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Employing a limiting case of a conjecture for constructing piecewise separable-variables functions, the elements of the Pseudoanalytic Function Theory are used for numerically approaching solutions of the forward Dirichlet boundary value…
In this paper, we propose an incremental abstraction method for dynamically over-approximating nonlinear systems in a bounded domain by solving a sequence of linear programs, resulting in a sequence of affine upper and lower hyperplanes…
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…
Synthesizing programs from examples requires searching over a vast, combinatorial space of possible programs. In this search process, a key challenge is representing the behavior of a partially written program before it can be executed, to…
Program verification techniques typically focus on finding counter-examples that violate properties of a program. Constraint programming offers a convenient way to verify programs by modeling their state transformations and specifying…
Modeling continuous-time dynamics from sparse and irregularly-sampled time series remains a fundamental challenge. Neural controlled differential equations provide a principled framework for such tasks, yet their performance is highly…
We present an elastic simulator for domains defined as evolving implicit functions, which is efficient, robust, and differentiable with respect to both shape and material. This simulator is motivated by applications in 3D reconstruction: it…
We introduce a new domain for finding precise numerical invariants of programs by abstract interpretation. This domain, which consists of level sets of non-linear functions, generalizes the domain of linear "templates" introduced by Manna,…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure…
We construct compositional continuous approximations for an interconnection of infinitely many discrete-time switched systems. An approximation (known as abstraction) is itself a continuous-space system, which can be used as a replacement…
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order evolutionary equation involves the square root of an elliptic operator of second order. Finite element approximation in space is employed.…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
Verification of numerical accuracy properties in modern software remains an important and challenging task. This paper describes an original framework combining different solutions for numerical accuracy. First, we extend an existing…
A recurrent task in coordinated systems is managing (estimating, predicting, or controlling) signals that vary in space, such as distributed sensed data or computation outcomes. Especially in large-scale settings, the problem can be…
In this work we use intersection of different pseudo-orbits obtained by interval extensions to reduce the bounds of the exact solution provided by the toolbox Intlab. The method is applied on the logistic map.
We propose here a number of approaches to implement constraint propagation for arithmetic constraints on integer intervals. To this end we introduce integer interval arithmetic. Each approach is explained using appropriate proof rules that…
We present Decapodes, a diagrammatic tool for representing, composing, and solving partial differential equations. Decapodes provides an intuitive diagrammatic representation of the relationships between variables in a system of equations,…
The ISO 5725 series frames interlaboratory precision through repeatability, between-laboratory, and reproducibility variances, yet practical guidance on deploying bootstrap methods within this one-way random-effects setting remains limited.…
Automated techniques for rigorous floating-point round-off error analysis are important in areas including formal verification of correctness and precision tuning. Existing tools and techniques, while providing tight bounds, fail to analyze…