Here is a list of my academic publications. See my Google Scholar page for further details. You can also read about some highlights from my research.
Submitted publications and preprints
- (2023). How adversarial attacks can disrupt seemingly stable accurate classifiers, arxiv:2309.03665
- (2022). Towards a mathematical understanding of learning from few examples with nonlinear feature maps, arXiv:2211.03607
- (2022). Efficient high-order space-angle-energy polytopic discontinuous Galerkin finite element methods for linear Boltzmann transport, arxiv:2304.09592
Peer reviewed publications
- (2023). The boundaries of verifiable accuracy, robustness, and generalisation in deep learning, International Conference on Artificial Neural Networks (ICANN) 2023 vol 14254, pp 530-541, Springer, Cham
- (2023). Relative intrinsic dimensionality is intrinsic to learning, International Conference on Artificial Neural Networks (ICANN) 2023 vol 14254, pp 516-529, Springer, Cham
- (2023). A geometric view on the role of nonlinear feature maps in few-shot learning, Geometric Science of Information (GSI) 2023 vol 14071, pp 560-568, Springer, Cham
- (2023). Learning from few examples with nonlinear feature maps, Science and Information Conference (2023) vol 711, pp 210-225, Springer, Cham. Winner of best paper award
- (2023). Neuromorphic tuning of feature spaces to overcome the challenge of low-sample high-dimensional data, International Joint Conference on Neural Networks (IJCNN) 2023 IEEE
- (2021). Residual-based a posteriori error estimates for hp-discontinuous Galerkin discretisations of the biharmonic problem, SIAM Journal on Numerical Analysis 59 (3) 1273-1298
- (2021). Adaptive non-hierarchical Galerkin methods for parabolic problems with application to moving mesh and virtual element methods, Mathematical Models and Methods in Applied Sciences 31 (4) 711-751
- (2020). Long-time L∞(L2) a posteriori error estimates for fully discrete parabolic problems, IMA Journal of Numerical Analysis Volume 40, Issue 1, 498–529.
- (2018). Revealing new dynamical patterns in a reaction-diffusion model with cyclic competition via a novel computational framework, Proceedings of the Royal Society A 474 20170608
- (2017). The virtual element method in 50 lines of MATLAB, Numerical Algorithms 75(4), 1141-1159 The full code is available on GitHub.
- (2017). A posteriori error estimates for the virtual element method, Numerische Mathematik 137(4), 857-893
- (2017). Conforming and nonconforming virtual element methods for elliptic problems, IMA Journal of Numerical Analysis 37(3), 1317-1354
- (2017). Virtual element methods for elliptic problems on polygonal meshes, K. Hormann and N. Sukumar, ed., Generalized Barycentric Coordinates in Computer Graphics and Computational Mechanics 1st ed. CRC Press
- (2017). Virtual element methods, PhD Thesis, University of Leicester
- (2014). The Conforming Virtual Element Method for the convection-diffusion-reaction equation with variable coefficients, Technical report LA-UR-14-27710, Los Alamos National Laboratory
- (2014). Numerical results using the conforming VEM for the convection-diffusion-reaction equation with variable coefficients, Technical report LA-UR-14-27709, Los Alamos National Laboratory