Related papers: A Variational Formulation of Resolvent Analysis
In this paper we present a technique for constructing robust solvers for stiff algebraic source terms, such as those typically used for modelling relaxation processes in hyperbolic systems of partial differential equations describing…
Covariance regression analysis is an approach to linking the covariance of responses to a set of explanatory variables $X$, where $X$ can be a vector, matrix, or tensor. Most of the literature on this topic focuses on the "Fixed-$X$"…
This study presents the application of variable-order (VO) fractional calculus to the modeling of nonlocal solids. The reformulation of nonlocal fractional-order continuum mechanic framework, by means of VO kinematics, enables a unique…
We develop a new paradigm for finding bifurcations of solutions of nonlinear problems, which is based on the detection of extreme values of new type of variational functional associated with the considering problem. The variational…
A novel data-driven method of modal analysis for complex flow dynamics, termed as reduced-order variational mode decomposition (RVMD), has been proposed, combining the idea of the separation of variables and a state-of-the-art nonstationary…
The present study reports comprehensive bifurcation analysis of flow past a rotating cylinder at a fixed rotation rate by varying free-stream Reynolds number ($Re_{\infty}$) from 1000-6000 in intervals of 50. Two-dimensional compressible…
A variational model for learning convolutional image atoms from corrupted and/or incomplete data is introduced and analyzed both in function space and numerically. Building on lifting and relaxation strategies, the proposed approach is…
In fluid physics, data-driven models to enhance or accelerate solution methods are becoming increasingly popular for many application domains, such as alternatives to turbulence closures, system surrogates, or for new physics discovery. In…
Variational inference (VI) is a specific type of approximate Bayesian inference that approximates an intractable posterior distribution with a tractable one. VI casts the inference problem as an optimization problem, more specifically, the…
We study stochastic optimization from a joint continuous-discrete point of view. Starting from a second-order stochastic differential equation interpreted as a noisy accelerated gradient flow, we discretize the dynamics by a fully implicit…
We present the application of the variational-wavelet analysis to the quasiclassical calculations of the solutions of Wigner/von Neumann/Moyal and related equations corresponding to the nonlinear (polynomial) dynamical problems. (Naive)…
We consider a variational approach to solve parabolic problems by minimising a functional over time and space. To achieve existence results we investigate the notion of $\mathscr{A}$-quasiconvexity for non-homogeneous operators in…
Conventional inverse optimization inputs a solution and finds the parameters of an optimization model that render a given solution optimal. The literature mostly focuses on inferring the objective function in linear problems when accepted…
This work primarily focuses on the study of three gradient reconstruction techniques applied to the calculation of viscous terms in a cell-centered, finite volume formulation for general unstructured grids. The work also addresses different…
In this paper we analyze the theoretical properties of a stochastic representation of the incompressible Navier-Stokes equations defined in the framework of the modeling under location uncertainty (LU). This setup built from a stochastic…
Modern reinforcement learning (RL) algorithms have found success by using powerful probabilistic models, such as transformers, energy-based models, and diffusion/flow-based models. To this end, RL researchers often choose to pay the price…
This paper introduces a very fast method for the computation of the resolvent of fractional powers of operators. The analysis is kept in the continuous setting of (potentially unbounded) self adjoint positive operators in Hilbert spaces.…
The recently introduced harmonic resolvent framework is concerned with the study of the input-output dynamics of nonlinear flows in the proximity of a known time-periodic orbit. These dynamics are governed by the harmonic resolvent…
This paper focuses on the so-called Weighted Inertia-Dissipation-Energy (WIDE) variational approach for the approximation of unsteady Leray-Hopf solutions of the incompressible Navier-Stokes system. Initiated in [56], this variational…
Incorporating relational reasoning into neural networks has greatly expanded their capabilities and scope. One defining trait of relational reasoning is that it operates on a set of entities, as opposed to standard vector representations.…