Related papers: Statistical Finite Elements via Interacting Partic…
In this article, we introduce a new partially penalized immersed finite element method (IFEM) for solving elliptic interface problems with multi-domains and triple-junction points. We construct new IFE functions on elements intersected with…
In this paper we consider the filtering of a class of partially observed piecewise deterministic Markov processes (PDMPs). In particular, we assume that an ordinary differential equation (ODE) drives the deterministic element and can only…
Partial differential equations (PDEs) underlie our understanding and prediction of natural phenomena across numerous fields, including physics, engineering, and finance. However, solving parametric PDEs is a complex task that necessitates…
We use the ideas of goal-oriented error estimation and adaptivity to design and implement an efficient adaptive algorithm for approximating linear quantities of interest derived from solutions to elliptic partial differential equations…
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo derivative of order $\alpha\in(3/2, 2)$ in the leading term and…
In this paper, we propose a systematic approach for accelerating finite element-type methods by machine learning for the numerical solution of partial differential equations (PDEs). The main idea is to use a neural network to learn the…
We consider the numerical approximation of general semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive space-time noise. In contrast to the standard time stepping methods which uses basic increments of…
The proximal Galerkin finite element method is a high-order, low-iteration complexity, nonlinear numerical method that preserves the geometric and algebraic structure of point-wise bound constraints in infinite-dimensional function spaces.…
Automatic machine learning of empirical models from experimental data has recently become possible as a result of increased availability of computational power and dedicated algorithms. Despite the successes of non-parametric inference and…
We introduce a derivative-free computational framework for approximating solutions to nonlinear PDE-constrained inverse problems. The aim is to merge ideas from iterative regularization with ensemble Kalman methods from Bayesian inference…
In this work, we investigate the numerical approximation of the second order non-autonomous semilnear parabolic partial differential equation (PDE) using the finite element method. To the best of our knowledge, only the linear case is…
Solving inverse problems without the use of derivatives or adjoints of the forward model is highly desirable in many applications arising in science and engineering. In this paper, we propose a new version of such a methodology, a framework…
The scope of this research is the identification of unknown piecewise constant parameters of linear regression equation under the finite excitation condition. Compared to the known methods, to make the computational burden lower, only one…
Latent-variable energy-based models (LVEBMs) assign a single normalized energy to joint pairs of observed data and latent variables, offering expressive generative modeling while capturing hidden structure. We recast maximum-likelihood…
In this paper, we present an algorithm for stability analysis of systems described by coupled linear Partial Differential Equations (PDEs) with constant coefficients and mixed boundary conditions. Our approach uses positive matrices to…
Partial Differential Equations (PDE) are fundamental to model different phenomena in science and engineering mathematically. Solving them is a crucial step towards a precise knowledge of the behaviour of natural and engineered systems. In…
We present two effective methods for solving high-dimensional partial differential equations (PDE) based on randomized neural networks. Motivated by the universal approximation property of this type of networks, both methods extend the…
This paper presents a general theory and isogeometric finite element implementation for studying mass conserving phase transitions on deforming surfaces. The mathematical problem is governed by two coupled fourth-order nonlinear partial…
We consider the problem of parameter estimation for a stochastic McKean-Vlasov equation, and the associated system of weakly interacting particles. We study two cases: one in which we observe multiple independent trajectories of the…
An adaptive finite element method is presented for the elastic scattering of a time-harmonic plane wave by a periodic surface. First, the unbounded physical domain is truncated into a bounded computational domain by introducing the…