Simple implementation of Deep Operator Networks (DeepONets) in the JAX deep learning framework together with Equinox.
This is a simple tutorial that uses the aligned antiderivative dataset of the tutorial of the DeepXDE library.
📺 Here you can find a video with detailed explanations to code along.
💽 Want more Machine Learning & Simulation? Check out this repo with more codes and handwritten notes.
Deep Operator Networks are neural operators that do not return the full output field of the operator but allow to query it at arbitrary coordinates (both in space and time, if applicable). As such, they are different from, e.g., Fourier Neural Operators.
To do so, the input field and the query coordinate are mapped to a latent representation via a branch and a trunk net, respectively. Ultimately, the output at the query coordinate is found as the inner product of the two latent vectors.
Implementing DeepONets in JAX & Equinox is fantastic because we design them
single batch (one input field & one query coordinate). Then we can use JAX'
automatic vectorization (via jax.vmap) to get more evaluation formats for
free.