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Lagrangian particle methods based on detailed atomic and molecular models are powerful computational tools for studying the dynamics of microscale and nanoscale systems. However, the maximum time step is limited by the smallest oscillation…
Chemical reactions inside cells are generally considered to happen within fixed-size compartments. Needless to say, cells and their compartments are highly dynamic. Thus, such stringent assumptions may not reflect biochemical reality, and…
The goal of this paper is to outline a scenario of emerging stochasticity in high-dimensional highly nonlinear systems, such as genetic regulatory networks (GRN). We focus attention on the fact that in such systems confluence of all the…
We develop a Split Reactive Brownian Dynamics (SRBD) algorithm for particle simulations of reaction-diffusion systems based on the Doi or volume reactivity model, in which pairs of particles react with a specified Poisson rate if they are…
Chemical space exploration underlies drug discovery, yet most generative models treat chemical space as a fixed, implicitly learned distribution, focusing on sampling molecules rather than deliberately designing the space itself. We…
Generators of space-time dynamics in bioimaging have become essential to build ground truth datasets for image processing algorithm evaluation such as biomolecule detectors and trackers, as well as to generate training datasets for deep…
Brownian Dynamics algorithms are widely used for simulating soft-matter and biochemical systems. In recent times, their application has been extended to the simulation of coarse-grained models of cellular networks in simple organisms. In…
We present a novel multiscale simulation approach for modeling stochasticity in chemical reaction networks. The approach seamlessly integrates exact-stochastic and "leaping" methodologies into a single "partitioned leaping" algorithmic…
Models invoking the chemical master equation are used in many areas of science, and, hence, their simulation is of interest to many researchers. The complexity of the problems at hand often requires considerable computational power, so a…
Molecular dynamics simulations can generate atomically detailed trajectories of complex systems, but analyzing these dynamics can be challenging when systems lack well-established quantitative descriptors (features). Graph neural networks…
Discrete-state, continuous-time Markov models are becoming commonplace in the modelling of biochemical processes. The mathematical formulations that such models lead to are opaque, and, due to their complexity, are often considered…
We consider stochastic descriptions of chemical reaction networks in which there are both fast and slow reactions, and for which the time scales are widely separated. We develop a computational algorithm that produces the generator of the…
Astrochemical simulations are a powerful tool for revealing chemical evolution in the interstellar medium. Astrochemical calculations require efficient processing of large matrices for the chemical networks. The large chemical reaction…
We propose a universal approach for analysis and fast simulations of stiff stochastic biochemical kinetics networks, which rests on elimination of fast chemical species without a loss of information about mesoscopic, non-Poissonian…
Real-time nonequilibrium Green functions (NEGF) have been very successful to simulate the dynamics of correlated many-particle systems far from equilibrium. However, NEGF simulations are computationally expensive since the effort scales…
From AlexNet to Inception, autoencoders to diffusion models, the development of novel and powerful deep learning models and learning algorithms has proceeded at breakneck speeds. In part, we believe that rapid iteration of model…
We present a real-time second-order Green's function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of $O(N_{\rm e}^3$), where $N_{\rm e}$ is the number of electrons. The cubic scaling…
Based on a rate equation model for single-mode two-level lasers, two algorithms for stochastically simulating the dynamics and steady-state behaviour of micro- and nanolasers are described in detail. Both methods lead to steady-state photon…
While existing mathematical descriptions can accurately account for phenomena at microscopic scales (e.g. molecular dynamics), these are often high-dimensional, stochastic and their applicability over macroscopic time scales of physical…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…