Topological concepts open many new horizons for photonic devices, from integrated optics to lasers. The complexity of large scale topological devices asks for an effective solution of the inverse problem: how best to engineer the topology for a specific application? We introduce a novel machine learning approach to the topological inverse problem. We train a neural network system with the band structure of the Aubry-Andre-Harper model and then adopt the network for solving the inverse problem. Our application is able to identify the parameters of a complex topological insulator in order to obtain protected edge states at target frequencies. One challenging aspect is handling the multivalued branches of the direct problem and discarding unphysical solutions. We overcome this problem by adopting a self-consistent method to only select physically relevant solutions. We demonstrate our technique in a realistic topological laser design and by resorting to the widely available open-source TensorFlow library. Our results are general and scalable to thousands of topological components. This new inverse design technique based on machine learning potentially extends the applications of topological photonics, for example, to frequency combs, quantum sources, neuromorphic computing and metrology.

# Category: Data-driven Physics

## Designing Beauty: The Art of Cellular Automata

A new book on the Game of Life, and specifically on the Art of the Game of Life has been published by Springer. Edited by A. Adamatzky and Genaro J. Martinez, the book is part of the Series on Emergence, Complexity and Computation with artistic representations from simple mathematical models at the edge of physics and biology. The book contains a chapter by C. Conti on the Enlightened Game of Life.

## Physics without equations? (school/workshop at ROME!)

**July 24 – August 4**

People think that **equations are not needed** if we have a lot of data and the way to organize them… is this true?

**Are equations useless for complex systems?**

**Are computers able to derive models for complex-systems more effectively than humans?**

We are announcing the International School and Workshop in collaboration with the University of Washington in Rome!

**Data-Driven Methods for Multi-Scale Physics and Complex Systems**

An interdisciplinary initiative aimed at committing together different disciplines with the data-driven physics!