Related papers: Variational multiscale analysis: the fine-scale Gr…
In this work, we have developed a variational Bayesian inference theory of elasticity, which is accomplished by using a mixed Variational Bayesian inference Finite Element Method (VBI-FEM) that can be used to solve the inverse deformation…
Variational inference is an alternative estimation technique for Bayesian models. Recent work shows that variational methods provide consistent estimation via efficient, deterministic algorithms. Other tools, such as model selection using…
We study system design problems stated as parameterized stochastic programs with a chance-constraint set. We adopt a Bayesian approach that requires the computation of a posterior predictive integral which is usually intractable. In…
Existing deterministic variational inference approaches for diffusion processes use simple proposals and target the marginal density of the posterior. We construct the variational process as a controlled version of the prior process and…
The solution for non-linear, complex partial differential Equations (PDEs) is achieved through numerical approximations, which yield a linear system of equations. This approach is prevalent in Computational Fluid Dynamics (CFD), but it…
In this paper, based on the idea of direct discrete modeling (DDM) with equilibrium distribution functions (EDFs), we develop a general framework of the mesoscopic numerical method (MesoNM) for macroscopic partial differential equations…
The study gives a brief overview of existing modifications of the method of functional separation of variables for nonlinear PDEs. It proposes a more general approach to the construction of exact solutions to nonlinear equations of applied…
We identify effective stochastic differential equations (SDE) for coarse observables of fine-grained particle- or agent-based simulations; these SDE then provide useful coarse surrogate models of the fine scale dynamics. We approximate the…
We study large deviation properties of systems of weakly interacting particles modeled by It\^{o} stochastic differential equations (SDEs). It is known under certain conditions that the corresponding sequence of empirical measures…
In the present work we introduce a novel refinement algorithm for two-dimensional elliptic partial differential equations discretized with Virtual Element Method (VEM). The algorithm improves the numerical solution accuracy and the mesh…
Unique existence of analytically strong solutions to stochastic partial differential equations (SPDE) with drift given by the subdifferential of a quasi-convex function and with general multiplicative noise is proven. The proof applies a…
In image reconstruction, an accurate quantification of uncertainty is of great importance for informed decision making. Here, the Bayesian approach to inverse problems can be used: the image is represented through a random function that…
We present a novel variational framework for performing inference in (neural) stochastic differential equations (SDEs) driven by Markov-approximate fractional Brownian motion (fBM). SDEs offer a versatile tool for modeling real-world…
When solving partial differential equations using classical schemes such as finite difference or finite volume methods, sufficiently fine meshes and carefully designed schemes are required to achieve high-order accuracy of numerical…
Multiscale and multiphysics problems need novel numerical methods in order for them to be solved correctly and predictively. To that end, we develop a wavelet based technique to solve a coupled system of nonlinear partial differential…
Stochastic differential equations (SDEs) are increasingly used in longitudinal data analysis, compartmental models, growth modelling, and other applications in a number of disciplines. Parameter estimation, however, currently requires…
We develop the method of stochastic modified equations (SME), in which stochastic gradient algorithms are approximated in the weak sense by continuous-time stochastic differential equations. We exploit the continuous formulation together…
Due to the wide range of timescales that are present in macromolecular systems, hierarchical multiscale strategies are necessary for their computational study. Coarse-graining (CG) allows to establish a link between different system…
This paper derives a free analog of the Euler-Maruyama method (fEMM) to numerically approximate solutions of free stochastic differential equations (fSDEs). Simply speaking fSDEs are stochastic differential equations in the context of…
Many partial differential equations (PDEs) such as Navier--Stokes equations in fluid mechanics, inelastic deformation in solids, and transient parabolic and hyperbolic equations do not have an exact, primal variational structure. Recently,…