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We consider the problem of embedding the nodes of a hypergraph into Euclidean space under the assumption that the interactions arose through closeness to unknown hyperedge centres. In this way, we tackle the inverse problem associated with…
Complex networks, which are the abstractions of many real-world systems, present a persistent challenge across disciplines for people to decipher their underlying information. Recently, hyperbolic geometry of latent spaces has gained…
We consider a stochastic convex optimization problem that requires minimizing a sum of misspecified agentspecific expectation-valued convex functions over the intersection of a collection of agent-specific convex sets. This misspecification…
This article presents an immersed finite element (IFE) method for solving the typical three-dimensional second order elliptic interface problem with an interface-independent Cartesian mesh. The local IFE space on each interface element…
This work focuses on a class of elliptic boundary value problems with diffusive, advective and reactive terms, motivated by the study of three-dimensional heterogeneous physical systems composed of two or more media separated by a selective…
Roof plane segmentation is one of the key procedures for reconstructing three-dimensional (3D) building models at levels of detail (LoD) 2 and 3 from airborne light detection and ranging (LiDAR) point clouds. The majority of current…
A cost functional involving the eigenvalues of an elastic structure, that is described by a multi-phase-field equation, is optimized. This allows us to handle topology changes and multiple materials. We prove continuity and…
Based on the work of Xu and Zhou [Math.Comput., 69(2000), pp.881-909], we establish new three-level and multilevel finite element discretizations by local defect-correction technique. Theoretical analysis and numerical experiments show that…
The reliability of machine learning in multiscale physical systems depends on how physical structure is embedded into the learning process. We investigate this in the context of turbulent multiphase flows, focusing on the prediction of…
The convergence and optimality of adaptive mixed finite element methods for the Poisson equation are established in this paper. The main difficulty for mixed finite element methods is the lack of minimization principle and thus the failure…
Stochastic bilevel optimization, which captures the inherent nested structure of machine learning problems, is gaining popularity in many recent applications. Existing works on bilevel optimization mostly consider either unconstrained…
We present a locally adapted parametric finite element method for interface problems. For this adapted finite element method we show optimal convergence for elliptic interface problems with a discontinuous diffusion parameter. The method is…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
Exceptional points play a pivotal role in the topology of non-Hermitian systems, and significant advances have been made in classifying exceptional points and exploring the associated phenomena. Exceptional surfaces, which are hypersurfaces…
The level crossing problem and associated geometric terms are neatly formulated by using the second quantization technique both in the operator and path integral formulations. The analysis of geometric phases is then reduced to the familiar…
This article presents a novel approach to identifying and classifying intersections for semantic and topological mapping. More specifically, the proposed novel approach has the merit of generating a semantically meaningful map containing…
We review the main features of an unfitted finite element method for interface and fluid-structure interaction problems based on a distributed Lagrange multiplier in the spirit of the fictitious domain approach. We recall our theoretical…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
Studying neural network loss landscapes provides insights into the nature of the underlying optimization problems. Unfortunately, loss landscapes are notoriously difficult to visualize in a human-comprehensible fashion. One common way to…
In this paper, we propose an extended mixed finite element method for elliptic interface problems. By adding some stabilization terms, we present a mixed approximation form based on Brezzi-Douglas-Marini element space and the piecewise…