reusable
Compatible with hierarchical modeling
Easier to interpret after training
Once trained, you can even apply symbolic regression to the neural submodel, revealing equations that approximate what the network encoded.
Why It Matters
Dyad’s approach unifies physical insight with data-driven learning:
Engineers keep structure and interpretability
Neural networks provide flexibility and adaptation
Symbolic regression returns discoverable equations instead of black-box weights
It’s a bridge between modeling and discovery - the best of both worlds.
Closing Thoughts
Dyad’s approach unifies physical insight with data-driven learning:
Engineers keep structure and interpretability
Neural networks provide flexibility and adaptation
Symbolic regression returns discoverable equations instead of black-box weights
It’s a bridge between modeling and discovery, with the best of both worlds. By combining physics-based structure with neural flexibility, engineers can move beyond fitting data and instead reveal the missing pieces of complex systems. Whether you’re tuning a control model, studying unmodeled dynamics, or exploring data-driven design, Dyad Model Discovery turns uncertainty into insight - bridging the gap between what we know, what we measure, and what we can now learn.
Learn More
Tutorial: https://help.juliahub.com/dyad/dev/analyses/udes.html
