Related papers: Sparse Data Structures for Efficient State-to-Stat…
Sparsity constraints on the control inputs of a linear dynamical system naturally arise in several practical applications such as networked control, computer vision, seismic signal processing, and cyber-physical systems. In this work, we…
Recovering dynamical equations from observed noisy data is the central challenge of system identification. We develop a statistical mechanics approach to analyze sparse equation discovery algorithms, which typically balance data fit and…
The challenging problem of conducting fully Bayesian inference for the reaction rate constants governing stochastic kinetic models (SKMs) is considered. Given the challenges underlying this problem, the Markov jump process representation is…
By exploiting the complexity intrinsic to quantum dynamics, quantum technologies promise a whole host of computational advantages. One such advantage lies in the field of stochastic modelling, where it has been shown that quantum stochastic…
Stokesian Dynamics (SD) is a powerful computational framework for simulating the motion of particles in a viscous Newtonian fluid under Stokes-flow conditions. Traditional SD implementations can be computationally expensive as they rely on…
In this work it is shown how the immersed boundary method of (Peskin2002) for modeling flexible structures immersed in a fluid can be extended to include thermal fluctuations. A stochastic numerical method is proposed which deals with…
Steady states and traveling waves play a fundamental role in understanding hydrodynamic problems. Even when unstable, these states provide the bifurcation-theoretic explanation for the origin of the observed states. In turbulent…
In biochemical systems some of the chemical species are present with only small numbers of molecules. In this situation discrete and stochastic simulation approaches are more relevant than continuous and deterministic ones. The fundamental…
Stochastic kinetic models (SKMs) are increasingly used to account for the inherent stochasticity exhibited by interacting populations of species in areas such as epidemiology, population ecology and systems biology. Species numbers are…
The Quasi-Steady State Approximation (QSSA) can be an effective tool for reducing the size and stiffness of chemical mechanisms for implementation in computational reacting flow solvers. However, for many applications, stiffness remains,…
Simulation of quantum chemistry is expected to be a principal application of quantum computing. In quantum simulation, a complicated Hamiltonian describing the dynamics of a quantum system is decomposed into its constituent terms, where the…
Convective features, represented here as warm bubble-like patterns, reveal essential high-level information about how short-term weather dynamics evolve within a high-dimensional state space. In this paper, we introduce a data-driven…
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such…
State-space models (SSMs) are a powerful statistical tool for modelling time-varying systems via a latent state. In these models, the latent state is never directly observed. Instead, a sequence of data points related to the state are…
This thesis is interested in the application of statistical physics methods and inference to sparse linear estimation problems. The main tools are the graphical models and approximate message-passing algorithm together with the cavity…
In the current era of Noisy Intermediate Scale Quantum (NISQ) computing, efficient digital simulation of quantum systems holds significant importance for quantum algorithm development, verification and validation. However, analysis of…
Semidefinite programs (SDPs) are a particular class of convex optimization problems with applications in combinatorial optimization, operational research, and quantum information science. Seminal work by Brand\~{a}o and Svore shows that a…
Capturing the correlation emerging between constituents of many-body systems accurately is one of the key challenges for the appropriate description of various systems whose properties are underpinned by quantum mechanical fundamentals.…
Stochasticity plays a fundamental role in various biochemical processes, such as cell regulatory networks and enzyme cascades. Isothermal, well-mixed systems can be modelled as Markov processes, typically simulated using the Gillespie…
Non-Markovian models have great expressive power, at the cost of complex analysis of the stochastic process. The method of Stochastic State Classes (SSCs) derives closed-form analytical expressions for the joint Probability Density…