Books

  1. J. M. Budd and Y. van Gennip, Differential Equations and Variational Methods on Graphs: With Applications in Machine Learning and Image Analysis, to appear in Cambridge University Press.
  2. J. M. Budd and Y. van Gennip, A prolegomenon to differential equations and variational methods on graphs, Cambridge University Press (Elements in Non-local Data Interactions: Foundations and Applications), 2025.

Publications and pre-prints

  1. J. M. Budd, J. Ideami, B. M. Rynne, K. Duggar, R. Balestriero, SplInterp: Improving our Understanding and Training of Sparse Autoencoders, arXiv preprint, arXiv: 2505.11836 [cs.LG], 2025.
  2. O. Pinti, J. M. Budd, F. Hoffmann, A. A. Oberai, Graph Laplacian-based Bayesian Multi-fidelity Modeling, Comput. Methods in Appl. Mech. Eng. 435 (2025), 117647.
  3. Z. Shumaylov, J. M. Budd, S. Mukherjee, and C.-B. Schönlieb, Weakly Convex Regularisers for Inverse Problems: Convergence of Critical Points and Primal-Dual Optimisation, Forty-first International Conference on Machine Learning, 2024.
  4. Z. Shumaylov, J. M. Budd, S. Mukherjee, and C.-B. Schönlieb, Provably Convergent Data-Driven Convex-Nonconvex Regularization, NeurIPS 2023 Deep Learning and Inverse Problems Workshop, 2023.
  5. J. M. Budd, Y. van Gennip, J. Latz, S. Parisotto, and C.-B. Schönlieb, Joint reconstruction-segmentation on graphs, SIAM J. Imaging Sci. 16 (2023), pp. 911-947. Doi:10.1137/22M151546X.
  6. J. M. Budd, Theory and Applications of Differential Equation Methods for Graph-based Learning, PhD thesis, Technische Universiteit Delft (2022). Doi:10.4233/uuid:b8e0648c-d38e-4f95-bcd7-b99a943cb2d1.
  7. J. M. Budd and Y. van Gennip, Mass-conserving diffusion-based dynamics on graphs, European Journal of Applied Mathematics (2021), pp. 1–49.
  8. J. M. Budd, Y. van Gennip, and J. Latz, Classification and image processing with a semi-discrete scheme for fidelity forced Allen–Cahn on graphs, GAMM-Mitteilungen 44 (2021), e202100004.
  9. J. M. Budd and Y. van Gennip, Graph Merriman–Bence–Osher as a SemiDiscrete Implicit Euler Scheme for Graph Allen–Cahn Flow, SIAM J. Math. Anal. 52 (2020), pp. 4101–4139. Doi:10.1137/19M1277394.

Industrial Workshop Proceedings

  1. G. Oyedele, L. Schewe, J. M. Budd, D. Byrne, and X. O’Neill, Developing The Public Health Scotland Whole System Model: A Report, Mathematics in Industry Reports (2023). Doi: 10.33774/miir-2023-b53jt.
  2. J. M. Budd, R. Enguica, Y. Kim, J. Koellermeier, S. van Mourik, A. Sarkar, F. Soares, and N. Thomsen, Top Dutch Solar Racing: A novel strategy model approach for the Bridgestone World Solar Challenge, Scientific Proceedings of the 170th European Study Group Mathematics with Industry (2023).
  3. J. M. Budd, C. Dent, D. Maxwell, R. Tovey, F. G. Woodhouse, A. Wilson, and S. Zachary, The value of information in managing the electricity system, Mathematics in Industry Reports (2021). Doi: 10.33774/miir-2021-gjpjq.
  4. A. Babic, J. M. Budd, F. van de Bult, S. Cambie, T. Gomez, D. Kok, R. Lambers, Y. Murakami, L. Spek, E. te Winkel, and B. van de Wup, SWI – Tennis rating for KNLTB, Scientific Proceedings 157th European Study Group with Industry (2020).
  5. J. Field, R. Brussee, E.-J. Bakker, J. M. Budd, R. de Verclos, S. Fleuren, S. G. Riedel, E. Keizer, H. Stigter, G. ten Broeke, and M. van den Bergh, Smart Traffic: Intelligent Traffic Light Control, Proceedings of the 148th European Study Group Mathematics with Industry (2019).
  6. A. Bakhta, J. M. Budd, F. Cheriet, K. Deutscher, F. M’hiri, M. Lamoureux, and H. Wragg, Registration of Hyperspectral Images of the Retina, Proceedings: Eighth Montreal Industrial Problem Solving Workshop (2017).