97 citations · 403 across the 15 of their papers we have counts for
17 papers
The inverse problem for neural networks
Marcelo Forets, Christian Schilling
We study the problem of computing the preimage of a set under a neural network with piecewise-affine activation functions. We recall an old result that the preimage of a polyhedral…
Verification of Neural-Network Control Systems by Integrating Taylor Models and Zonotopes
Christian Schilling, Marcelo Forets, Sebastian Guadalupe
We study the verification problem for closed-loop dynamical systems with neural-network controllers (NNCS). This problem is commonly reduced to computing the set of reachable state…
Conservative Time Discretization: A Comparative Study
Marcelo Forets, Christian Schilling
We present the first review of methods to overapproximate the set of reachable states of linear time-invariant systems subject to uncertain initial states and input signals for sho…
LazySets.jl: Scalable Symbolic-Numeric Set Computations
Marcelo Forets, Christian Schilling
LazySets.jl is a Julia library that provides ways to symbolically represent sets of points as geometric shapes, with a special focus on convex sets and polyhedral approximations. L…
Reachability of weakly nonlinear systems using Carleman linearization
Marcelo Forets, Christian Schilling
In this article we introduce a solution method for a special class of nonlinear initial-value problems using set-based propagation techniques. The novelty of the approach is that w…
Combining Set Propagation with Finite Element Methods for Time Integration in Transient Solid Mechanics Problems
Marcelo Forets, Daniel Freire Caporale, Jorge M. Pérez Zerpa
The Finite Element Method (FEM) is the gold standard for spatial discretization in numerical simulations for a wide spectrum of real-world engineering problems. Prototypical areas…
Efficient reachability analysis of parametric linear hybrid systems with time-triggered transitions
Marcelo Forets, Daniel Freire, Christian Schilling
Efficiently handling time-triggered and possibly nondeterministic switches for hybrid systems reachability is a challenging task. In this paper we present an approach based on cons…
Reachability analysis of linear hybrid systems via block decomposition
Sergiy Bogomolov, Marcelo Forets, Goran Frehse +2
Reachability analysis aims at identifying states reachable by a system within a given time horizon. This task is known to be computationally expensive for linear hybrid systems. Re…
JuliaReach: a Toolbox for Set-Based Reachability
Sergiy Bogomolov, Marcelo Forets, Goran Frehse +2
We present JuliaReach, a toolbox for set-based reachability analysis of dynamical systems. JuliaReach consists of two main packages: Reachability, containing implementations of rea…
Semidefinite Approximations of Invariant Measures for Polynomial Systems
Victor Magron, Marcelo Forets, Didier Henrion
We consider the problem of approximating numerically the moments and the supports of measures which are invariant with respect to the dynamics of continuous- and discrete-time poly…
Reach Set Approximation through Decomposition with Low-dimensional Sets and High-dimensional Matrices
Sergiy Bogomolov, Marcelo Forets, Goran Frehse +3
Approximating the set of reachable states of a dynamical system is an algorithmic yet mathematically rigorous way to reason about its safety. Although progress has been made in the…
Explicit Error Bounds for Carleman Linearization
Marcelo Forets, Amaury Pouly
We revisit the method of Carleman linearization for systems of ordinary differential equations with polynomial right-hand sides. This transformation provides an approximate lineari…
Occupation measure methods for modelling and analysis of biological hybrid automata
Alexandre Rocca, Marcelo Forets, Victor Magron +2
Mechanistic models in biology often involve numerous parameters about which we do not have direct experimental information. The traditional approach is to fit these parameters usin…
Quantum walking in curved spacetime
Pablo Arrighi, Stefano Facchini, Marcelo Forets
A discrete-time Quantum Walk (QW) is essentially a unitary operator driving the evolution of a single particle on the lattice. Some QWs admit a continuum limit, leading to familiar…
Discrete Lorentz covariance for Quantum Walks and Quantum Cellular Automata
Pablo Arrighi, Stefano Facchini, Marcelo Forets
We formalize a notion of discrete Lorentz transforms for Quantum Walks (QW) and Quantum Cellular Automata (QCA), in (1 + 1)-dimensional discrete spacetime. The theory admits a diag…
The Dirac equation as a quantum walk: higher dimensions, observational convergence
Pablo Arrighi, Marcelo Forets, Vincent Nesme
The Dirac equation can be modelled as a quantum walk, with the quantum walk being: discrete in time and space (i.e. a unitary evolution of the wave-function of a particle on a latt…
Spatial quantum search in a triangular network
G. Abal, R. Donangelo, M. Forets +1
The spatial search problem consists in minimizing the number of steps required to find a given site in a network, under the restriction that only oracle queries or translations to…