Related papers: The Spatial Regime Conversion Method
We develop and analyze a stochastic genetic interacting particle method (SGIP) for reaction-diffusion-advection (RDA) equations. The SGIP method employs operator splitting to approximate the advection-diffusion and reaction processes,…
A combination of reaction-diffusion models with moving-boundary problems yields a system in which the diffusion (spreading and penetration) and reaction (transformation) evolve the system's state and geometry over time. These systems can be…
The Direct Simulation Monte Carlo (DSMC) method is widely employed for simulating rarefied nonequilibrium gas flows. With advances in aerospace engineering and micro/nano-scale technologies, gas flows exhibit the coexistence of rarefied and…
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…
Spatial control methods using additional modules on pretrained diffusion models have gained attention for enabling conditional generation in natural images. These methods guide the generation process with new conditions while leveraging the…
We present three algorithms for calculating rate constants and sampling transition paths for rare events in simulations with stochastic dynamics. The methods do not require a priori knowledge of the phase space density and are suitable for…
The stochastic reaction-diffusion model driven by a multiplicative noise is examined. We construct the gradient discretisation method (GDM), an abstract framework combining several numerical method families. The paper provides the…
Hybrid quantum mechanical-molecular mechanical (QM/MM) simulations are widely used in enzyme simulation. Over ten convergence studies of QM/MM methods have revealed over the past several years that key energetic and structural properties…
Accurate and robust surrogate modeling is essential for the real-time control and optimization of large-scale subsurface systems, such as geological CO2 storage and waterflood management. This study investigates the limits of classical…
Electromagnetic (EM) wave scattering in electrically large, irregularly shaped, environments is a common phenomenon. The deterministic, or first principles, study of this process is usually computationally expensive and the results exhibit…
Earth system models (ESMs) are fundamental for understanding Earth's complex climate system. However, the computational demands and storage requirements of ESM simulations limit their utility. For the newly published CESM2-LENS2 data, which…
Open biochemical systems of interacting molecules are ubiquitous in life-related processes. However, established computational methodologies, like molecular dynamics, are still mostly constrained to closed systems and timescales too small…
Semantic image synthesis (SIS) is a task to generate realistic images corresponding to semantic maps (labels). However, in real-world applications, SIS often encounters noisy user inputs. To address this, we propose Stochastic Conditional…
Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing…
Regional Climate Models (RCM) describe the meso scale global atmospheric and oceanic dynamics and serve as dynamical downscaling models. In other words, RCMs use atmospheric and oceanic climate output from General Circulation Models (GCM)…
In synaptic molecular communication, the activation of postsynaptic receptors by neurotransmitters (NTs) is governed by a stochastic reaction-diffusion process and, hence, inherently random. It is currently not fully understood how this…
Random Batch Methods (RBM) for mean-field interacting particle systems enable the reduction of the quadratic computational cost associated with particle interactions to a near-linear cost. The essence of these algorithms lies in the random…
In this paper, we propose a dynamically low-dimensional approximation method to solve a class of time-dependent multiscale stochastic diffusion equations. A dynamically bi-orthogonal (DyBO) method was developed to explore low-dimensional…
Complex behaviour in many systems arises from the stochastic interactions of spatially distributed particles or agents. Stochastic reaction-diffusion processes are widely used to model such behaviour in disciplines ranging from biology to…
The quantum computer offers significant advantages in simulating physical systems, particularly those with exponentially large state spaces, such as quantum systems. Stochastic reaction-diffusion systems, characterized by their stochastic…