Related papers: A route to the hydrodynamic limit of a reaction-di…
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…
Motivated by models of signaling pathways in B lymphocytes, which have extremely large nuclei, we study the question of how reaction-diffusion equations in thin $2D$ domains may be approximated by diffusion equations in regions of smaller…
Elucidating reaction mechanisms hinges on efficiently generating transition states (TSs), products, and complete reaction networks. Recent generative models, such as diffusion models for TS sampling and sequence-based architectures for…
Many complex multiphysics systems in fluid dynamics involve using solvers with varied levels of approximations in different regions of the computational domain to resolve multiple spatiotemporal scales present in the flow. The accuracy of…
We propose a new geometric approach to describe the qualitative dynamics of chemical reactions networks. By this method we identify metastable regimes, defined as low dimensional regions of the phase space close to which the dynamics is…
Systems of reaction-diffusion partial differential equations (RD-PDEs) are widely applied for modelling life science and physico-chemical phenomena. In particular, the coupling between diffusion and nonlinear kinetics can lead to the…
The discrete chemical master equation (dCME) provides a fundamental framework for studying stochasticity in mesoscopic networks. Because of the multi-scale nature of many networks where reaction rates have large disparity, directly solving…
The evolution of chemical reaction networks is often analyzed through kinetic models and energy landscapes, but these approaches fail to capture the deeper structural constraints governing complexity growth. In chemical reaction networks,…
This paper studies the robustness of a PDE backstepping delay-compensated boundary controller for a reaction-diffusion partial differential equation (PDE) with respect to a nominal delay subject to stochastic error disturbance. The…
The nonlinear coupled reaction-diffusion (NCRD) systems are important in the formation of spatiotemporal patterns in many scientific and engineering fields, including physical and chemical processes, biology, electrochemical processes,…
Deep Generative Models (DGMs), including Energy-Based Models (EBMs) and Score-based Generative Models (SGMs), have advanced high-fidelity data generation and complex continuous distribution approximation. However, their application in…
In this work, we aimed to replicate and extend the results presented in the DiffFluid paper[1]. The DiffFluid model showed that diffusion models combined with Transformers are capable of predicting fluid dynamics. It uses a denoising…
We analyze the mixed frame equations of radiation hydrodynamics under the approximations of flux-limited diffusion and a thermal radiation field, and derive the minimal set of evolution equations that includes all terms that are of leading…
The Lagrange-mesh $R$-matrix method is generalized to inhomogeneous equations. This method is numerically stable and efficient. It can be directly used for transfer reactions with the formalism discussed by Ascuitto and Glendenning [Phys.…
A growing body of literature has been leveraging techniques of machine learning (ML) to build novel approaches to approximating the solutions to partial differential equations. Noticeably absent from the literature is a systematic…
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…
Diffusion models have recently emerged as powerful stochastic frameworks for high-dimensional inference and generation. However, existing applications to partial differential equations (PDEs) predominantly rely on physics-informed training…
We propose a new, unified approach to solving jump-diffusion partial integro-differential equations (PIDEs) that often appear in mathematical finance. Our method consists of the following steps. First, a second-order operator splitting on…
In large-eddy simulations of atmospheric boundary layer turbulence, the lumped coefficient in the eddy-diffusion subgrid-scale (SGS) model is known to depend on scale for the case of inert scalars. This scale dependence is predominant near…
Fluctuating hydrodynamics (FHD) provides a framework for modeling microscopic fluctuations in a manner consistent with statistical mechanics and nonequilibrium thermodynamics. This paper presents an FHD formulation for isothermal reactive…