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In this paper, we describe a novel unsupervised learning scheme for accelerating the solution of a family of mixed integer programming (MIP) problems. Distinct substantially from existing learning-to-optimize methods, our proposal seeks to…

We present a novel interface-capturing scheme, THINC-scaling, to unify the VOF (volume of fluid) and the level set methods, which have been developed as two completely different approaches widely used in various applications. The…

We propose a novel solution framework for inverse mixed-integer optimization based on analytic center concepts from interior point methods. We characterize the optimality gap of a given solution, provide structural results, and propose…

The development of large-scale identification systems that ensure the privacy protection of enrolled subjects represents a major challenge. Biometric deployments that provide interoperability and usability by including efficient…

We propose an adaptive iteratively linearized finite element method (AILFEM) in the context of strongly monotone nonlinear operators in Hilbert spaces. The approach combines adaptive mesh-refinement with an energy-contractive linearization…

Central finite difference schemes have long been avoided in the context of two-phase flows for the advection of the phase indicator function due to numerical overshoots and undershoots associated with their dispersion errors. We will show…

This paper develops and analyzes a general iterative framework for solving parameter-dependent and random convection-diffusion problems. It is inspired by the multi-modes method of [7,8] and the ensemble method of [20] and extends those…

Many systems exhibit a mixture of continuous and discrete dynamics. We consider a family of mixed-integer non-convex non-linear optimisation problems obtained in discretisations of optimal control of such systems. For this family, a…

This paper investigates an elliptic interface problem with discontinuous diffusion coefficients on unfitted meshes, employing the CutFEM method. The main contribution is the a posteriori error analysis based on equilibrated fluxes belonging…

We propose a variational finite volume scheme to approximate the solutions to Wasserstein gradient flows. The time discretization is based on an implicit linearization of the Wasserstein distance expressed thanks to Benamou-Brenier formula,…

We introduce a new "subpixel-smoothed projection" (SSP) formulation for differentiable binarization in topology optimization (TopOpt) as a drop-in replacement for previous projection schemes, which suffer from near-non-differentiability and…

Purpose: This is an attempt to better bridge the gap between the mathematical and the engineering/physical aspects of the topic. We trace the different sources of non-convexification in the context of topology optimization problems starting…

We introduce a family of hybrid discretisations for the numerical approximation of optimal control problems governed by the equations of immiscible displacement in porous media. The proposed schemes are based on mixed and discontinuous…

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector…

Dense conditional random fields (CRF) with Gaussian pairwise potentials have emerged as a popular framework for several computer vision applications such as stereo correspondence and semantic segmentation. By modeling long-range…

In recent years, there has been an increasing demand on efficient algorithms for large scale change point detection problems. To this end, we propose seeded binary segmentation, an approach relying on a deterministic construction of…

We show that the physics-informed neural networks (PINNs), in combination with some recently developed discontinuity capturing neural networks, can be applied to solve optimal control problems subject to partial differential equations…

We present a convex mixed-integer programming formulation for non-rigid shape matching. To this end, we propose a novel shape deformation model based on an efficient low-dimensional discrete model, so that finding a globally optimal…

Persistence diagrams have been widely used to quantify the underlying features of filtered topological spaces in data visualization. In many applications, computing distances between diagrams is essential; however, computing these distances…

We develop a new finite element method for solving planar elasticity problems involving of heterogeneous materials with a mesh not necessarily aligning with the interface of the materials. This method is based on the `broken'…