Related papers: Stochastic electromechanical bidomain model
Neural differential equations predict the derivative of a stochastic process. This allows irregular forecasting with arbitrary time-steps. However, the expressive temporal flexibility often comes with a high sensitivity to noise. In…
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Stochastic partial differential equations (SPDE) on graphs were introduced by Cerrai and Freidlin [Ann. Inst. Henri Poincar\'e Probab. Stat. 53 (2017) 865-899]. This class of stochastic equations in infinite dimensions provides a minimal…
A new asymptotic expansion scheme for backward SDEs (BSDEs) is proposed.The perturbation parameter is introduced just to scale the forward stochastic variables within a BSDE. In contrast to the standard small-diffusion asymptotic expansion…
In this paper, we extend the dynamical low-rank approximation method to the space of finite signed measures. Under this framework, we derive stochastic low-rank dynamics for stochastic differential equations (SDEs) coming from classical…
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Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…
Sticky diffusion models a Markovian particle experiencing reflection and temporary adhesion phenomena at the boundary. Numerous numerical schemes exist for approximating stopped or reflected stochastic differential equations (SDEs), but…
The thermodynamical model of visco-elastic deformable solids at finite strains is formulated in a fully Eulerian way in rates. Also effects of thermal expansion or buoyancy due to evolving mass density in a gravity field are covered. The…
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The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
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In this work, we present an iteratively decoupled algorithm for solving the quasi-static multiple-network poroelastic model. Our approach employs a total-pressure-based formulation with solid displacement, total pressure, and network…
Realistic physical phenomena exhibit random fluctuations across many scales in the input and output processes. Models of these phenomena require stochastic PDEs. For three-dimensional coupled (vector-valued) stochastic PDEs (SPDEs), for…
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This manuscript reports the first step towards building a robust and efficient model reduction methodology to capture transient dynamics in a transmission level electric power system. Such dynamics is normally modeled on…
We derive equations for the strongly coupled system of light and dense atomic ensembles. The formalism includes an arbitrary internal level structure for the atoms and is not restricted to weak excitation of atoms by light. In the low light…