Daniel Worrall

Digital Twins Lead, CuspAI

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Daniel Worrall
Figure 1: The author.

Abstract

I work on scientific machine learning, building high precision machine learning models that can rival and surpass classical numerical methods. On 1 December 2026 I join CuspAI as Digital Twins Lead. At Google DeepMind I worked on the discovery of unstable singularities in the equations of fluid dynamics and on AI weather prediction. Before that I worked on equivariance, normalizing flows, uncertainty quantification, combinatorial optimization, and medical imaging.

1Selected papers

Third unstable self-similar solution of the IPM equation (Fig. 2a)

Discovery of Unstable Singularities

Y Wang, M Bennani, J Martens, S Racanière, S Blackwell, A Matthews, DE Worrall, et al.

arXiv preprint, 2025

arXiv · blog · Quanta · Hannah Fry

New families of unstable self-similar solutions to fluid equations, found with physics-informed networks trained to near machine precision.

2D smoke inflow at 25, 50, 75 and 100 s: ground truth above, MP-PDE prediction below (Fig. 12)

Message Passing Neural PDE Solvers

J Brandstetter, DE Worrall, M Welling

ICLR, 2022

arXiv

A neural solver built end to end from message passing, stable over long rollouts and across PDE families.

Equivariant attention on a point cloud (Fig. 1B)

SE(3)-Transformers: 3D Roto-Translation Equivariant Attention Networks

FB Fuchs, DE Worrall, V Fischer, M Welling

NeurIPS, 2020

arXiv

Self-attention for 3D point clouds and graphs that is equivariant to rotations and translations.

Harmonic Network feature maps of an MNIST 8, arrows showing phase (Fig. 11)

Harmonic Networks: Deep Translation and Rotation Equivariance

DE Worrall, SJ Garbin, D Turmukhambetov, GJ Brostow

CVPR, 2017

arXiv

CNNs whose features rotate predictably with the input, using circular harmonic filters.

All publications and patents

2Writing

Hyper-dual numbers and higher-order derivatives2026.02.21

Extending dual numbers with multiple independent infinitesimals gives a clean, recursive route to higher-order automatic differentiation, connecting to the labeled rooted trees of Faà di Bruno’s formula.

On rooted trees and differentiation2023.11.22

The chain rule for higher order derivatives boasts a wealth of beautiful mathematical structure touching special rooted trees, group theory, integer partitions and order theory.

Dual numbers2021.08.09

A generalisation of the complex numbers where i² = 0. Evaluate a function at x + i and you can read off its derivative.

Reversible optimisers2020.12.20

Reversibility is built into many modern neural optimisers, perhaps serendipitously.

On the ‘invention’ of randomness2019.12.15

Jaynes essentially claims that randomness does not exist. After lecturing Bayesian statistics for two years, I felt confident in my understanding. It seems I was wrong.

All posts

3News

Table 1: Recent events, newest first.
DateEvent
Oct 2026I have left Google DeepMind and will be joining CuspAI as Digital Twins Lead on 1 December 2026.
Sep 2025New preprint: Discovery of Unstable Singularities. Blog · Quanta · Hannah Fry
2024New preprint: Spectral Shaping for Neural PDE Surrogates, with M. Cranmer, JN Kutz and P. Battaglia.
Apr 2023Neural Simulated Annealing published at AISTATS 2023.
Jul 2022Lecturing at the PALMS 2022 Machine Learning Summer School.
Apr 2022Joined the Weather team at DeepMind as a Senior Research Scientist.
Mar 2021Talk at the ELLIS Symposium on Geometric Deep Learning for Medical Imaging: Equivariance: Trends and Challenges. Video
Feb 2021Talk at IBM Research on Exploiting Symmetries for Deep Learning.
Sep 2020Joined Qualcomm AI Research as a Staff Engineer.
Aug 2020Lectured at the Machine Learning Summer School Indonesia.

4Career

Table 2: Positions held.
YearsPosition
Dec 2026 –Digital Twins Lead, CuspAI
2022 – 2026Senior Research Scientist, Weather team, Google DeepMind, London
2020 – 2022Staff Engineer, Machine Learning for Combinatorial Optimization, Qualcomm AI Research, Amsterdam
2018 – 2020Postdoctoral Researcher, Amsterdam Machine Learning Lab, University of Amsterdam, with Max Welling. Lectured Bayesian Statistics for ML; lab manager for the Philips Lab at UvA.
2014 – 2018PhD in Computer Vision, University College London, with Gabriel J. Brostow and Dr Clare Wilson FRCOphth
2010 – 2014MEng Engineering, Sidney Sussex College, University of Cambridge (Scholar)

5Previous masters students

  • Alessandra van Ree · Neural PDE Solvers
  • Eli de Smet · Saddle-Free Newton Descent
  • Jan Huiskes · Fast Fourier Transform Neural Networks
  • Rob Hesselink · Contrastive Equivariant Representations
  • Vivian van Oijen · Esophageal Histopathology
  • Bryan Cardenas · Esophageal Histopathology
  • Christina Winkler · Conditional Normalizing Flows
  • Nichita Diaconu · Learning Convolutions
  • Jonas M J Braun · Non-geometric Equivariance
  • Marios Fournarakis · Equivariance for Tracking
  • Tycho van der Ouderaa · Reversible Networks for Medical Imaging
  • Saki Shinoda · Semi-supervised Learning