Related papers: Model adaptation for hyperbolic balance laws
The paper has two goals: It presents basic ideas, notions, and methods for reduction of reaction kinetics models: quasi-steady-state, quasi-equilibrium, slow invariant manifolds, and limiting steps. It describes briefly the current state of…
Mathematical modeling of fluid flow in a porous medium is usually described by a continuity equation and a chosen constitutive law. The latter, depending on the problem at hand, may be a nonlinear relation between the fluid's pressure…
It is well-known that inverse dynamics models can improve tracking performance in robot control. These models need to precisely capture the robot dynamics, which consist of well-understood components, e.g., rigid body dynamics, and effects…
Chemically reacting systems exhibiting a repeatable delay period before a visible and sudden change are referred to as clock reactions; they have a long history in education and provide an idealisation of various biochemical and industrial…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
The trend to equilibrium for reaction-diffusion systems modelling chemical reaction networks is investigated, in the case when reaction processes happen on subsets of the domain. We prove the convergence to equilibrium by directly showing…
The entanglement entropy of the ground state of a quantum lattice model with local interactions usually satisfies an area law. However, in 1D systems some violations may appear in inhomogeneous systems or in random systems. In our…
For constrained linear systems with bounded disturbances and parametric uncertainty, we propose a robust adaptive model predictive control strategy with online parameter estimation. Constraints enforcing persistently exciting closed loop…
People organize in groups and contagions spread across them. A simple stochastic process, yet complex to model due to dynamical correlations within and between groups. Moreover, groups can evolve if agents join or leave in response to…
Extended Thermodynamics is a very important theory: for example, it predicts hyperbolicity, finite speeds of propagation waves as well as continuous dependence on initial data. Therefore, it constitutes a significative improvement of…
We consider adaptive finite element methods for solving a multiscale system consisting of a macroscale model comprising a system of reaction-diffusion partial differential equations coupled to a microscale model comprising a system of…
Learned image compression methods have attracted great research interest and exhibited superior rate-distortion performance to the best classical image compression standards of the present. The entropy model plays a key role in learned…
We propose a novel model reduction approach for the approximation of non linear hyperbolic equations in the scalar and the system cases. The approach relies on an offline computation of a dictionary of solutions together with an online…
In this work we present new scalable, information theory-based variational methods for the efficient model reduction of high-dimensional deterministic and stochastic reaction networks. The proposed methodology combines, (a) information…
We discuss a class of coupled systems of nonlocal nonlinear balance laws modeling multilane traffic, with the nonlocality present in both convective and source terms. The uniqueness and existence of the entropy solution are proven via…
The Bayesian uncertainty quantification technique has become well established in turbulence modeling over the past few years. However, it is computationally expensive to construct a globally accurate surrogate model for Bayesian inference…
We consider the task of inferring is-a relationships from large text corpora. For this purpose, we propose a new method combining hyperbolic embeddings and Hearst patterns. This approach allows us to set appropriate constraints for…
We introduce an approximation technique for nonlinear hyperbolic systems with sources that is invariant domain preserving. The method is discretization-independent provided elementary symmetry and skew-symmetry properties are satisfied by…
The global existence of renormalised solutions and convergence to equilibrium for reaction-diffusion systems with non-linear diffusion are investigated. The system is assumed to have quasi-positive non-linearities and to satisfy an entropy…
The stability of stationary solutions of first-order systems of PDE's are considered. They may include some singular geometric terms, leading to discontinuous flux and non-conservative products. Based on several examples in Fluid Mechanics,…