Applied Mathematics and Mathematical
Physics Section
180 Queen’s
Gate
Department of Mathematics
Imperial College London
London SW7 2AZ
UK
|
Office |
Huxley Building Room 736a |
|
Voice |
(+44) (0)20 7594 8564 |
|
pavl at ic.ac.uk |
·
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.
· My Citations
(Google Scholar)
·
My publications at the arXiv
·
My publications at Mathscinet
·
I am the Head of the Applied Mathematics and
Mathematical Physics (AMMP) Section
· cv (Last updated: November 2021)
· Book: Multiscale
Methods: Averaging and Homogenization
· Book: Stochastic Processes and Applications.
PUBLICATIONS-PREPRINTS
BOOKS
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.
PREPRINTS
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.
Friston, L.
Da Costa, N.
Sajid, C.
Heins, K.
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. Delgadino, R. 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.
Sharrock, N.
Kantas, P.
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.
PUBLICATIONS
IN REFEREED JOURNALS
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. https://doi.org/10.1016/bs.host.2022.03.005
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 Costa, K.
Friston, C.
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, https://doi.org/10.1007/s10208-021-09541-9
(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.
REFEREED
CONFERENCE PROCEEDINGS AND BOOK CHAPTERS
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.
THESES, UNPUBLISHED
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.