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Diffusion-based models have achieved notable empirical successes in reinforcement learning (RL) due to their expressiveness in modeling complex distributions. Despite existing methods being promising, the key challenge of extending existing…

In this work, we introduce a new Hybrid High-Order method for the numerical simulation of fracture propagation based on phase-field models. The proposed method supports general meshes made of polygonal/polyhedral elements, which provides…

Shallow water surface flows commonly entrain sediments, resulting in scouring and/or deposition of the underlying substrate that may strongly influence the pattern of subsequent flow. These coupled phenomena, which can be investigated…

In this paper, a thermal-dynamical consistent model for mass transfer across permeable moving interfaces is proposed by using the energy variation method. We consider a restricted diffusion problem where the flux across the interface…

In this work, we present an efficient approach to solve nonlinear high-contrast multiscale diffusion problems. We incorporate the explicit-implicit-null (EIN) method to separate the nonlinear term into a linear term and a damping term, and…

This paper aims at reviewing nonlinear methods for model order reduction of structures with geometric nonlinearity, with a special emphasis on the techniques based on invariant manifold theory. Nonlinear methods differ from linear based…

This paper introduces a generalised 3rd-order Spectral Representation Method for the simulation of multi-dimensional stochastic fields with asymmetric non-linearities. The simulated random fields satisfy a prescribed Power Spectrum and…

In recent years, large-scale numerical simulations played an essential role in estimating the effects of explosion events in urban environments, for the purpose of ensuring the security and safety of cities. Such simulations are…

Spectral methods provide highly accurate numerical solutions for partial differential equations, exhibiting exponential convergence with the number of spectral nodes. Traditionally, in addressing time-dependent nonlinear problems, attention…

The paper introduces a reduced order model (ROM) for numerical integration of a dynamical system which depends on multiple parameters. The ROM is a projection of the dynamical system on a low dimensional space that is both problem-dependent…

This paper presents a novel non-linear model reduction method: Probabilistic Manifold Decomposition (PMD), which provides a powerful framework for constructing non-intrusive reduced-order models (ROMs) by embedding a high-dimensional system…

We present a high-order method for flow simulation on unstructured curved nonconforming sliding meshes. This method utilizes dynamic transfinite mortar elements to exchange flow information between the two sides of a sliding interface. The…

Reduced Order Modeling (ROM) for engineering applications has been a major research focus in the past few decades due to the unprecedented physical insight into turbulence offered by high-fidelity CFD. The primary goal of a ROM is to model…

We present a finite-difference integration algorithm for solution of a system of differential equations containing a diffusion equation with nonlinear terms. The approach is based on Crank-Nicolson method with predictor-corrector algorithm…

Spatiotemporally chaotic systems, such as the solutions of some nonlinear partial differential equations, are dynamical systems that evolve toward a lower dimensional manifold. This manifold has an intricate geometry with heterogeneous…

Seamlessly moving objects within a scene is a common requirement for image editing, but it is still a challenge for existing editing methods. Especially for real-world images, the occlusion situation further increases the difficulty. The…

In this paper, we propose and analyze a new semi-implicit stochastic multiscale method for the radiative heat transfer problem with additive noise fluctuation in composite materials. In the proposed method, the strong nonlinearity term…

We present a flexible discretization technique for computational models of thin tubular networks embedded in a bulk domain, for example a porous medium. These systems occur in the simulation of fluid flow in vascularized biological tissue,…

Direct numerical simulation of Stokes flow through an impermeable, rigid body matrix by finite elements requires meshes fine enough to resolve the pore-size scale and is thus a computationally expensive task. The cost is significantly…

The goal of this paper is to assess the utility of Reduced-Order Models (ROMs) developed from 3D physics-based models for predicting transient thermal power output for an enhanced geothermal reservoir while explicitly accounting for…