相关论文: Chemical Case Studies in KeYmaera X
Molecular dynamics simulation is now a widespread approach for understanding complex systems on the atomistic scale. It finds applications from physics and chemistry to engineering, life and medical science. In the last decade, the approach…
We demonstrate the first end-to-end integration of high-performance computing (HPC), reliable quantum computing, and AI in a case study on catalytic reactions producing chiral molecules. We present a hybrid computation workflow to determine…
Safe deployment of autonomous robots in diverse scenarios requires agents that are capable of efficiently adapting to new environments while satisfying constraints. In this work, we propose a practical and theoretically-justified approach…
A system of $N$ particles in a chemical medium in $\mathbb{R}^{d}$ is studied in a discrete time setting. Underlying interacting particle system in continuous time can be expressed as \begin{eqnarray} dX_{i}(t) &=&[-(I-A)X_{i}(t) +…
Frontier artificial intelligence (AI) systems present both benefits and risks to society. Safety cases - structured arguments supported by evidence - are one way to help ensure the safe development and deployment of these systems. Yet the…
Model-based process simulation can be used to derive designs and operating conditions of chemical processes that optimally balance multiple objectives, such as quality, costs, or environmental impacts. This work focuses on identifying…
We present a new approach to automated scenario-based testing of the safety of autonomous vehicles, especially those using advanced artificial intelligence-based components, spanning both simulation-based evaluation as well as testing in…
Formal verification has been successfully developed in computer science for verifying combinatorial classes of models and specifications. In like manner, formal verification methods have been developed for dynamical systems. However, the…
Mathematical models are increasingly being used to understand complex biochemical systems, to analyze experimental data and make predictions about unobserved quantities. However, we rarely know how robust our conclusions are with respect to…
We study a proof methodology for verifying the safety of data invariants of highly-available distributed applications that replicate state. The proof is (1) modular: one can reason about each individual operation separately, and (2)…
This paper introduces a proof calculus for real-analytic differential-algebraic dynamic logic, enabling correct transformations of differential-algebraic equations. Applications include index reductions from differential-algebraic equations…
Reaction systems are discrete dynamical systems inspired by bio-chemical processes, whose dynamical behaviour is expressed by set-theoretic operations on finite sets. Reaction systems thus provide a description of bio-chemical phenomena…
The dynamics of physical theories is usually described by differential equations. Difference equations then appear mainly as an approximation which can be used for a numerical analysis. As such, they have to fulfill certain conditions to…
The desire to use reinforcement learning in safety-critical settings has inspired a recent interest in formal methods for learning algorithms. Existing formal methods for learning and optimization primarily consider the problem of…
Rigid bodies, plastic impact, persistent contact, Coulomb friction, and massless limbs are ubiquitous simplifications introduced to reduce the complexity of mechanics models despite the obvious physical inaccuracies that each incurs…
Machine learning recently has been used to identify the governing equations for dynamics in physical systems. The promising results from applications on systems such as fluid dynamics and chemical kinetics inspire further investigation of…
We study dynamic risk measures in a very general framework enabling to model uncertainty and processes with jumps. We previously showed the existence of a canonical equivalence class of probability measures hidden behind a given set of…
This article presents an axiomatic approach for deductive verification of existence and liveness for ordinary differential equations (ODEs) with differential dynamic logic (dL). The approach yields proofs that the solution of a given ODE…
Several methods in nonadiabatic molecular dynamics are based on Madelung's hydrodynamic description of nuclear motion, while the electronic component is treated as a finite-dimensional quantum system. In this context, the quantum potential…
Diffusion models (DMs) have been investigated in various domains due to their ability to generate high-quality data, thereby attracting significant attention. However, similar to traditional deep learning systems, there also exist potential…