相关论文: Equation-Free Multiscale Computation: enabling mic…
Numerical models are widely used to simulate the earth system, but they are computationally expensive and often depend on many uncertain input parameters. Their effective use requires calibration and uncertainty quantification, which…
The complexity of biological systems and processes, spanning molecular to macroscopic scales, necessitates the use of multiscale simulations to get a comprehensive understanding. Quantum mechanics/molecular mechanics (QM/MM) molecular…
Phase-field methods offer a versatile computational framework for simulating large-scale morphological evolution. However, the applicability and predictability of phase-field models are inherently limited by their ad hoc nature, and there…
The Equation-Free approach to efficient multiscale numerical computation marries trusted micro-scale simulations to a framework for numerical macro-scale reduction -- the patch dynamics scheme. A recent novel patch scheme empowered the…
The modelling of electrokinetic flows is a critical aspect spanning many industrial applications and research fields. This has introduced great demand in flexible numerical solvers to describe these flows. The underlying phenomena are…
This chapter discusses the development and implementation of algorithms based on Equation-Free/Dynamic Data Driven Applications Systems (EF/DDDAS) protocols for the computer-assisted study of the bifurcation structure of complex dynamical…
We demonstrate how direct simulation of stochastic, individual-based models can be combined with continuum numerical analysis techniques to study the dynamics of evolving diseases. % Sidestepping the necessity of obtaining explicit…
A common approach to studying high-dimensional systems with emergent low-dimensional behavior is based on lift-evolve-restrict maps (called equation-free methods): first, a user-defined lifting operator maps a set of low-dimensional…
Models of stochastic processes are widely used in almost all fields of science. Theory validation, parameter estimation, and prediction all require model calibration and statistical inference using data. However, data are almost always…
Developments in dynamical systems theory provides new support for the macroscale modelling of pdes and other microscale systems such as Lattice Boltzmann, Monte Carlo or Molecular Dynamics simulators. By systematically resolving subgrid…
When simulating multiscale stochastic differential equations (SDEs) in high-dimensions, separation of timescales, stochastic noise and high-dimensionality can make simulations prohibitively expensive. The computational cost is dictated by…
These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Discuss a mix of new mathematical approaches for multiscale…
Equations governing physico-chemical processes are usually known at microscopic spatial scales, yet one suspects that there exist equations, e.g. in the form of Partial Differential Equations (PDEs), that can explain the system evolution at…
Sparse coding aims to model data vectors as sparse linear combinations of basis elements, but a majority of related studies are restricted to continuous data without spatial or temporal structure. A new model-based sparse coding (MSC)…
Modeling microstructure evolution in electrochemical systems is vital for understanding the mechanism of various electrochemical processes. In this work, we propose a general phase field framework that is fully variational and thus…
A meta-model of the input-output data of a computationally expensive simulation is often employed for prediction, optimization, or sensitivity analysis purposes. Fitting is enabled by a designed experiment, and for computationally expensive…
This paper introduces Low-EFFourth (LEF4), a MATLAB-based computational framework designed for generating and studying multilevel model ensembles in continuous dynamical systems. Initially developed to address questions in climate…
Understanding the functional architecture of complex systems is crucial to illuminate their inner workings and enable effective methods for their prediction and control. Recent advances have introduced tools to characterise emergent…
Spatially distributed problems are often approximately modelled in terms of partial differential equations (PDEs) for appropriate coarse-grained quantities (e.g. concentrations). The derivation of accurate such PDEs starting from finer…
MiMiC is a framework for performing multiscale simulations in which loosely coupled external programs describe individual subsystems at different resolutions and levels of theory. To make it highly efficient and flexible, we adopt an…