Here are some recent published papers grouped roughly in three directions

Approximation Theory for deep learning

• A Brief Survey on the Approximation Theory for Sequence Modelling: In this recent review paper, we survey past and present works on the approximation theory of modelling sequential relationships, including those using recurrent networks, convolutional networks, encoder-decoder networks, and the transformers family of architectures. This should serve as a starting point for researchers who are interested in problems on the intersection of approximation theory, nonlinear dynamics and sequence modelling (chatGPT!). This is published in the newly established journal, Journal of Machine Learning.
• Forward and Inverse Approximation Theory for Linear Temporal Convolutional Networks: In this paper, we further develop the approximation theory of temporal convolutional architectures, including a refined Jackson-type estimate for the approximation error, as well as a new Bernstein-estimate. This furthers the understanding of the structural bias of temporal (dilated) convolutional networks for sequence modelling. This will be presented as an oral talk at GSI 2023.
• Approximation Analysis of Convolutional Neural Networks: In this work, we establish some approximation results for convolutional networks, paying particular attention to the compositional structure and how it can lead to (efficient) approximation. This is published in the East Asian Journal on Applied Mathematics.

Machine learning + scientific computing + control

• Principled Acceleration of Iterative Numerical Methods Using Machine Learning: In this paper, we investigate the application of meta-learning type approaches to speed up iterative algorithms in scientific computing. An example is guessing the initial condition for a Jacobi solver (say for the Poisson equation as a sub-step in a Navier-Stokes equation solver). We show that a naive application of meta-learning (MAML algorithm) does not necessarily lead to gains in performance – contrary to what has been suggested in many recent empirical works. We concretely investigate this phenomena through analytical examples, and propose principled solutions to this dilemma. This work is published in ICML 2023.
• Fairness In a Non-Stationary Environment From an Optimal Control Perspective: In this work, we connect the fairness problem in machine learning with control theory: in particular, ensuring that a machine learning model is fair to all demographic groups in a changing environment can be understood as an optimal control problem – in particular some sort of stabilisation problem. This allows us to design control strategies to promote fairness dynamically. This work is presented as a workshop paper in ICML 2023.

Machine learning + materials science

• Knowledge-integrated machine learning for materials: lessons from gameplaying and robotics: In this perspective paper, we review and envision the fusion of machine learning and materials science research, making parallels to the development of game playing and robotics. This is published in Nature Reviews Materials.
• Fast Bayesian optimization of Needle-in-a-Haystack problems using zooming memory-based initialization (ZoMBI): In this paper, we propose a modified Bayesian optimisation method that are shown to be effective for a class of optimisation problems involving the inverse design for materials discovery. This is the full publication corresponding to our earlier neurIPS workshop paper, and is now published in npj Computational Materials.
• Tackling data scarcity with transfer learning: a case study of thickness characterization from optical spectra of perovskite thin films: In this paper, we tackle the data-scarcity issue in the application of machine learning in experimental sciences. In particular, we investigate the characterisation of thickness in perovskite thin films using data-driven techniques, yielding a transfer-learning framework that can be used for more general problems. This work is published in Digital Discovery.