Where to go from here

Where to go from here#

Now that you have taken the first steps in machine learning with neural networks, what is next?

Immediate steps#

Using what you learned so far, you can directly do the following, maybe even on the basis of the code provided here:

  • speed up simulations (map initial conditions to result, map geometrical design to resulting properties, …)

  • interpret noisy measurement traces

  • recognize experimental images

  • learn resolution enhancement of images

Note that you may want to look into jax-based libraries like flax or haiku. These provide an object-oriented way to define neural networks. Even though the code for the network definition itself is not really shorter than what we did using pure jax, the parameter initialization is automatically taken care of.

Brainstorming

Think about what would be the simplest task in your own research that you could tackle using machine learning with neural networks! Good options are often: speeding up some simulation, solving an inverse problem, or analysing noisy measurement data. Think carefully about what exactly would be the input and the desired output and how you would get the training data.

Advanced topics#

I just mention a few keywords so you can look them up and learn about them. These lead to the forefront of current machine learning research.

  • use various versions of “autoencoders” to learn good compressed representations of unlabeled data

  • use “residual networks” and “U-Nets” for advanced image processing

  • use “recurrent networks” to analyze time series

  • use “graph neural networks” for input like molecular structures and other data of variable size

  • use “reinforcement learning” to discover control strategies

  • use “normalizing flows” or “diffusion models” to generate new data similar to existing data

  • use “transformers” to analyze and produce sequences with long dependencies

Two useful lecture series#

Over the years I have developed two courses dealing with machine learning for an audience of physicists. They go into much more detail than these three lessons.

Feedback and Outlook#

Feedback

If you have feedback or suggestions or notice a little bug in this online book, please use the github octocat icon at the top of the page to “open an issue” and leave a note. If you like this book, spread the word and pass along the link via social media or hand it to your friends.

Outlook

Have fun and start applying what you learned here! Maybe in the end you can also contribute to some of the long-term visions we like to think about in my group, like building an ‘artificial scientist’ that comes up with new hypotheses and is able to independently understand the world.

Visit the homepage of the theory division at the Max Planck Institute for the Science of Light. We regularly have postdoc and PhD positions available for physicists and mathematicians and computer scientists who like to work on either artificial scientific discovery or neuromorphic computing (designing novel learning machines).

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