24 citations · 87 across the 18 of their papers we have counts for
19 papers
Prob-GParareal: A Probabilistic Numerical Parallel-in-Time Solver for Differential Equations
Guglielmo Gattiglio, Lyudmila Grigoryeva, Massimiliano Tamborrino
We introduce Prob-GParareal, a probabilistic extension of the GParareal algorithm designed to provide uncertainty quantification for the Parallel-in-Time (PinT) solution of (ordina…
RandNet-Parareal: a time-parallel PDE solver using Random Neural Networks
Guglielmo Gattiglio, Lyudmila Grigoryeva, Massimiliano Tamborrino
Parallel-in-time (PinT) techniques have been proposed to solve systems of time-dependent differential equations by parallelizing the temporal domain. Among them, Parareal computes…
Inference for the stochastic FitzHugh-Nagumo model from real action potential data via approximate Bayesian computation
Adeline Samson, Massimiliano Tamborrino, Irene Tubikanec
The stochastic FitzHugh-Nagumo (FHN) model is a two-dimensional nonlinear stochastic differential equation with additive degenerate noise, whose first component, the only one obser…
Nearest Neighbors GParareal: Improving Scalability of Gaussian Processes for Parallel-in-Time Solvers
Guglielmo Gattiglio, Lyudmila Grigoryeva, Massimiliano Tamborrino
With the advent of supercomputers, multi-processor environments and parallel-in-time (PinT) algorithms offer ways to solve initial value problems for ordinary and partial different…
Network inference via approximate Bayesian computation. Illustration on a stochastic multi-population neural mass model
Susanne Ditlevsen, Massimiliano Tamborrino, Irene Tubikanec
In this article, we propose an adapted sequential Monte Carlo approximate Bayesian computation (SMC-ABC) algorithm for network inference in coupled stochastic differential equation…
Error bound analysis of the stochastic parareal algorithm
Kamran Pentland, Massimiliano Tamborrino, T. J. Sullivan
Stochastic parareal (SParareal) is a probabilistic variant of the popular parallel-in-time algorithm known as parareal. Similarly to parareal, it combines fine- and coarse-grained…
Boundary crossing problems and functional transformations for Ornstein-Uhlenbeck processes
Aria Ahari, Larbi Alili, Massimiliano Tamborrino
We are interested in the law of the first passage time of an Ornstein-Uhlenbeck process to time-varying thresholds. We show that this problem is connected to the laws of the first…
Guided sequential ABC schemes for intractable Bayesian models
Umberto Picchini, Massimiliano Tamborrino
Sequential algorithms such as sequential importance sampling (SIS) and sequential Monte Carlo (SMC) have proven fundamental in Bayesian inference for models not admitting a readily…
GParareal: A time-parallel ODE solver using Gaussian process emulation
Kamran Pentland, Massimiliano Tamborrino, T. J. Sullivan +2
Sequential numerical methods for integrating initial value problems (IVPs) can be prohibitively expensive when high numerical accuracy is required over the entire interval of integ…
Stochastic parareal: an application of probabilistic methods to time-parallelisation
Kamran Pentland, Massimiliano Tamborrino, D. Samaddar +1
Parareal is a well-studied algorithm for numerically integrating systems of time-dependent differential equations by parallelising the temporal domain. Given approximate initial va…
A splitting method for SDEs with locally Lipschitz drift: Illustration on the FitzHugh-Nagumo model
Evelyn Buckwar, Adeline Samson, Massimiliano Tamborrino +1
In this article, we construct and analyse an explicit numerical splitting method for a class of semi-linear stochastic differential equations (SDEs) with additive noise, where the…
Shot noise, weak convergence and diffusion approximations
Massimiliano Tamborrino, Petr Lansky
Shot noise processes have been extensively studied due to their mathematical properties and their relevance in several applications. Here, we consider nonnegative shot noise proces…
Qualitative properties of numerical methods for the inhomogeneous geometric Brownian motion
Irene Tubikanec, Massimiliano Tamborrino, Petr Lansky +1
We provide a comparative analysis of qualitative features of different numerical methods for the inhomogeneous geometric Brownian motion (IGBM). The conditional and asymptotic mean…
Inhibition enhances the coherence in the Jacobi neuronal model
Giuseppe D'Onofrio, Petr Lansky, Massimiliano Tamborrino
The output signal is examined for the Jacobi neuronal model which is characterized by input-dependent multiplicative noise. The dependence of the noise on the rate of inhibition tu…
Spectral Density-Based and Measure-Preserving ABC for partially observed diffusion processes. An illustration on Hamiltonian SDEs
Evelyn Buckwar, Massimiliano Tamborrino, Irene Tubikanec
Approximate Bayesian Computation (ABC) has become one of the major tools of likelihood-free statistical inference in complex mathematical models. Simultaneously, stochastic differe…
Approximation of the first passage time density of a Wiener process to an exponentially decaying threshold by two-piecewise linear threshold. Application to neuronal spiking activity
Massimiliano Tamborrino
The first passage time density of a diffusion process to a time varying threshold is of primary interest in different fields. Here we consider a Brownian motion in presence of an e…
Parameter inference from hitting times for perturbed Brownian motion
M. Tamborrino, S. Ditlevsen, P Lansky
A latent internal process describes the state of some system, e.g. the social tension in a political conflict, the strength of an industrial component or the health status of a per…
Weak convergence of marked point processes generated by crossings of multivariate jump processes. Applications to neural network modeling
Massimiliano Tamborrino, Laura Sacerdote, Martin Jacobsen
We consider the multivariate point process determined by the crossing times of the components of a multivariate jump process through a multivariate boundary, assuming to reset each…
First passage times of two-correlated processes: analytical results for the Wiener process and a numerical method for diffusion processes
Laura Sacerdote, Massimiliano Tamborrino, Cristina Zucca
Given a two-dimensional correlated diffusion process, we determine the joint density of the first passage times of the process to some constant boundaries. This quantity depends on…