# Examples

This section links to reproducible, runnable Phydrax examples as public [Marimo](https://marimo.io) notebooks.

## Wave Equation (1D)

A tutorial notebook showing PCI enforced overlays, latent-factorized modeling, and efficient JVP-based differential operators for the 1D wave equation, with comparisons to the [Nvidia PhysicsNeMo](https://docs.nvidia.com/physicsnemo/latest/physicsnemo-sym/user_guide/foundational/1d_wave_equation.html) implementation.

- Public notebook: [wave1d](https://static.marimo.app/static/wave1d-ul81)

## Coupled Spring-Mass ODE

A benchmark notebook for the coupled 3-DOF spring-mass system in matrix form, with normalized-time training, exact initial-condition enforcement, and comparison context against the [NVIDIA PhysicsNeMo spring-mass example](https://docs.nvidia.com/physicsnemo/25.11/physicsnemo-sym/user_guide/foundational/ode_spring_mass.html).

- Public notebook: [spring-mass-ode](https://static.marimo.app/static/spring-mass-ode-xuq3)
