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This paper presents Orthogonal Subspace Clustering (OSC), an innovative method for high-dimensional data clustering. We first establish a theoretical theorem proving that high-dimensional data can be decomposed into orthogonal subspaces in…
We introduce two block coordinate descent algorithms for solving optimization problems with ordinary differential equations (ODEs) as dynamical constraints. The algorithms do not need to implement direct or adjoint sensitivity analysis…
Persistence diagrams (PDs) are now routinely used to summarize the underlying topology of complex data. Despite several appealing properties, incorporating PDs in learning pipelines can be challenging because their natural geometry is not…
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in…
We propose a new deflation strategy to accelerate the convergence of the preconditioned conjugate gradient(PCG) method for solving parametric large-scale linear systems of equations. Unlike traditional deflation techniques that rely on…
Bilevel optimization provides a powerful framework for modelling hierarchical decision-making systems. This work presents a sensitivity-based algorithm that addresses the bilevel structure directly by treating the lower-level optimal…
Optimization tasks over relational data, such as clustering, often suffer from the prohibitive cost of join operations, which are necessary to access the full dataset. While geometric data structures like BBD trees yield fast approximation…
The choice of molecular orbitals is decisive in configuration interaction calculations. In this letter, a democratic description of the ground and excited states follows an orthogonally constrained orbitals optimization to produce…
This work presents a novel framework governing the development of an efficient, accurate, and transferable coarse-grained (CG) model of a polyether material. The proposed framework combines the two fundamentally different classical…
In recent years, topology optimization has been developed sufficiently and many researchers have concentrated on enhancing to computationally numerical algorithms for computational effectiveness of this method. Along with the development of…
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…
We introduce a computational method to optimize target physical properties in the full configuration space regarding atomic composition, chemical stoichiometry, and crystal structure. The approach combines the universal potential of the…
Acceleration schemes can dramatically improve existing optimization procedures. In most of the work on these schemes, such as nonlinear Generalized Minimal Residual (N-GMRES), acceleration is based on minimizing the $\ell_2$ norm of some…
Conic optimization is the minimization of a differentiable convex objective function subject to conic constraints. We propose a novel primal-dual first-order method for conic optimization, named proportional-integral projected gradient…
The ionization potential (IP) is an important parameter providing essential insights into the reactivity of chemical systems. IPs are also crucial for designing, optimizing, and understanding the functionality of modern technological…
We introduce a dual contouring method that provides state-of-the-art performance for occupancy functions while achieving computation times of a few seconds. Our method is learning-free and carefully designed to maximize the use of GPU…
Correcting scan-positional errors is critical in achieving electron ptychography with both high resolution and high precision. This is a demanding and challenging task due to the sheer number of parameters that need to be optimized. For…
Bilevel optimization is a central tool in machine learning for high-dimensional hyperparameter tuning. Its applications are vast; for instance, in imaging it can be used for learning data-adaptive regularizers and optimizing forward…
The Projected Gradient Descent (PGD) algorithm is a widely used and efficient first-order method for solving constrained optimization problems due to its simplicity and scalability in large design spaces. Building on recent advancements in…
We present, QP-SBGD, a novel layer-wise stochastic optimiser tailored towards training neural networks with binary weights, known as binary neural networks (BNNs), on quantum hardware. BNNs reduce the computational requirements and energy…