Related papers: Interval Reachability Analysis using Second-Order …
The literature on reachability analysis methods for neural networks currently only focuses on uncertainties on the network's inputs. In this paper, we introduce two new approaches for the reachability analysis of neural networks with…
Temporal networks are a class of time-varying networks, which change their topology according to a given time-ordered sequence of static networks (known as subsystems). This paper investigates the reachability and controllability of…
In this paper, we provide novel characterizations of the weakly unobservable and the strongly reachable subspaces corresponding to a given state-space system. These characterizations provide closed-form representations for the said…
We develop a method based on martingales to study first-passage problems of time-additive observables exiting an interval of finite width in a Markov process. In the limit that the interval width is large, we derive generic expressions for…
Reachability analysis is a critical tool for the formal verification of dynamical systems and the synthesis of controllers for them. Due to their computational complexity, many reachability analysis methods are restricted to systems with…
In this work, we introduce a notion of reachability entropy to characterize the smallest data rate which is sufficient enough to enforce reach-while-stay specification. We also define data rates of coder-controllers that can enforce this…
Sensitivity analysis is concerned with understanding how the model output depends on uncertainties (variances) in inputs and then identifies which inputs are important in contributing to the prediction imprecision. Uncertainty determination…
Reachability analysis is a powerful tool for computing the set of states or outputs reachable for a system. While previous work has focused on systems described by state-space models, we present the first methods to compute reachable sets…
Variational inequalities represent a broad class of problems, including minimization and min-max problems, commonly found in machine learning. Existing second-order and high-order methods for variational inequalities require precise…
The development of global sensitivity analysis of numerical model outputs has recently raised new issues on 1-dimensional Poincar\'e inequalities. Typically two kind of sensitivity indices are linked by a Poincar\'e type inequality, which…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity. Second-order methods, while able to provide faster convergence, have been much less explored…
Estimation of the degree of stability and the bounds of solutions to non-autonomous nonlinear systems present major concerns in numerous applied problems. Yet, current techniques are frequently yield overconservative conditions which are…
Sufficient conditions for the design of a simple class of interval observers for linear impulsive systems subject to minimum and range dwell-time constraints are obtained and formulated in terms of infinite-dimensional linear programs. The…
This work presents an illustrative application of the second-order adjoint sensitivity analysis procedure (SO-ASAP) to a paradigm neutron diffusion problem, which is sufficiently simple to admit an exact solution, thereby making transparent…
Computing reachability probabilities is a fundamental problem in the analysis of probabilistic programs. This paper aims at a comprehensive and comparative account on various martingale-based methods for over- and under-approximating…
This paper addresses the synthesis of interval observers for partially unknown nonlinear systems subject to bounded noise, aiming to simultaneously estimate system states and learn a model of the unknown dynamics. Our approach leverages…
We study approximation of non-autonomous linear differential equations with variable delay over infinite intervals. We use piecewise constant argument to obtain a corresponding discrete difference equation. The study of numerical…
Reachability analysis is a formal method to guarantee safety of dynamical systems under the influence of uncertainties. A substantial bottleneck of all reachability algorithms is the necessity to adequately tune specific algorithm…
We consider the problem of proving that each point in a given set of states ("target set") can indeed be reached by a given nondeterministic continuous-time dynamical system from some initial state. We consider this problem for abstract…