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It is challenging to transform an arbitrary quantum circuit into a form protected by surface code quantum error correcting codes (a variant of topological quantum error correction), especially if the goal is to minimise overhead. One of the…
We present a robust and scalable preconditioner for the solution of large-scale linear systems that arise from the discretization of elliptic PDEs amenable to rank compression. The preconditioner is based on hierarchical low-rank…
We study the finite element approximation of linear second-order elliptic partial differential equations in nondivergence form with highly heterogeneous diffusion and drift coefficients. A generalized Cordes condition is imposed to…
We develop a new coarse-scale approximation strategy for the nonlinear single-continuum Richards equation as an unsaturated flow over heterogeneous non-periodic media, using the online generalized multiscale finite element method (online…
Offline model-based optimization aims to find a design that maximizes a property of interest using only an offline dataset, with applications in robot, protein, and molecule design, among others. A prevalent approach is gradient ascent,…
Offline black-box optimization aims to discover novel designs with high property scores using only a static dataset, a task fundamentally challenged by the out-of-distribution (OOD) extrapolation problem. Existing approaches typically…
The numerical simulation of large-scale multiphase flow in porous media is of considerable importance across various application fields, particularly in the petroleum industry. The fully implicit method is preferred in reservoir simulations…
We present a subsampling strategy for the offline stage of the Reduced Basis Method. The approach is aimed at bringing down the considerable offline costs associated with using a finely-sampled training set. The proposed algorithm exploits…
We introduce a Monte Carlo Virtual Element estimator based on Virtual Element discretizations for stochastic elliptic partial differential equations with random diffusion coefficients. We prove estimates for the statistical approximation…
Stochastic balancing domain decomposition by constraints (BDDC) algorithms are developed and analyzed for the sampling of the solutions of linear stochastic elliptic equations with random coefficients. Different from the deterministic BDDC…
We propose an algorithm for the computational homogenization of locally periodic hyperelastic structures undergoing large deformations due to external quasi-static loading. The algorithm performs clustering of macroscopic deformations into…
Many engineered systems must balance competing objectives, such as performance and safety, cost and reliability, or efficiency and sustainability, and are naturally modeled as compositions of interacting subsystems. We study online…
First-order conic optimization solvers are sensitive to problem conditioning and typically perform poorly in the face of ill-conditioned problem data. To mitigate this, we propose an approach to preconditioning--the hypersphere…
Recently, diffusion model shines as a promising backbone for the sequence modeling paradigm in offline reinforcement learning(RL). However, these works mostly lack the generalization ability across tasks with reward or dynamics change. To…
We consider numerical solution of elliptic problems with heterogeneous diffusion coefficients containing thin highly conductive structures. Such problems arise e.g. in fractured porous media, reinforced materials, and electric circuits. The…
This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M{\aa}lqvist and Peterseim [Math. Comp. 2014], which is based on orthogonal subspace decomposition, is…
We propose nodal auxiliary space preconditioners for facet and edge virtual elements of lowest order by deriving discrete regular decompositions on polytopal grids and generalizing the Hiptmair-Xu preconditioner to the virtual element…
In this paper, we develop and analyze an adaptive multiscale approach for heterogeneous problems in perforated domains. In many applications, these problems have a multiscale nature arising because of the perforations, their geometries, the…
In this paper, based on the overlapping domain decomposition method (DDM) proposed in \cite{Leng2015}, an one step preconditioner is proposed to solve 2D high frequency Helmholtz equation. The computation domain is decomposed in both $x$…
A domain decomposition method for the solution of general variable-coefficient elliptic partial differential equations on regular domains is introduced. The method is based on tessellating the domain into overlapping thin slabs or shells,…