108 citations · 1.6k across the 73 of their papers we have counts for
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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…
An effective solution to convex -body -representability
Federico Castillo, Jean-Philippe Labbé, Julia Liebert +3
From a geometric point of view, Pauli's exclusion principle defines a hypersimplex. This convex polytope describes the compatibility of -fermion and -fermion density matrices…
Ensemble reduced density matrix functional theory for excited states and hierarchical generalization of Pauli's exclusion principle
Christian Schilling, Stefano Pittalis
We propose and work out a reduced density matrix functional theory (RDMFT) for calculating energies of eigenstates of interacting many-electron systems beyond the ground state. Var…
Foundation of one-particle reduced density matrix functional theory for excited states
Julia Liebert, Federico Castillo, Jean-Philippe Labbé +1
In [Phys. Rev. Lett. 127, 023001 (2021)] a reduced density matrix functional theory (RDMFT) has been proposed for calculating energies of selected eigenstates of interacting many-f…