相关论文: Chemical Case Studies in KeYmaera X

We consider a biochemical model that consists of a system of partial differential equations based on reaction terms and subject to non--homogeneous Dirichlet boundary conditions. The model is discretised using the gradient discretisation…

We consider various modeling levels for spatially homogeneous chemical reaction systems, namely the chemical master equation, the chemical Langevin dynamics, and the reaction-rate equation. Throughout we restrict our study to the case where…

Safety cases - clear, assessable arguments for the safety of a system in a given context - are a widely-used technique across various industries for showing a decision-maker (e.g. boards, customers, third parties) that a system is safe. In…

Molecular dynamics simulations are used to study structure formation in simple model polymer chains that are subject to excluded volume and torsional interactions. The changing conformations exhibited by chains of different lengths under…

This paper presents a dynamic logic $d\mathcal{L}_\text{CHP}$ for compositional deductive verification of communicating hybrid programs (CHPs). CHPs go beyond the traditional mixed discrete and continuous dynamics of hybrid systems by…

Computational science relies on scientific software as its primary instrument for scientific discovery. Therefore, similar to the use of other types of scientific instruments, correct software and the correct operation of the software is…

This article discusses a new technique to automatically generate test cases for object oriented programs. At the state of the art, the problem of generating adequate sets of complete test cases has not been satisfactorily solved yet. There…

Learning-based methods have been successful in solving complex control tasks without significant prior knowledge about the system. However, these methods typically do not provide any safety guarantees, which prevents their use in…

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical…

Data-driven techniques have a large potential to transform and accelerate the chemical sciences. However, chemical sciences also pose the unique challenge of very diverse, small, fuzzy datasets that are difficult to leverage in conventional…

Hybrid games model cyber-physical systems (CPS), like cars, trains, and airplanes, where discrete control decisions interact with continuous physical dynamics. We use Large Language Models (LLMs) to scale formal verification and synthesis…

Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…

Model-based engineering promises to boost productivity and quality of complex systems development. In the context of safety-critical systems, a traditionally highly regulated and conservative domain, the use of models gained importance in…

Models play an essential role in the design process of cyber-physical systems. They form the basis for simulation and analysis and help in identifying design problems as early as possible. However, the construction of models that comprise…

We investigate the use of hybrid techniques in complex processes of infectious diseases. Since predictive disease models in biomedicine require a multiscale approach for understanding the molecule-cell-tissue-organ-body interactions,…

Chimera states are one of the most intriguing phenomena in nonlinear dynamics, characterized by the coexistence of coherent and incoherent behavior in systems of coupled identical oscillators. Despite extensive studies and numerous…

Mass-action chemical reaction systems are frequently used in Computational Biology. The corresponding polynomial dynamical systems are often large (consisting of tens or even hundreds of ordinary differential equations) and poorly…

We consider temporal logic verification of (possibly nonlinear) dynamical systems evolving over continuous state spaces. Our approach combines automata-based verification and the use of so-called barrier certificates. Automata-based…

The general theory of a complex system of nonlinear chemical reactions is a primary language of chemistry that includes chemical engineering and cellular biochemistry. Its significance as an analytical framework, however, has not been fully…

Is it possible to understand the intricacies of a dynamical system not solely from its input/output pattern, but also by observing the behavior of other systems within the same class? This central question drives the study presented in this…