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We study the quadratic family of one-dimensional maps $f_a (x) = a - x^2$. We conduct comprehensive numerical analysis of collections of finite orbits of the critical point, computed for intervals of parameter values using rigorous…
We present a technique to infer lower bounds on the worst-case runtime complexity of integer programs, where in contrast to earlier work, our approach is not restricted to tail-recursion. Our technique constructs symbolic representations of…
Solving a system of nonlinear inequalities is an important problem for which conventional numerical analysis has no satisfactory method. With a box-consistency algorithm one can compute a cover for the solution set to arbitrarily close…
For data-driven iterative learning control (ILC) methods, both the model estimation and controller design problems are converted to parameter estimation problems for some chosen model structures. It is well-known that if the model order is…
The problem of behaviour prediction for linear parameter-varying systems is considered in the interval framework. It is assumed that the system is subject to uncertain inputs and the vector of scheduling parameters is unmeasurable, but all…
Algorithms operating on real numbers are implemented as floating-point computations in practice, but floating-point operations introduce roundoff errors that can degrade the accuracy of the result. We propose $\Lambda_{num}$, a functional…
Model checking is a powerful method widely explored in formal verification. Given a model of a system, e.g., a Kripke structure, and a formula specifying its expected behaviour, one can verify whether the system meets the behaviour by…
In this paper, balancing based model order reduction (MOR) for large-scale linear discrete-time time-invariant systems in prescribed finite time intervals is studied. The first main topic is the development of error bounds regarding the…
We reexamine Smale's alpha theory as a way to certify a numerical solution to an analytic system. For a given point and a system, Smale's alpha theory determines whether Newton's method applied to this point shows the quadratic convergence…
Real world evolves in continuous time but computations are done from finite samples. Therefore, we study algorithms using finite observations in continuous-time linear dynamical systems. We first study the system identification problem, and…
Randomized algorithms, such as randomized sketching or stochastic optimization, are a promising approach to ease the computational burden in analyzing large datasets. However, randomized algorithms also produce non-deterministic outputs,…
This paper studies the numerical computation of integrals, representing estimates or predictions, over the output $f(x)$ of a computational model with respect to a distribution $p(\mathrm{d}x)$ over uncertain inputs $x$ to the model. For…
Runtime Verification deals with the question of whether a run of a system adheres to its specification. This paper studies runtime verification in the presence of partial knowledge about the observed run, particularly where input values may…
The influence-matrix formalism provides an alternative route to the classical simulation of quantum dynamics. Because influence matrices retain information only about the effective bath seen by local observables, they are expected to be…
Prediction intervals are a valuable way of quantifying uncertainty in regression problems. Good prediction intervals should be both correct, containing the actual value between the lower and upper bound at least a target percentage of the…
We introduce an effective algorithmic method for the computation of a lower bound for uniform expansion in one-dimensional dynamics. The approach employs interval arithmetic and thus provides a rigorous numerical result (computer-assisted…
This paper focuses on the identification of dynamical systems with tailor-made model structures, where neural networks are used to approximate uncertain components and domain knowledge is retained, if available. These model structures are…
In this paper, we propose a computationally efficient framework for interval reachability of systems with neural network controllers. Our approach leverages inclusion functions for the open-loop system and the neural network controller to…
Models that contain intersample behavior are important for control design of systems with slow-rate outputs. The aim of this paper is to develop a system identification technique for fast-rate models of systems where only slow-rate output…
Annealed importance sampling (AIS) is a common algorithm to estimate partition functions of useful stochastic models. One important problem for obtaining accurate AIS estimates is the selection of an annealing schedule. Conventionally, an…