The Dynamics, Data and Deep Learning Workshop brought 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 focussed on recent advancements at the interface of deep learning and dynamical systems. The covered topics included 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 were also discussed to improve model accuracy. The workshop also encouraged 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 continuoustime modelling of differential equations. This workshop aimed to facilitate discussions between NDE researchers and leading experts at the interface of scientific modelling and datadriven machine learning.
Koopman and transfer spectral theory represents finitedimensional nonlinear dynamical systems using an infinitedimensional 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 realworld applications. However, there remain many challenges. A goal was to discuss ideas (and crossfertilisation of communities) to drive future progress in this field.
Rough path theory provides mathematical and computational tools for modelling the influence of continuoustime signals on dynamical systems. In recent years, it has started to play a key role in the design of stateoftheart machine learning algorithms for processing noisy highdimensional 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 intended to bring together researchers and broaden these connections – “sowing the seeds” for future interdisciplinary research.
The workshop was organised by:
Time 
Talk / Activity 
Speaker 
10.00 – 10.25  Arrival, tea & coffee and registration  
10.25 – 10.30  Welcome and Introduction  Prof Chris Budd, University of Bath 
10.30 – 12.15  Session 1 – Rough paths theme  Chaired by Dr James Foster, University of Bath 
10.30 – 10.55  The Mathematics of Complex Streamed Data  Professor Terry Lyons, University of Oxford 
10.55 – 11.20  A highorder numerical method for computing signature kernels  Dr Maud Lemercier, University of Oxford 
11.20 – 11.45  Scaling limits of random recurrentresidual neural networks  Dr Cris Salvi, Imperial College London 
11.45 – 12.15  Panel discussion  
12.15 – 13.15  Lunch  
13.15 – 15.00  Session 2 – Neural networks and kernels theme  Chaired by Dr Robert Szalai, University of Bristol 
13.15 – 13.40  Symbolic Regression via Neural Networks  Professor Jeff Moehlis, University of California, Santa Barbara 
13.40 – 14.05  Supervised machine learning with tensor network kernel machines  Professor Kim Batselier, Delft University of Technology 
14.05 – 14.30  Nonlinear dynamics of recurrent neural network function and malfunction  Professor Peter Ashwin, University of Exeter 
14.30 – 15.00  Panel discussion  
15.00 – 15.20  Coffee  
15.20 – 16.40  Session 3 – Applications theme (a)  Chaired by Dr Kweku Abraham, University of Cambridge 
15.20 – 15.45  Dynamic Models from Data  Professor Nathan Kutz, University of Washington 
15.45 – 16.10  Generative Modelling of Stochastic Parametrisations for Geophysical Fluid Dynamics  Dr Alex Lobbe, Imperial College London 
16.10 – 16.40  Panel discussion  
16.45 – 18.00  Poster reception  
19.00  Dinner at Côte Brasserie, Clifton. 
Time 
Talk / Activity 
Speaker 
9.00 – 9.30  Arrival, tea & coffee  
9.30 – 12.00  Session 4 – Operator learning theme  Chaired by Dr Matt Colbrook, University of Cambridge 
9.30 – 9.55  Dynamic mode decomposition for analytic interval maps  Dr Oscar Bandtlow, Queen Mary University London 
9.55 – 10.20  EDMD for expanding circle maps: spectral approximation results  Dr Julia Slipantschuk, University of Warwick 
10.20 – 10.45  Operator learning without the adjoint –  Dr Nicolas Boullé, University of Cambridge 
10.45 – 11.30  Analyzing Climate Scenarios Using Dynamic Mode Decomposition With Control  Dr Nathan Mankovich, University of Valencia 
11.30 – 12.00  Panel discussion  
12.00 – 13.15  Lunch  
13.15 – 15.25  Session 5 – Applications theme (b)  Chaired by Prof Mark Sandler, Queen Mary University London 
13.15 – 13.40  Machine learning reduced order models  Dr Robert Szalai, University of Bristol 
13.40 – 14.05  Learning methodologies for music and audio data  Dr Emmanouil Benetos, Queen Mary University London 
14.05 – 14.30  Rigged DMD: DataDriven Koopman Decompositions via Generalized Eigenfunctions  Dr Catherine Drysdale, University of Birmingham 
14.30 – 15.25 
Applications of path Signature methods to electric battery lifetime prognostics 
Dr Gonçalo dos Reis, University of Edinburgh 
15.25 – 15.55 
Panel discussion 

15.55 – 16.20  Coffee and finish 
University of Edinburgh
The Path signature is a rich mathematical structure originating from the field of rough path theory. It is characterized by the ability to extract highlevel information from a stream of data using a few summary parameters, which can then be used as features for a machine learning model.
In this talk, we overview recent applications of path signature methods in te development of lifetime predictor models for electric batteries. We present our findings as two engineering use cases. From a mathematical point of view, our results are achieved by leveraging key properties of path signatures: signature invariance under time reparametrizations, and to use the signature’s rich expressivity inside a Markovian model to model the highly nonlinear nonMarkovian degration of electric batteries.
These are joint research works with: R. Ibraheem (UoE), Y. Wu (Strathclyde), T. Lyons (Oxford), P. Dechent (Aachen–Oxford).
#1 Ibraheem, R., Wu, Y., Lyons, T. and Dos Reis, G., 2023. Early prediction of Lithiumion cell degradation trajectories using signatures of voltage curves up to 4minute subsampling rates. Applied Energy, 352, p.121974. https://doi.org/10.1016/j.apenergy.2023.121974
#2 “Path SignatureBased Life Prognostics of Liion Battery Using Pulse Test Data”,
Rasheed Ibraheem, Philipp Dechent, Goncalo dos Reis, 2024 Mar, Preprint
Registration is now closed.
Dinner
The workshop dinner took place on Monday 25 March at Côte Brasserie, Clifton, Bristol.
Travel
The workshop took 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: