The Dynamics, Data and Deep Learning Workshop will bring together academic experts and industrial practitioners to think about new ways to discover, identify and augment mathematical models of dynamic processes using data in a rigorous and explainable fashion, and will focus on recent advancements at the interface of deep learning and dynamical systems. The covered topics will include mathematical concepts such as neural differential equations, Koopman and transfer spectral theory, rough path methodologies, (variational) autoencoders, invariant foliations, dynamic mode decomposition which are supplemented by various function approximators, like neural networks, compressed tensors, compressed sensing, etc. Parameter identification methods, such as online and/or stochastic optimisation techniques, sparse regression techniques could also be discussed to improve model accuracy. The workshop will also encourage discussion on application specific issues and tricks of the trade related to various computational implementations.

Neural differential equations (NDEs) have emerged as one of the central modelling frameworks in machine learning. In scientific applications, NDEs have shown great promise due to their ability to harness both the powerful approximation capabilities of neural networks and the continuous-time modelling of differential equations. This workshop aims to facilitate discussions between NDE researchers and leading experts at the interface of scientific modelling and data-driven machine learning.

Koopman and transfer spectral theory represents finite-dimensional nonlinear dynamical systems using an infinite-dimensional linear operator. This representation potentially enables easier prediction, estimation, and control of nonlinear systems. There have been numerous theoretical and algorithmic developments over the past decade, with many real-world applications. However, there remain many challenges. A goal is to discuss ideas (and cross-fertilisation of communities) to drive future progress in this field.

Rough path theory provides mathematical and computational tools for modelling the influence of continuous-time signals on dynamical systems. In recent years, it has started to play a key role in the design of state-of-the-art machine learning algorithms for processing noisy high-dimensional data streams in a wide range of contexts including finance, data assimilation, cybersecurity and medicine. Whilst rough paths have some known interactions with NDEs, the workshop intends to bring together researchers and broaden these connections – “sowing the seeds” for future interdisciplinary research.

The workshop is being organised by:

- Maths4DL team members (Prof Chris Budd, Dr Kweku Abraham, Dr James Foster and Helena Lake)
- Dr Robert Szalai (University of Bristol)
- Prof Mark Sandler (Queen Mary University of London)
- Dr Matt Colbrook (University of Cambridge)

## Time |
## Talk / Activity |

10.00 – 10.30 | Arrival, tea & coffee and registration |

10.30 – 10.55 | The Mathematics of Complex Streamed Data – Professor Terry Lyons |

10.55 – 11.20 | A high-order numerical method for computing signature kernels – Dr Maud Lemercier |

11.20 – 11.45 | Scaling limits of random recurrent-residual neural networks – Dr Cris Salvi |

11.45 – 12.15 | Panel discussion |

12.15 – 13.15 | Lunch |

13.15 – 13.40 | Symbolic Regression via Neural Networks – Professor Jeff Moehlis |

13.40 – 14.05 | Supervised machine learning with tensor network kernel machines – Professor Kim Batselier |

14.05 – 14.30 | Nonlinear dynamics of recurrent neural network function and malfunction – Professor Peter Ashwin |

14.30 – 15.00 | Panel discussion |

15.00 – 15.20 | Coffee |

15.20 – 15.45 | Dynamic Models from Data – Professor Nathan Kutz |

15.45 – 16.10 | Dr Alex Lobbe |

16.10 – 16.40 | Panel discussion |

16.45 – 18.00 | Poster reception |

19.00 | Dinner at Côte Brasserie, Clifton. |

## Time |
## Talk / Activity |

9.00 – 9.30 | Arrival, tea & coffee |

9.30 – 9.55 | Dynamic mode decomposition for analytic interval maps – Dr Oscar Bandtlow |

9.55 – 10.20 | EDMD for expanding circle maps: spectral approximation results – Dr Julia Slipantschuk |

10.20 – 10.45 | Operator learning without the adjoint – Dr Nicolas Boullé |

10.45 – 11.30 | Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control – Professor Gustau Camps-Valls |

11.30 – 12.00 | Panel discussion |

12.00 – 13.15 | Lunch |

13.15 – 13.40 | Professor Tim Dodwell |

13.40 – 14.05 | Learning methodologies for music and audio data – Dr Emmanouil Benetos |

14.05 – 14.30 |
Rigged DMD: Data-Driven Koopman Decompositions via Generalized Eigenfunctions – Dr Catherine Drysdale |

14.30 – 14.55 | Dr Gonçalo dos Reis |

14.55 – 15.25 | Panel discussion |

15.25 – 16.00 | Coffee and finish |

Registration is now closed.

**Dinner**

The workshop dinner will take place from 7pm on Monday 25 March. The venue is Côte Brasserie, Clifton, Bristol. You will be contacted nearer the time regarding your menu choices if you selected Yes or Maybe to attend the dinner when you registered.

**Travel**

The workshop is taking place at Engineers’ House in Bristol.

Engineers’ House

The Promenade

Clifton Down

Avon

Bristol

BS8 3NB

For information on how to get there, please visit their website.

**Accommodation**

Brsitol has a wide variety of accommodation to suit all tastes and budgets. There are lots of options in and around the Clifton area where the workshop is located.

Below are a few hotels located nearby:

These hotels are located more centrally:

Delegates are required to book their own accommodation. We encourage delegates to book accommodation as early as possible.