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Delay differential equations are of great importance in science, engineering, medicine and biological models. These type of models include time delay phenomena which is helpful for characterising the real-world applications in machine…
Large-scale network systems describe a wide class of complex dynamical systems composed of many interacting subsystems. A large number of subsystems and their high-dimensional dynamics often result in highly complex topology and dynamics,…
Dynamical system theory is a widely used technique in the analysis of cosmological models. Within this framework, the equations describing the dynamics of a model are recast in terms of dimensionless variables, which evolve according to a…
Closure modeling - the statistical modeling of missing dynamics in the natural sciences and engineering - is a growing and active area of research. Existing methods for closure modeling are often computationally prohibitive, lack…
Sampling the collective, dynamical fluctuations that lead to nonequilibrium pattern formation requires probing rare regions of trajectory space. Recent approaches to this problem based on importance sampling, cloning, and spectral…
Approximate Bayesian Computation (ABC) methods have gained in their popularity over the last decade because they expand the horizon of Bayesian parameter inference methods to the range of models for which only forward simulation is…
In this article, I provide significant mathematical evidence in support of the existence of short-time approximations of any polynomial order for the computation of density matrices of physical systems described by arbitrarily smooth and…
The physical sciences are replete with dynamical systems that require the resolution of a wide range of length and time scales. This presents significant computational challenges since direct numerical simulation requires discretization at…
Monte Carlo simulations of systems with a complex action are known to be extremely difficult. A new approach to this problem based on a factorization property of distribution functions of observables has been proposed recently. The method…
Sampling from distributions play a crucial role in aiding practitioners with statistical inference. However, in numerous situations, obtaining exact samples from complex distributions is infeasible. Consequently, researchers often turn to…
We develop a validated numerical procedure for continuation of local stable/unstable manifold patches attached to equilibrium solutions of ordinary differential equations. The procedure has two steps. First we compute an accurate high order…
This work is motivated by two problems: 1) The approach of manifolds and spaces by triangulations. 2) The complexity growth in sequences of polyhedra. Considering both problems as related, new criteria and methods for approximating smooth…
Condensed ionic systems are described in the framework of a combined approach that takes into account both long-range and short-range interactions. Short-range interaction is expressed in terms of mean potentials and long-range interaction…
A central problem in machine learning is often formulated as follows: Given a dataset $\{(x_j, y_j)\}_{j=1}^M$, which is a sample drawn from an unknown probability distribution, the goal is to construct a functional model $f$ such that…
Growth patterns generated by filamentous organisms (e.g. actinomycetes and fungi) involve spatial and temporal dynamics at different length scales. Several mathematical models have been proposed in the last thirty years to address these…
We adapt Vertex models to understand the physical origin of the formation of long-range ordered structures in repulsive soft particles. The model incorporates contributions from the volume and surface area of each particle. Sampling using…
Force-based multiphysics coupling methods have become popular since they provide a simple and efficient coupling mechanism, avoiding the difficulties in formulating and implementing a consistent coupling energy. They are also the only known…
Discrete time, spatially extended models play an important role in ecology, modelling population dynamics of species ranging from micro-organisms to birds. An important question is how 'bottom up', individual-based models can be…
In this paper, we consider the problem of manifold approximation with affine subspaces. Our objective is to discover a set of low dimensional affine subspaces that represents manifold data accurately while preserving the manifold's…
In this paper we present a method of discrete modeling and analysis of multi-level dynamics of complex large-scale hierarchical dynamic systems subject to external dynamic control mechanism. In a model each state describes parallel dynamics…