Related papers: Variational approach to coarse-graining of general…
Dual gradient descent combined with early stopping represents an efficient alternative to the Tikhonov variational approach when the regularizer is strongly convex. However, for many relevant applications, it is crucial to deal with…
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural…
In this note we study the singular vanishing-viscosity limit of a gradient flow set in a finite-dimensional Hilbert space and driven by a smooth, but possibly non convex, time-dependent energy functional. We resort to ideas and techniques…
Dynamical systems with large state-spaces are often expensive to thoroughly explore experimentally. Coarse-graining methods aim to define simpler systems which are more amenable to analysis and exploration; most current methods, however,…
In this work we exploit agglomeration based $h$-multigrid preconditioners to speed-up the iterative solution of discontinuous Galerkin discretizations of the Stokes and Navier-Stokes equations. As a distinctive feature $h$-coarsened mesh…
We present a data-driven machine-learning approach for modeling space-time socioeconomic dynamics. Through coarse-graining fine-scale observations, our modeling framework simplifies these complex systems to a set of tractable mechanistic…
We introduce an RG-inspired coarse-graining for extracting the collective features of data. The key to successful coarse-graining lies in finding appropriate pairs of data sets. We coarse-grain the two closest data in a regular real-space…
We consider the covariance steering problem for nonlinear control-affine systems. Our objective is to find an optimal control strategy to steer the state of a system from an initial distribution to a target one whose mean and covariance are…
This article introduces the splitting method to systems responding to rough paths as external stimuli. The focus is on nonlinear partial differential equations with rough noise but we also cover rough differential equations. Applications to…
We introduce a generalized machine learning framework to probabilistically parameterize upper-scale models in the form of nonlinear PDEs consistent with a continuum theory, based on coarse-grained atomistic simulation data of mechanical…
Variational principles in mechanics, field theory and geometric analysis are usually formulated on closed admissible classes, where boundary variations are either fixed or independently cancelled through natural boundary conditions.…
Bayesian inference plays an important role in advancing machine learning, but faces computational challenges when applied to complex models such as deep neural networks. Variational inference circumvents these challenges by formulating…
We evaluate an efficient overset grid method for two-dimensional and three-dimensional particulate flows for small numbers of particles at finite Reynolds number. The rigid particles are discretised using moving overset grids overlaid on a…
The computational study of strongly-coupled, gas-solid flows at scales relevant to most environmental and engineering applications requires the use of `coarse-grained' methodologies such as the two-fluid model, particle-in-cell approach or…
Galilean invariance is a cornerstone of classical mechanics. It states that for closed systems the equations of motion of the microscopic degrees of freedom do not change under Galilean transformations to different inertial frames. However,…
This paper introduces a novel approach to algebraic multigrid methods for large systems of linear equations coming from finite element discretizations of certain elliptic second order partial differential equations. Based on a discrete…
We present the conceptual and technical background required to describe and understand the correlations and fluctuations of the empirical density and current of steady-state diffusion processes on all time scales -- observables central to…
We propose a method for finding approximate compilations of quantum unitary transformations, based on techniques from policy gradient reinforcement learning. The choice of a stochastic policy allows us to rephrase the optimization problem…
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…
Statistical (machine learning) tools for equation discovery require large amounts of data that are typically computer generated rather than experimentally observed. Multiscale modeling and stochastic simulations are two areas where learning…