94 citations · 364 across the 34 of their papers we have counts for
35 papers
Optimal scaling of MCMC algorithms: the Hamiltonian approach
P. Dobson, J. M. Sanz-Serna, K. C. Zygalakis
We present a simple, yet general approach to study the scaling properties as the dimensionality of Metropolised MCMC sampling algorithms increases. The study relies on the symmetri…
Accelerated optimization algorithms and ordinary differential equations: the convex non Euclidean case
Paul Dobson, Jesus María Sanz-Serna, Konstantinos C. Zygalakis
We study the connections between ordinary differential equations and optimization algorithms in a non-Euclidean setting. We propose a novel accelerated algorithm for minimising con…
Stroboscopic averaging methods to study autoresonance and other problems with slowly varying forcing frequencies
M. P. Calvo, J. M. Sanz-Serna, Beibei Zhu
Autoresonance is a phenomenon of physical interest that may take place when a nonlinear oscillator is forced at a frequency that varies slowly. The stroboscopic averaging method (S…
Accelerated Bayesian imaging by relaxed proximal-point Langevin sampling
Teresa Klatzer, Paul Dobson, Yoann Altmann +3
This paper presents a new accelerated proximal Markov chain Monte Carlo methodology to perform Bayesian inference in imaging inverse problems with an underlying convex geometry. Th…
Adaptive multi-stage integration schemes for Hamiltonian Monte Carlo
Lorenzo Nagar, Mario Fernández-Pendás, Jesús María Sanz-Serna +1
Hamiltonian Monte Carlo (HMC) is a powerful tool for Bayesian statistical inference due to its potential to rapidly explore high dimensional state space, avoiding the random walk b…
On the connections between optimization algorithms, Lyapunov functions, and differential equations: theory and insights
Paul Dobson, Jesus Maria Sanz-Serna, Konstantinos Zygalakis
We revisit the general framework introduced by Fazylab et al. (SIAM J. Optim. 28, 2018) to construct Lyapunov functions for optimization algorithms in discrete and continuous time.…
A New Optimality Property of Strang's Splitting
Fernando Casas, Jesús María Sanz-Serna, Luke Shaw
For systems of the form , , common in many applications, we analyze splitting integrators based on the (linear/nonlinear) split systems $\dot…
Split Hamiltonian Monte Carlo revisited
Fernando Casas, Jesús María Sanz-Serna, Luke Shaw
We study Hamiltonian Monte Carlo (HMC) samplers based on splitting the Hamiltonian as , where is quadratic and small. We show that, in general, suc…
Wasserstein distance estimates for the distributions of numerical approximations to ergodic stochastic differential equations
J. M. Sanz-Serna, Konstantinos C. Zygalakis
We present a framework that allows for the non-asymptotic study of the -Wasserstein distance between the invariant distribution of an ergodic stochastic differential equation an…
Symmetrically processed splitting integrators for enhanced Hamiltonian Monte Carlo sampling
S. Blanes, M. P. Calvo, F. Casas +1
We construct integrators to be used in Hamiltonian (or Hybrid) Monte Carlo sampling. The new integrators are easily implementable and, for a given computational budget, may deliver…
The connections between Lyapunov functions for some optimization algorithms and differential equations
J. M. Sanz-Serna, Konstantinos C. Zygalakis
In this manuscript, we study the properties of a family of second-order differential equations with damping, its discretizations and their connections with accelerated optimization…
Is the NUTS algorithm correct?
J. M. Sanz-Serna
This paper is devoted to investigate whether the popular No U-turn (NUTS) sampling algorithm is correct, i.e.\ whether the target probability distribution is \emph{exactly} conserv…
HMC: avoiding rejections by not using leapfrog and some results on the acceptance rate
M. P. Calvo, D. Sanz-Alonso, J. M. Sanz-Serna
The leapfrog integrator is routinely used within the Hamiltonian Monte Carlo method and its variants. We give strong numerical evidence that alternative, easy to implement algorith…
Contractivity of Runge-Kutta methods for convex gradient systems
J. M. Sanz-Serna, Konstantinos C. Zygalakis
We consider the application of Runge-Kutta (RK) methods to gradient systems , where, as in many optimization problems, is convex and (globall…
Word-series high-order averaging of highly oscillatory differential equations with delay
J. M. Sanz-Serna, Beibei Zhu
We show that, for appropriate combinations of the values of the delay and the forcing frequency, it is possible to obtain easily high-order averaged versions of periodically forced…
High-order stroboscopic averaging methods for highly oscillatory delay problems
M. P. Calvo, J. M. Sanz-Serna, Beibei Zhu
We introduce and analyze a family of heterogeneous multiscale methods for the numerical integration of highly oscillatory systems of delay differential equations with constant dela…
Multi-stage splitting integrators for sampling with modified Hamiltonian Monte Carlo methods
Tijana Radivojević, Mario Fernández-Pendás, Jesús María Sanz-Serna +1
Modified Hamiltonian Monte Carlo (MHMC) methods combine the ideas behind two popular sampling approaches: Hamiltonian Monte Carlo (HMC) and importance sampling. As in the HMC case,…
Word combinatorics for stochastic differential equations: splitting integrators
A. Alamo, J. M. Sanz-Serna
We present an analysis based on word combinatorics of splitting integrators for Ito or Stratonovich systems of stochastic differential equations. In particular we present a techniq…
Geometric integrators and the Hamiltonian Monte Carlo method
Nawaf Bou-Rabee, Jesús María Sanz-Serna
This paper surveys in detail the relations between numerical integration and the Hamiltonian (or hybrid) Monte Carlo method (HMC). Since the computational cost of HMC mainly lies i…
Bogdanov-Takens resonance in time-delayed systems
Mattia Coccolo, BeiBei Zhu, Miguel A. F. Sanjuán +1
We analyze the oscillatory dynamics of a time-delayed dynamical system subjected to a periodic external forcing. We show that, for certain values of the delay, the response can be…
Palindromic 3-stage splitting integrators, a roadmap
Cédric M. Campos, J. M. Sanz-Serna
The implementation of multi-stage splitting integrators is essentially the same as the implementation of the familiar Strang/Verlet method. Therefore multi-stage formulas may be ea…
A stroboscopic averaging algorithm for highly oscillatory delay problems
J. M. Sanz-Serna, Beibei Zhu
We propose and analyze a heterogenous multiscale method for the efficient integration of constant-delay differential equations subject to fast periodic forcing. The stroboscopic av…
Hopf algebra techniques to handle dynamical systems and numerical integrators
A. Murua, J. M. Sanz-Serna
In a series of papers the present authors and their coworkers have developed a family of algebraic techniques to solve a number of problems in the theory of discrete or continuous…
Vibrational resonance: a study with high-order word-series averaging
Ander Murua, J. M. Sanz-Serna
We study a model problem describing vibrational resonance by means of a high-order averaging technique based on so-called word series. With the tech- nique applied here, the tasks…