K. C. Zygalakis

Publications

Konstantinos C. Zygalakis · School of Mathematics, University of Edinburgh

Preprints

  1. I. Almuslimani, G. Vilmart, K.C. Zygalakis. Explicit stabilized implementation of singly diagonally implicit Runge-Kutta methods. 2026.arXiv
  2. P. Dobson, J.M. Sanz-Serna, K.C. Zygalakis. Optimal scaling of MCMC algorithms: exploiting the symmetry of the Metropolis-Hastings formula. 2026.arXiv
  3. C.J. Beltran, A. Teckentrup, A. Vergari, K.C. Zygalakis. Neural network surrogates with uncertainty quantification for inverse problems in partial differential equations. 2026.arXiv
  4. J. Spence, T.I. Liaudat, K.C. Zygalakis, M. Pereyra. Deep unfolding of MCMC kernels: scalable, modular & explainable GANs for high-dimensional posterior sampling. 2026.arXiv
  5. Y. Xi, K.C. Zygalakis, M. Pereyra. Hypothesis Testing in Imaging Inverse Problems. 2026.arXiv
  6. H. Maskan, K.C. Zygalakis, A. Eftekhari, A. Yurtsever. A Unified Model for High-Resolution ODEs: New Insights on Accelerated Methods. 2026.arXiv

Published in refereed journals & conferences

  1. J.T. Demano, P. Dobson, K.C. Zygalakis. Piecewise Deterministic Sampling for Constrained Distributions. Statistics and Computing, 2026.arXiv
  2. P. Dobson, J.M. Sanz-Serna, K.C. Zygalakis. Accelerated optimization algorithms and ordinary differential equations: the convex non-Euclidean case. BIT Numerical Mathematics, 66(2):35, 2026.arXiv
  3. T. Klatzer, S. Melidonis, M. Pereyra, K.C. Zygalakis. Efficient Bayesian computation using plug & play priors for Poisson inverse problems. SIAM Journal on Imaging Sciences, 19(2):1325--1363, 2026.arXiv
  4. E. Crovini, S. Cotter, K.C. Zygalakis, A. Duncan. Batch Bayesian Optimization via Particle Gradient Flows. SIAM/ASA Journal on Uncertainty Quantification, 14(1):197--220, 2026.arXiv
  5. H.A. Abdul-Lateef, M. Pereyra, L. Shaw, K.C. Zygalakis. Bayesian computation with generative diffusion models by Multilevel Monte Carlo. Philosophical Transactions of the Royal Society A, 383:20240333, 2025.arXiv
  6. S. Melidonis, Y. Xi, K.C. Zygalakis, Y. Altmann, M. Pereyra. Score-Based Denoising Diffusion Models for Photon-Starved Image Restoration Problems. Transactions on Machine Learning Research, 2835--8856, 2025.link
  7. P. Dobson, J.M. Sanz-Serna, K.C. Zygalakis. On the connections between optimization algorithms, Lyapunov functions, and differential equations: theory and insights. SIAM Journal on Optimization, 35(1):537--566, 2025.arXiv
  8. C. Tarpau, M. Fang, K.C. Zygalakis, M. Pereyra, A. Di Fulvio, Y. Altmann. Statistical modelling and Bayesian inversion for a Compton imaging system: application to radioactive source localization. Inverse Problems, 40:125028, 2024.DOI · arXiv
  9. T.T. Trindade, K.C. Zygalakis. A hybrid tau-leap for simulating chemical kinetics with applications to parameter estimation. Royal Society Open Science, 11:240157, 2024.DOI · arXiv
  10. T. Bai, A. Teckentrup, K.C. Zygalakis. Gaussian processes for Bayesian inverse problems associated with linear partial differential equations. Statistics and Computing, 34:139, 2024.arXiv
  11. X. Gong, D.J. Higham, K.C. Zygalakis, G. Bianconi. Higher-order Connection Laplacians for Directed Simplicial Complexes. Journal of Physics: Complexity, 5:015022, 2024.arXiv
  12. C.J. Beltran, A. Vergari, A. Teckentrup, K.C. Zygalakis. Galerkin meets Laplace: Fast uncertainty estimation in neural PDEs. ICLR 2024 Workshop on AI4DifferentialEquations In Science, 2024.link
  13. S.D. Giovacchino, D.J. Higham, K.C. Zygalakis. Backward error analysis and the qualitative behaviour of stochastic optimization algorithms: Application to stochastic coordinate descent. Journal of Computational Dynamics, 11(4):453--467, 2024.arXiv
  14. S. Melidonis, M. Holden, M. Pereyra, K.C. Zygalakis, Y. Altmann. Empirical Bayesian Imaging with Large-Scale Push-Forward Generative Priors. IEEE Signal Processing Letters, 31:631--635, 2024.link
  15. T. Klatzer, P. Dobson, Y. Altmann, M. Pereyra, J.M. Sanz-Serna, K.C. Zygalakis. Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling. SIAM Journal on Imaging Sciences, 17(2):1078--1117, 2024.arXiv
  16. T. Helin, A.M. Stuart, A. Teckentrup, K.C. Zygalakis. Introduction to Gaussian Process Regression In Bayesian Inverse Problems, With New Results On Experimental Design For Weighted Error Measures. Monte Carlo and Quasi-Monte Carlo Methods 2022, Springer Verlag, 2022.arXiv
  17. H. Maskan, K.C. Zygalakis, A. Yurtsever. A Variational Perspective on High-Resolution ODEs. Advances in Neural Information Processing Systems, 2023.arXiv
  18. O.M. Crook, M. Cucuringu, T. Hurst, C.-B. Schönlieb, M. Thorpe, K.C. Zygalakis. A Linear Transportation Lp Distance for Pattern Recognition. Pattern Recognition, 147:110080, 2024.arXiv
  19. S. Melidonis, P. Dobson, Y. Altmann, M. Pereyra, K.C. Zygalakis. Efficient Bayesian computation for low-photon imaging problems. SIAM Journal on Imaging Sciences, 16(3):1197--1236, 2023.DOI · arXiv
  20. L. Vargas, M. Pereyra, K.C. Zygalakis. The split Gibbs sampler revisited: improvements to its algorithmic structure and augmented target distribution. SIAM Journal on Imaging Sciences, 16(4):2040--2071, 2023.arXiv
  21. A. Eftekhari, L. Vargas, K.C. Zygalakis. The Forward-Backward Envelope for Sampling with the Overdamped Langevin Algorithm. Statistics and Computing, 33(4):85, 2023.arXiv
  22. X. Gong, D.J. Higham, K.C. Zygalakis. Generative Hypergraph Models and Spectral Embedding. Scientific Reports, 13:540, 2023.DOI · arXiv
  23. S.D. Giovacchino, D.J. Higham, K.C. Zygalakis. A Hierarchy of Network Models Giving Bistability Under Triadic Closure. SIAM Multiscale Modeling & Simulation, 20:1394--1410, 2022.arXiv
  24. M. Holden, M. Pereyra, K.C. Zygalakis. Bayesian Imaging With Data-Driven Priors Encoded by Neural Networks. SIAM Journal on Imaging Sciences, 15(2):892--924, 2022.arXiv
  25. J.M. Sanz Serna, K.C. Zygalakis. Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations. Journal of Machine Learning Research, 22:1--37, 2021.link
  26. X. Gong, D.J. Higham, K.C. Zygalakis. Directed Network Laplacians and Random Graph Models. Royal Society Open Science, 8:211144, 2021.DOI · arXiv
  27. J.M. Sanz Serna, K.C. Zygalakis. The connections between Lyapunov functions for some optimization algorithms and differential equations. SIAM Journal on Numerical Analysis, 59(3):1542--1565, 2021.DOI · arXiv
  28. A. Eftekhari, B. Vandereycken, G. Vilmart, K.C. Zygalakis. Explicit Stabilised Gradient Descent for Faster Strongly Convex Optimisation. BIT Numerical Mathematics, 61:119--139, 2021.DOI · arXiv
  29. C.A. Yates, A.B. Duncan, A. Jordana, C. Smith, A. George, K.C. Zygalakis. A hybrid framework for the simulation of stochastic reaction-diffusion processes. Journal of the Royal Society Interface, 17:20200563, 2020.DOI · arXiv
  30. L. Vargas, M. Pereyra, K.C. Zygalakis. Accelerating proximal Markov Chain Monte Carlo by using explicit stabilised methods. SIAM Journal on Imaging Sciences, 13(2):905--935, 2020.DOI · arXiv
  31. J.M. Sanz Serna, K.C. Zygalakis. Contractivity of Runge-Kutta methods for convex gradient systems. SIAM Journal on Numerical Analysis, 58(4):2079--2092, 2020.DOI · arXiv
  32. L. Szpruch, S. Vollmer, K.C. Zygalakis, M.B. Giles. Multi Level Monte Carlo methods for a class of ergodic stochastic differential equations. Statistics and Computing, 30:507--524, 2020.DOI
  33. A.L. Bertozzi, X. Luo, A.M. Stuart, K.C. Zygalakis. Uncertainty Quantification in the Classification of High Dimensional Data. SIAM/ASA Journal on Uncertainty Quantification, 6(2):568--595, 2018.DOI
  34. T. Plesa, K.C. Zygalakis, D.F. Anderson, R. Erban. Noise control for molecular computing. Journal of the Royal Society Interface, 15(144):20180199, 2018.DOI
  35. S.D. Keyes, K.C. Zygalakis, T. Roose. An explicit structural model of micro-scale root-hair and rhizosphere interactions parameterized by synchrotron X-ray computed tomography. Bulletin of Mathematical Biology, 79:2785--2813, 2017.DOI
  36. S. Kontogeorgaki, R.J. Sanchez-Garcia, R.M. Ewing, K.C. Zygalakis, B.D. MacArthur. Noise-processing by signalling networks. Scientific Reports, 532, 2017.DOI
  37. A. Durmus, G.O. Roberts, G. Vilmart, K.C. Zygalakis. Fast Langevin based algorithm for MCMC in high dimensions. Annals of Applied Probability, 27(4):2195--2237, 2017.DOI
  38. A. Duncan, R. Erban, K.C. Zygalakis. Hybrid framework for the simulation of stochastic chemical kinetics. Journal of Computational Physics, 326:398--419, 2016.DOI
  39. O. Teymour, K.C. Zygalakis, B. Carlderhead. Probabilistic Linear Multistep Methods. Advances in Neural Information Processing Systems 29, 4321--4328, 2016.link
  40. J. Heppell, S. Payvandi, P. Talboys, K.C. Zygalakis, D. Langton, R. Sylvester-Bradley, R. Walker, D.L. Jones, T. Roose. Use of a coupled soil-root-leaf model to optimise phosphate fertiliser use efficiency in barley. Plant and Soil, 406(1--2):341--357, 2016.DOI
  41. P.R. Conrad, M. Girolami, S. Sarkka, A.M. Stuart, K.C. Zygalakis. Statistical analysis of differential equations: introducing probability measures on numerical solutions. Statistics and Computing, 27(4):1065--1082, 2017.DOI
  42. P.M. Goggin, K.C. Zygalakis, R.O.C. Oreffo, P. Schneider. High-resolution 3D imaging of osteocytes and computational modelling in mechanobiology: Insights on bone development, ageing, health and disease. European Cells and Materials, 31:264--295, 2016.DOI
  43. S.J. Vollmer, K.C. Zygalakis, Y.W. Teh. Exploration of the (Non-)asymptotic Bias and Variance of Stochastic Gradient Langevin Dynamics. Journal of Machine Learning Research, 17(159):1--48, 2016.link
  44. J. Heppell, S. Payvandi, P. Talboys, K.C. Zygalakis, J. Fliege, D. Langton, R. Sylvester-Bradley, R. Walker, D.L. Jones, T. Roose. Modelling the optimal phosphate fertiliser and soil management strategy for crops. Plant and Soil, 401(1):135--149, 2016.DOI
  45. S. Ridden, K.C. Zygalakis, B.D. MacArthur. Bet-hedging and collective decision-making by mammalian progenitor cells. Physical Review Letters, 115:208103, 2015.DOI
  46. A. Abdulle, G. Vilmart, K.C. Zygalakis. Long time accuracy of Lie-Trotter splitting methods for Langevin dynamics. SIAM Journal on Numerical Analysis, 53(1):1--16, 2015.DOI
  47. J. Heppell, P. Talboys, S. Payvandi, K.C. Zygalakis, J. Fliege, P. Withers, D.L. Jones, T. Roose. How changing root system architecture can help tackle a reduction in soil phosphate (P) levels for better plant P acquisition. Plant, Cell & Environment, 38:118--128, 2015.DOI
  48. S. Payvandi, K.R. Daly, K.C. Zygalakis, T. Roose. Modelling the effects of diffusion on phloem flow. Bulletin of Mathematical Biology, 76:2834--2865, 2014.DOI
  49. T. Székely, K. Burrage, K.C. Zygalakis, M. Barrio. Efficient simulation of stochastic chemical kinetics with the stochastic Bulirsch-Stöer method. BMC Systems Biology, 8(1):71, 2014.DOI
  50. A. Abdulle, G. Vilmart, K.C. Zygalakis. High order numerical approximation of the invariant measure of ergodic SDEs. SIAM Journal on Numerical Analysis, 52(4):1600--1622, 2014.DOI
  51. J. Heppell, S. Payvandi, K.C. Zygalakis, J. Smethurst, J. Fliege, T. Roose. Validation of a spatial-temporal soil water movement and plant water uptake model. Géotechnique, 64:526--539, 2014.DOI
  52. S. Payvandi, K.R. Daly, D.L. Jones, P. Talboys, K.C. Zygalakis, T. Roose. A mathematical model of water and nutrient transport in xylem vessels of a wheat plant. Bulletin of Mathematical Biology, 76:566--596, 2014.DOI
  53. A. Abdulle, G. Vilmart, K.C. Zygalakis. Second weak order explicit stabilized methods for stiff stochastic differential equations. SIAM Journal on Scientific Computing, 35(4):A1792--A1814, 2013.DOI
  54. D. Blömker, K. Law, A.M. Stuart, K.C. Zygalakis. Accuracy and stability of the continuous-time 3DVAR filter for the Navier-Stokes equation. Nonlinearity, 26:2193--2219, 2013.DOI
  55. A. Abdulle, G. Vilmart, K.C. Zygalakis. Mean-square A-stable diagonally drift-implicit integrators of weak second order for stiff Itô stochastic differential equations. BIT Numerical Mathematics, 53(4):827--840, 2013.DOI
  56. G. Iyer, K.C. Zygalakis. Numerical studies of homogenization under a fast cellular flow. SIAM Multiscale Modeling & Simulation, 10(3):1046--1058, 2012.DOI
  57. T. Székely, K. Burrage, R. Erban, K.C. Zygalakis. Higher-order numerical methods for stochastic simulation of chemical reaction systems. BMC Systems Biology, 6:85, 2012.DOI
  58. A. Abdulle, D. Cohen, G. Vilmart, K.C. Zygalakis. High order weak methods for stochastic differential equations based on modified equations. SIAM Journal on Scientific Computing, 34(3):A1800--A1823, 2012.DOI
  59. K.C. Zygalakis, T. Roose. A mathematical model for investigating the effect of cluster roots on plant nutrient uptake. European Physical Journal: Special Topics, 204(1):103--118, 2012.DOI
  60. S.L. Cotter, K.C. Zygalakis, I. Kevrekidis, R. Erban. A Constrained Approach to Multiscale Stochastic Simulation of Chemically Reacting Systems. Journal of Chemical Physics, 135:094102, 2011.DOI
  61. K.C. Zygalakis, G.D.J. Kirk, D.L. Jones, M. Wissuwa, T. Roose. A dual porosity model of nutrient uptake by root hairs. New Phytologist, 192(3):676--688, 2011.DOI
  62. E. Oburger, D. Leitner, D.L. Jones, K.C. Zygalakis, A. Schnepf, T. Roose. Fate of organic acid anions in soil: sorption dynamics of citric acid. European Journal of Soil Science, 62(5):733--742, 2011.DOI
  63. J. Lipkova, K.C. Zygalakis, S.J. Chapman, R. Erban. Analysis of Brownian Dynamics Simulations of Reversible Bimolecular Reactions. SIAM J. Appl. Math., 71:714--730, 2011.DOI
  64. K.C. Zygalakis. On the Existence and Applications of Modified Equations for Stochastic Differential Equations. SIAM Journal on Scientific Computing, 33(1):102--130, 2011.DOI
  65. B. Mélykúti, K. Burrage, K.C. Zygalakis. Faster Stochastic Simulation of Biochemical Reaction Systems by Alternative Formulations of the Chemical Langevin Equation. Journal of Chemical Physics, 132:164109, 2010.DOI
  66. G.A. Pavliotis, A.M. Stuart, K.C. Zygalakis. Calculating effective diffusiveness in the limit of vanishing molecular diffusion. Journal of Computational Physics, 228(4):1030--1055, 2009.DOI
  67. G.A. Pavliotis, A.M. Stuart, K.C. Zygalakis. Homogenization for inertial particles in a random flow. Communications in Mathematical Sciences, 5(3):507--531, 2007.link