Related papers: Over-Approximation of Fluid Models
Biological systems are often modeled as a system of ordinary differential equations (ODEs) with time-invariant parameters. However, cell signaling events or pharmacological interventions may alter the cellular state and induce multi-mode…
A method for adaptive model order reduction for nonsmooth discrete element simulation is developed and analysed in numerical experiments. Regions of the granular media that collectively move as rigid bodies are substituted with rigid bodies…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
This paper is about computationally tractable methods for power system parameter estimation and Optimal Experiment Design (OED). Here, the main motivation is that OED has the potential to significantly increase the accuracy of power system…
Filtering is concerned with the sequential estimation of the state, and uncertainties, of a Markovian system, given noisy observations. It is particularly difficult to achieve accurate filtering in complex dynamical systems, such as those…
This paper presents two stochastic model predictive control methods for linear time-invariant systems subject to unbounded additive uncertainties. The new methods are developed by formulating the chance constraints into deterministic form,…
In this article, we discuss a couple of nonlinear Galerkin method (NLG) in finite element set up for viscoelastic fluid flow, mainly equations of motion arising in the flow of 2D Oldroyd model. We obtain improved error estimate in…
A micro-scale model is proposed for the evolution of the limit order book. Within this model, the flows of orders (claims) are described by doubly stochastic Poisson processes taking account of the stochastic character of intensities of bid…
Many physical systems are formulated on domains which are relatively large in some directions but relatively thin in other directions. We expect such systems to have emergent structures that vary slowly over the large dimensions. Common…
In this work, we present a parametric finite element approximation of two-phase Navier-Stokes flow with viscoelasticity. The free boundary problem is given by the viscoelastic Navier-Stokes equations in the two fluid phases, connected by…
Mean-field models approximate large stochastic systems by simpler differential equations that are supposed to approximate the mean of the larger system. It is generally assumed that as the stochastic systems get larger (i.e., more people or…
Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers. Stochastic noise causes aleatoric uncertainty, whereas imprecise knowledge of model parameters leads to epistemic uncertainty. Several…
In this work, we address parametric non-stationary fluid dynamics problems within a model order reduction setting based on domain decomposition. Starting from the optimisation-based domain decomposition approach, we derive an optimal…
Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a…
Iterative trajectory optimization techniques for non-linear dynamical systems are among the most powerful and sample-efficient methods of model-based reinforcement learning and approximate optimal control. By leveraging time-variant local…
Modeling and simulation of complex systems is key to explore systems dynamics. Many scientific approaches were developed to represent dynamic structure systems but most of these approaches are efficient for some kinds of systems and…
Ordinary differential equations obtained as limits of Markov processes appear in many settings. They may arise by scaling large systems, or by averaging rapidly fluctuating systems, or in systems involving multiple time-scales, by a…
We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between…
Maglaras, Moallemi, and Zheng (2021) have introduced a flexible queueing model for fragmented limit-order markets, whose fluid limit remains remarkably tractable. In the present study we prove that, in the limit of small and frequent…
Augmenting mechanistic ordinary differential equation (ODE) models with machine-learnable structures is an novel approach to create highly accurate, low-dimensional models of engineering systems incorporating both expert knowledge and…