Related papers: A New Hybrid Automaton Framework with Partial Diff…
This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The study presents novel mathematical formulations and…
Modeling complex dynamical systems with only partial knowledge of their physical mechanisms is a crucial problem across all scientific and engineering disciplines. Purely data-driven approaches, which only make use of an artificial neural…
Differential complexes such as the de Rham complex have recently come to play an important role in the design and analysis of numerical methods for partial differential equations. The design of stable discretizations of systems of partial…
In this work, we present a hybrid numerical method for solving evolution partial differential equations (PDEs) by merging the time finite element method with deep neural networks. In contrast to the conventional deep learning-based…
We analysis some singular partial differential equations systems(PDAEs) with boundary conditions in high dimension bounded domain with sufficiently smooth boundary. With the eigenvalue theory of PDE the systems initially is formulated as an…
Trajectory optimization is a fundamental problem in robotics. While optimization of continuous control trajectories is well developed, many applications require both discrete and continuous, i.e., hybrid, controls. Finding an optimal…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
This paper proposed a novel method for autonomous parking. Autonomous parking has received a lot of attention because of its convenience, but due to the complex environment and the non-holonomic constraints of vehicle, it is difficult to…
The numerical solution of large-scale PDEs, such as those occurring in data-driven applications, unavoidably require powerful parallel computers and tailored parallel algorithms to make the best possible use of them. In fact, considerations…
In this work, we propose an abstraction and refinement methodology for the controller synthesis of discrete-time stochastic systems to enforce complex logical properties expressed by deterministic finite automata (a.k.a. DFA). Our proposed…
Humans cannot always be treated as oracles for collaborative sensing. Robots thus need to maintain beliefs over unknown world states when receiving semantic data from humans, as well as account for possible discrepancies between…
The present article presents a summarizing view at differential-algebraic equations (DAEs) and analyzes how new application fields and corresponding mathematical models lead to innovations both in theory and in numerical analysis for this…
The paper presents a model of lateral phase separation in a two component material surface. The resulting fourth order nonlinear PDE can be seen as a Cahn-Hilliard equation posed on a time-dependent surface. Only elementary tangential…
An open problem in artificial intelligence is how systems can flexibly learn discrete abstractions that are useful for solving inherently continuous problems. Previous work has demonstrated that a class of hybrid state-space model known as…
We generalize the notion of partial dynamical symmetry (PDS) to a system of interacting bosons and fermions. In a PDS, selected states of the Hamiltonian are solvable and preserve the symmetry exactly, while other states are mixed. As a…
We summarize a recent study of discrete (integer-valued) Hamiltonian cellular automata (CA) showing that their dynamics can only be consistently defined, if it is linear in the same sense as unitary evolution described by the Schr\"odinger…
The literature is rich with studies, analyses, and examples on parameter estimation for describing the evolution of chaotic dynamical systems based on measurements, even when only partial information is available through observations.…
Higher-dimensional automata (HDAs) are models of non-interleaving concurrency for analyzing concurrent systems. There is a rich literature that deals with bisimulations for concurrent systems, and some of them have been extended to HDAs.…
Multi-task dense prediction, which aims to jointly solve tasks like semantic segmentation and depth estimation, is crucial for robotics applications but suffers from domain shift when deploying models in new environments. While unsupervised…
We define a special class of hybrid automata, called Deterministic and Transversal Linear Hybrid Automata (DTLHA), whose continuous dynamics in each location are linear time-invariant (LTI) with a constant input, and for which every…