Applied Mathematics and Mathematical Physics Section­­­­

Department of Mathematics

Imperial College London



180 Queen’s Gate
Department of Mathematics
Imperial College London
London SW7 2AZ



Huxley Building Room 736a


(+44) (0)20 7594 8564


pavl at




·       Research interests:

o  Interacting Particle systems.

o  Algorithms for Inference, Sampling and Optimization.

o  Fokker-Planck equations and related PDEs.

o  Statistical Dynamics.

o   Multiscale analysis for Markov processes.

·       EPSRC Funding Profile


·       My Citations (Google Scholar)

·     Orcid Profile

·     My publications at the arXiv

·     My publications at Mathscinet

·     I am the Head of the Applied Mathematics and Mathematical Physics (AMMP) Section

·     My course at Caltech

·     My course at TU Munich

·     My course at EPFL

·         cv (Last updated: November 2021)

·     Book: Multiscale Methods: Averaging and Homogenization

·     Book: Stochastic Processes and Applications.







1.  Multiscale Methods: Averaging and Homogenization. Texts in Applied Mathematics, vol. 53. Springer, 2008.

2.  Stochastic Processes and Applications. Texts in Applied Mathematics, vol. 60. Springer, 2014.







3.  Nonreversible Langevin Samplers: Splitting Schemes, Analysis and Implementation (with A.B. Duncan and K.C. Zygalakis). Submitted, July (2022).

4.  Brownian motion in an N-scale periodic potential (with A.B. Duncan and H. Duong). Submitted, June 2022.

5.  Mobility estimation for Langevin dynamics using control variates (with G. Stoltz and U. Vaes). Submitted, June 2022

6.  Stochastic Mirror Descent for Convex Optimization with Consensus Constraints (with A. Borovykh, N. Kantas, P. Parpas). Submitted, January 2022.

7.  The free energy principle made simpler but not too simple (with K. FristonL. Da CostaN. SajidC. HeinsK. Ueltzhöffer T. Parr ), Preprint, January 2022.

8.  Phase transitions, logarithmic Sobolev inequalities, and uniform-in-time propagation of chaos for weakly interacting diffusions (with M. G. DelgadinoR. S. Gvalani S. A. Smith). Submitted, December 2021.

9.  Optimal friction matrix for underdamped Langevin sampling (with M. Chak, N. Kantas, T. Lelievre), preprint, December 2021.

10.       Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation (L. SharrockN. KantasP. Parpas), preprint, June 2021.

11.       On the Generalised Langevin Equation for Simulated Annealing (with M. Chak, N. Kantas) Submitted, March 2020.

12.       The sharp, the flat and the shallow: Can weakly interacting agents learn to escape bad minima?  (with N. Kantas and P. Parpas). Preprint, April 2019.

13.       The Thermodynamics of Urban and Regional Structure (with L. Ellam, M. Girolami, A. Wilson). Preprint, May 2018. 







14.       Eigenfunction martingale estimating functions and filtered data for drift estimation of discretely observed multiscale diffusions  (with A. Abdulle and A. Zanoni). Statistics and Computing, 32, Article number: 34 (2022).

15.       Eigenfunction martingale estimators for interacting particle systems and their mean field limit (with A. Zanoni). SIAM J. Appl Dyn. Systems, to appear (2022).

16.       Geometric Methods for Sampling, Optimisation, Inference and Adaptive Agents (with A Barp, L Da Costa, G França, K Friston, M Girolami, MI Jordan). May 2022. Handbook of Statistics.

17.  Derivative-Free Bayesian Inversion Using Multiscale Dynamics (with A.M. Stuart and U. Vaes). SIAM J. Appl Dyn. Syst. 21(1), 284–326 (2022).

18.  Bayesian Mechanics for Stationary Processes (with L. Da CostaK. FristonC. Heins), Proc. Roy. Soc. London A, 477 (2256) 20210518 (2021).

Noisy bounded confidence models for opinion dynamics: the effect of boundary conditions on phase transitions (with B. Goddard, B. Gooding, H. Short). IMA J. Appl. Math.  87(1), pp 80–110,  (2022).

19.       Drift Estimation of Multiscale Diffusions Based on Filtered Data (with A. Abdulle, G. Garegnani, A. Zanoni, A.M. Stuart) Foundations of Computational Mathematics, (2021).

20.       Spectroscopy of phase transitions for multiagent systems (with V. Lucarini and N. Zagli). CHAOS 31, 061103 (2021). 

21.       On the diffusive-mean field limit for weakly interacting diffusions exhibiting phase transitions (with M.G. Delgadino and R. Gvalani). Archive for Rational Mechanics and Analysis, 241, pp 91--148 (2021).

22.       On stochastic mirror descent with interacting particles: convergence properties and variance reduction (with A. Borovykh, N. Kantas, P. Parpas). Physica D. 418 (2021) 132844.

23.       Scaling limits for the generalized Langevin equation (with G. Stoltz and U. Vaes). J. Nonlinear Science 31(8) 2021.

24.       Response Theory and Phase Transitions for the Thermodynamic Limit of Interacting Identical Systems (with V. Lucarini and N. Zagli). Proc. Roy. Soc. London A. 476(2244)  (2020).

25.       Homogenization and hypocoercivity for Fokker-Planck equation driven by weakly compressible shear flows (with M. Coti-Zelati) IMA J. Appl. Math., 85(6) 951-979 (2020).

26.       A proof of the mean-field limit for λ-convex potentials using Γ-convergence. (with J.A. Carrillo and M.G. Delgadino). J. Func. Analysis 279 (10),  (2020), 108734

27.       Manifold learning for accelerating coarse-grained optimization (with Y. Kevrekidis et al). J. Comp. Dyn.  7(2); #14, (2020).

28.       Mean field limits for interacting diffusions with colored noise: phase transitions and spectral numerical methods (with S. Gomes and U. Vaes). SIAM J. MMS, 18(3) pp. 1343-1370 (2020).

29.       Long-time behaviour and phase transitions for the McKean-Vlasov equation on the torus  (with J. A. Carrillo, R. S. Gvalani, A. Schlichting). Archive for Rational Mechanics and Analysis, 235 (2020) 635-690.

30.       Accelerated convergence to equilibrium and reduced asymptotic variance for Langevin dynamics using Stratonovich perturbations (with A. Abdulle and G. Vilmart). Com. Rend.  Acad. Sci. 357  (2019) 349-354.

31.       Dynamics of the Desai-Zwanzig model in multi-well and random energy landscapes (with S.N. Gomes, S. Kalliadasis, P. Yatsyshin). Phys. Rev. E, 99, 032109 (2019).

32.       Constructing sampling schemes via coupling: Markov semigroups and optimal transport (with N. Nuesken). SIAM/ASA J. Uncertainty Quantification, 7(1), 324–382 (2019).

33.       Instability, rupture and fluctuations in thin liquid films: Theory and computations (with M. A.  Duran-Olivencia, R. Gvalani and S. Kalliadasis).  J. Stat. Phys. 174(3) 579-604 (2019).

34.       Optimal control of thin liquid films and transverse mode effects (with R.J. Tomlin, S.N. Gomes, D.T. Papageorgiou). SIAM J. Appl. Dyn. Syst., 18(1), 117–149 (2019).

35.       Recent advances in the evolution of interfaces: thermodynamics, upscaling, and universality (with M. Schmuck and S. Kalliadasis). Computational Materials Science 156, 441--451 (2019).

36.       Mean field limits for non-Markovian interacting particles: convergence to equilibrium, GENERIC formalism, asymptotic limits and phase transitions (with H. Duong). Comm. Math. Sci 16(8) (2018), pp. 2199-2230

37.       Cloaking via mapping for the heat equation (with R. Craster, S. Guenneau, H. Hutridurga).  SIAM J. MMS, 16(3), 1146–1174 (2018). 

38.       Stochastic Modeling of Urban Structure (with L. Ellam, M. Girolami and A. Wilson). Proceeding Roy. Soc. London A, 474(2213) (2018).

39.       Mean Field Limits for Interacting Diffusions in a Two-Scale Potential (with S.N. Gomes). J. Nonlinear Sci. 28(3), pp. 905-941, (2018). 

40.       Using Perturbed Underdamped Langevin Dynamics to Efficiently Sample from Probability Distributions (With A.B. Duncan and N . Nusken).  J. Stat. Phys. 169(6) pp. 1098-1131 (2017). 

41.       Three-dimensional wave evolution on electrified falling films  (with R.J. Tomlin and D.T. Papageorgiou). J. Fluid Mech. 822 pp. 54-79 (2017).  

42.       Spectral methods for multiscale stochastic differential equations (with A. Abdulle and U. Vaes). SIAM J. UQ, 5-1 (2017), pp. 720-761. 

43.         Controlling roughening processes in the stochastic Kuramoto-Sivashinsky equation (with S. Gomes, S. Kalliadasis, D.T.  Papageorgiou  and M. Pradas). Physica D   348 33--43 (2017) .

44.       Stabilizing nontrivial solutions of the generalized Kuramoto-Sivashinsky equation using feedback and optimal control (with   S.N.  Gomes and D.T. Papageorgiou). IMA J. Appl. Math. 82(1)  pp 158-195 (2017).

45.       Noise-induced transitions in rugged energy landscapes (with A.B. Duncan, S. Kalliadasis, M. Pradas). Phys. Rev. E, 94, 032107  (2016).

46.       Variance Reduction using Nonreversible Langevin Samplers (with A. Duncan and T. Lelievre). J. Stat. Phys. 163(3) pp 457-491, (2016).

47.       Efficient numerical calculation of drift and diffusion coefficients in the diffusion approximation of kinetic equations (with V. Bonnaillie-Noel,  J.A. Carrillo and T. Goudon). IMA J. Num. Analysis 36(4) pp. 1536--1569 (2016).

48.       Stabilising falling liquid film flows using feedback control (with A.B. Thompson, S.N. Gomes, D.T Papageorgiou). Phys. Fluids  28,   012107 (2016).

49.       Data-driven coarse graining in action: Modelling and prediction of complex systems (with S. Kalliadasis, S. Krumscheid and M. Pradas Gene). Phys. Rev. E 92, 042139 (2015)

50.       Controlling Spatiotemporal Chaos in Active Dissipative-Dispersive Nonlinear Systems. (with S. Gomes, S. Kalliadasis, D.T. Papageorgiou  and M. Pradas ). Phys Rev E 92, 022912 (2015).

51.         A new framework for extracting coarse-grained models from time series with multiscale structure (with S. Kalliadasis and S. Krumscheid). J. Comp. Phys.  296, pp. 314-328 (2015).

52.         Some remarks on degenerate hypoelliptic Ornstein-Uhlenbeck operators (with M. Ottobre and K. Pravda-Starov). J. Math. Analysis Appl.  429(2), pp. 676-712 (2015)

53.       A multiscale analysis of diffusions on rapidly varying surfaces (with A.B. Duncan, C.M. Elliott, A.M. Stuart). J. Nonlinear Science, 25(2), pp. 389-449  (2015).

54.       Langevin dynamics with space-time periodic nonequilibrium forcing (with R. Joubaud and G. Stoltz). J. Stat. Phys., 158(1) pp 1-36  (2015).

55.       A New Mode Reduction Strategy for the Generalized Kuramoto-Sivashinsky Equation (with M. Schmuck, M. Pradas Gene, S. Kalliadasis). IMA J. Appl. Math., 80(2), pp. 273-301 (2015).

56.        Optimal control of multiscale systems using reduced-order models (with W. Zhang, J.C. Latorre and C. Hartmann). J. Comp. Dyn. 1(2), pp 279-308,   (2014).

57.       Mapping multiplicative to additive noise (with K.J. Rubin and G. Pruessner). J. Physics A, 47 (2014) 195001.

58.       Rate of Convergence of Phase Field Equations in Strongly Heterogeneous Media towards their Homogenized Limit (with M. Schmuck and S. Kalliadasis). Appl. Math. Lett. 35 (2014) pp 12-17.

59.       Numerical Methods for Computing Effective Transport Properties of Flashing Brownian Motors (with J.C. Latorre and P.R. Kramer).  J. Comp. Phys., 257 Part A, pp. 57-82,  (2014).

60.       Derivation of effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media. (with M. Schmuck, M. Pradas and S. Kalliadasis).  Nonlinearity, 26(12) pp. 3259-3277, (2013).

61.       Nonlinear interfacial dynamics in stratified multilayer channel flows (with E.S. Papaefthymiou and D.T. Papageorgiou).  J. Fluid Mech. 734, pp 114-143 (2013).

62.       A new stochastic mode reduction strategy for dissipative systems (with M. Schmuck, M. Pradas, S. Kalliadasis) Phys. Rev. Lett. 110, 244101,  (2013).

63.       Semi-Parametric Drift and Diffusion Estimation for Multiscale Diffusions (with S. Krumcheid, S. Kalliadasis).  SIAM J. MMS, 11(2), 442–473 (2013).

64.       Optimal nonreversible linear drift for the convergence to equilibrium of a diffusion (with T. Lelievre and F. Nier). J. Stat. Phys. 152(2) 237-274 (2013).

65.       Corrections to Einstein's relation for Brownian motion in a tilted periodic potential (with J.C. Latorre and P.R. Kramer). J. Stat. Phys. 150(4), 776-803 (2013).

66.       Upscaled phase-field models for interfacial dynamics in strongly heterogeneous domains (with M. Schmuck,  M. Pradas Gene, S. Kalliadasis). Proc. Roy. Soc. London A, 468 , 3705-3724 (2012).

67.       Generalized Dynamical Density Functional Theory for Classical Fluids  (with B. Goddard, A. Nold, N. Savva,  S. Kalliadasis). Phys. Rev. Let. 109, 120603, (2012).

68.       The Overdamped Limit of dynamic Density Functional Theory: Rigorous Results (with B. Goddard and S. Kalliadasis). SIAM J. MMS, 10(2)  633-663 (2012).

69.       Additive Noise Effects in Active Nonlinear Spatially Extended Systems (with M. Pradas Gene, D. Tseluiko, S. Kalliadasis, D.T. Papageorgiou). Eur. J. Appl. Math. 23(5) 563-591  (2012).

70.       Numerical Methods for Stochastic Partial Differential Equations with Multiple Scales (with A. Abdulle). J. Comp. Phys, 231(6)  pp. 2482–2497 (2012).

71.       Exponential Return to Equilibrium for Hypoelliptic Quadratic Systems (with M. Ottobre and K. Pravda-Starov). J. Func. Analysis  262(9) pp. 4000-4039 (2012).

72.         Noise induced state transitions, intermittency and universality in the noisy Kuramoto-Sivashinksy equation. (With M. Pradas Gene, D. Tseluiko, S. Kalliadasis, D.T. Papageorgiou). Phys. Rev. Lett.  106, 060602 (2011).

73.         Asymptotic Analysis for the Generalized Langevin Equation. (with M. Ottobre) Nonlinearity, 24 (2011) 1629-1653.

74.         Contact lines over random topographical substrates. Part 2. Dynamics (with N. Savva and S. Kalliadasis). J. Fluid Mech., 672 pp. 384-410 (2011).

75.         Contact lines over random topographical substrates. Part 1. Statics (with N. Savva and S. Kalliadasis). J. Fluid Mech., 672 pp. 358-383 (2011).

76.         Asymptotic Analysis for Foreign Exhange Derivatives with Stochastic Volatility ( With C. Cuthbertson, A. Rafailidis and P. Wiberg).  Int. J. Theor. & Appl. Finance, 13(7) 1131-1147 (2010).

77.         Asymptotic Analysis of the Green-Kubo Formula.   IMA J. Appl. Math. 75(6) 951-967 (2010).

78.         Two-dimensional droplet spreading over random topographical substrates (with N. Savva and S. Kalliadasis). Phys. Rev. Lett. 104, 084501 (2010).

79.         Estimating Eddy Diffusivities from Noisy Lagrangian Observations (with C.J. Cotter). Comm. Math. Sci. 7(4), pp. 805-838 (2009).

80.         Frequency Domain Estimation of Integrated Volatility for Ito Processes in the Presence of Market-Microstructure Noise. (with A. Sykulski and S. Olhede) SIAM J. MMS, 8(2), pp. 393-427 (2009).

81.         Maximum Likelihood Drift Estimation for Multiscale Diffusions (with A. Papavasiliou and A.M. Stuart), Stoch. Proc. Appl. 119(10)  3173-3210  (2009).

82.         Calculating Effective Diffusivities in the Limit of  Vanishing Molecular Diffusion (with A.M. Stuart and K.C. Zygalakis) J. Comp. Phys. 228(4) 1030-1055 (2009).

83.         Diffusive Transport in Periodic Potentials: Underdamped dynamics (with T. Vogiannou), Fluct. Noise Lett., 8(2) L155-L173 (2008).

84.         From Ballistic to Diffusive Behavior in Periodic Potentials.  (with M. Hairer), J. Stat. Phys. 131(1) 175-202 (2008).

85.        Optimizing the Source Distribution in Fluid Mixing. (with J-L Thiffeault), Physica D, 237(7) 918-929 (2008).

86.        Homogenization for Inertial Particles in a Random Flow. (with A.M. Stuart and K.C. Zygalakis), Comm. Math. Sci. 5(3) 507-531 (2007).

87.        Multiscale Analysis for SPDEs with Quadratic Nonlinearities. (with D. Blomker and M. Hairer), Nonlinearity 20 1721-1744 (2007).

88.        Estimates for the Two-Dimensional Navier-Stokes Equations in Terms of the Reynolds Number. ( With J.D. Gibbon ), J. Math. Phys. 48, 065202 (2007). 

89.        Parameter Estimation for Multiscale Diffusions. ( With A.M. Stuart ), J. Stat. Phys. 127(4) 741-781, (2007).

90.       A Multiscale Approach to Brownian Motors. Physics Letters A, 344 (2005) 331-345.

91.       Periodic Homogenization for Inertial Particles. ( With A.M. Stuart), Physica D 204 (3-4) 161-187, (2005).

92.       Modulation Equations: Stochastic Bifurcation in Large Domains . ( With D. Bloemker and M. Hairer), Comm. Math. Phys. 258 (2005) 479-512.

93.       Analysis of White Noise Limits for Stochastic Systems with two Fast Relaxation Times. (with A.M. Stuart), SIAM J. MMS 4(1) 1-35, (2005).

94.       Periodic Homogenization for Hypoelliptic Diffusions. (with M. Hairer), J. Stat. Phys. 117 no. 1/2 (2004), 261-279.

95.       Ito versus Stratonovich White Noise Limits for Systems with Inertia and Colored Multiplicative Noise. (with R. Kupferman and A.M. Stuart), Phys. Rev. E, 70 036120 (2004).

96.       White Noise Limits for Inertial Particles in a Random Field. (with A.M. Stuart), SIAM J. MMS 1(4), 527--553, (2003).

97.       A Perturbation Based Numerical Method for Solving a Three Dimensional Axisymmetric Indentation Problem. (with M.H. Holmes), J. Eng. Math., 43 (2002) 1--17.

98.       Riemannian Curvature and Monoparametric Families of Trajectories. (with G. Bozis), Inverse Problems, 15 (1999) 141--153.






99.       Optimizing interacting Langevin dynamics using spectral gaps (with A. Borovykh; N. Kantas P. Parpas) July 2021. ICML workshop  Beyond First Order Methods in ML Systems.

100.  Stochastic Mirror Descent for Fast Distributed Optimization and Federated Learning (with A. Borovykh, N. Kantas, P. Parpas) OPT2020: 17th Annual Workshop on Optimization for Machine Learning (2020).

101.  To interact or not? The convergence properties of interacting stochastic mirror descent (with A. Borovykh, N. Kantas, P. Parpas)  Workshop on "Beyond first-order methods in ML systems" at 36th International Conference on Machine Learning (ICML) 2020.

102.  Regularized transformation optics for transient heat transfer.  (with Craster, R. Guenneau, S., Hutridurga, H.) 11TH INTERNATIONAL CONGRESS ON ENGINEERED MATERIALS PLATFORMS FOR NOVEL WAVE PHENOMENA (METAMATERIALS) pp. 127-129  (2017).

103.  Effective macroscopic Stokes-Cahn-Hilliard equations for periodic immiscible flows in porous media. (with M. Schmuck and S. Kalliadasis). Proceedings of the European Conference on Complex Systems 2012, Springer Proceedings in Complexity 2013, pp 1005-1010.

104.  Inertia and hydrodynamic interactions in dynamical density functional theory (with BD Goddard, A Nold, N Savva S Kalliadasis) Proceedings of the European Conference on Complex Systems 2012, Springer Proceedings in Complexity 2013, pp 999-1004.

105.   Multiscale Modelling and Inverse Problems (with J. Nolen and A.M. Stuart). in Numerical Analysis of Multiscale Problems, Edited by I.G. Graham, T. Hou, O. Lakkis and R. Scheichl, Lecture Notes in Computational Science and Engineering, Vol. 83, Springer, 2012. 

106.    Parameter Estimation for Multiscale Diffusions: an Overview. (with Y. Pokern and A.M. Stuart) in Statistical Methods for Stochastic Differential Equations edited by M. Kessler, A. Lindner, M. Sorensen, 2012.

107.    Some Remarks on Stabilization by Additive Noise (with D. Blomker and M. Hairer) in Stochastic Partial Differential Equations and Applications}, Edited by G. Da Prato and L. Tubaro,  Quaderni di Matematica, vol 25,pp. 37--50, 2011.

108.    Monte Carlo Studies of Effective Diffusivities for Inertial Particles. ( With A.M. Stuart and L. Band), Monte Carlo and quasi-Monte Carlo methods 2004, 431--441, Springer, Berlin, 2006.  

109.    Stochastic Swift--Hohenberg Equation Near a Change of Stability (with D. Bloemker and M. Hairer ), Proceedings  Equadiff-11, (2005), pp. 25-37.  




110.    Homogenized Transport by a Spatiotemporal Mean Flow with Small--Scale Inhomogeneities. (with P.R. Kramer), Preprint, November 2002.

111.   Homogenization Theory for Advection--Diffusion Equations with Mean Flow. PhD Thesis, May 2002.