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Rational approximation recently emerged as an efficient numerical tool for the solution of exterior wave propagation problems. Currently, this technique is limited to wave media which are invariant along the main propagation direction. We…
We propose an acceleration scheme for first-order methods (FOMs) for convex quadratic programs (QPs) that is analogous to Anderson acceleration and the Generalized Minimal Residual algorithm for linear systems. We motivate our proposed…
Quantum Krylov subspace methods can extract ground and excited states by diagonalizing the Hamiltonian in a compact variational space. In practice, these spaces are almost always generated by real or imaginary time evolution, forcing a…
We study stochastic convex optimization subjected to linear equality constraints. Traditional Stochastic Alternating Direction Method of Multipliers and its Nesterov's acceleration scheme can only achieve ergodic O(1/\sqrt{K}) convergence…
This paper presents a novel space-time topology optimisation framework for time-dependent thermal conduction problems, aiming to significantly reduce the time-to-solution. By treating time as an additional spatial dimension, we discretise…
This paper studies empirical risk minimization (ERM) problems for large-scale datasets and incorporates the idea of adaptive sample size methods to improve the guaranteed convergence bounds for first-order stochastic and deterministic…
Ensemble Kalman Inversion (EKI) methods are a family of iterative methods for solving weighted least-squares problems, especially those arising in scientific and engineering inverse problems in which unknown parameters or states are…
We develop an Evolutionary Markov Chain Monte Carlo (EMCMC) algorithm for sampling spatial partitions that lie within a large and complex spatial state space. Our algorithm combines the advantages of evolutionary algorithms (EAs) as…
We investigate the relationship between Krylov complexity and operator quantum speed limits (OQSLs) of the complexity operator and level repulsion in random/integrable matrices and many-body systems. An enhanced level-repulsion corresponds…
With the proliferation of electric vehicles (EVs), accurate charging demand and station occupancy forecasting are critical for optimizing urban energy and the profit of EVs aggregator. Existing approaches in this field usually struggle to…
One of the primary objectives for space-borne gravitational wave detectors is the detection of extreme-mass-ratio inspirals (EMRIs). This undertaking poses a substantial challenge because of the complex and long EMRI signals, further…
Evolution Strategies (ES) is a class of powerful black-box optimisation methods that are highly parallelisable and can handle non-differentiable and noisy objectives. However, na\"ive ES becomes prohibitively expensive at scale on GPUs due…
The rational Krylov subspace method (RKSM) and the low-rank alternating directions implicit (LR-ADI) iteration are established numerical tools for computing low-rank solution factors of large-scale Lyapunov equations. In order to generate…
Model order reduction (MOR) is essential in integrated circuit design, particularly when dealing with large-scale electromagnetic models extracted from complex designs. The numerous passive elements introduced in these models pose…
We explore the potential of optical intensity interferometry to extract angularly resolved information from supernova explosions, introducing the "expanding ejecta method" (EEM) as a robust alternative to the classical expanding photosphere…
Many scientific applications require the evaluation of the action of the matrix function over a vector and the most common methods for this task are those based on the Krylov subspace. Since the orthogonalization cost and memory requirement…
The performance of machine learning models under distribution shift has been the focus of the community in recent years. Most of current methods have been proposed to improve the robustness to distribution shift from the algorithmic…
Stencil computations are widely used to simulate the change of state of physical systems across a multidimensional grid over multiple timesteps. The state-of-the-art techniques in this area fall into three groups: cache-aware tiled looping…
This study presents an adaptive coupling peridynamic least-square minimization with the finite element method (PDLSM-FEM) for fracture analysis. The presented method utilizes the PDLSM modeling discontinuities while maximizing the FEM…
We present a new short-recurrence reaidual-optimal Krylov subspace recycling method for sequences of Hermitian systems of linear equations with a fixed system matrix and changing right-hand sides. Such sequences of linear systems occur…