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The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce…
Chemical component design is a computationally challenging procedure that often entails iterative numerical modeling and authentic experimental testing. We demonstrate a novel optimization method, Tensor train Optimization (TetraOpt), for…
We present a novel procedure for optimization based on the combination of efficient quantized tensor train representation and a generalized maximum matrix volume principle. We demonstrate the applicability of the new Tensor Train Optimizer…
In this paper, we aim at the problem of tensor data completion. Tensor-train decomposition is adopted because of its powerful representation ability and linear scalability to tensor order. We propose an algorithm named Sparse Tensor-train…
In the field of quantum computing, combinatorial optimization problems are typically addressed using QUBO (Quadratic Unconstrained Binary Optimization) solvers. However, these solvers are often insufficient for tackling higher-order…
We present an algorithm for accelerating the search of molecule's adsorption site based on global optimization of surface adsorbate geometries. Our approach uses a machine-learning interatomic potential (moment tensor potential) to…
Tensor train (TT) format is a common approach for computationally efficient work with multidimensional arrays, vectors, matrices, and discretized functions in a wide range of applications, including computational mathematics and machine…
The convergence of many numerical optimization techniques is highly dependent on the initial guess given to the solver. To address this issue, we propose a novel approach that utilizes tensor methods to initialize existing optimization…
In this paper, we aim at the completion problem of high order tensor data with missing entries. The existing tensor factorization and completion methods suffer from the curse of dimensionality when the order of tensor N>>3. To overcome this…
We present a novel quantum optimization-based route compression technique that significantly reduces storage requirements compared to conventional methods. Route optimization systems face critical challenges in efficiently storing selected…
In the last two decades, increased need for high-fidelity simulations of the time evolution and propagation of forces in granular media has spurred renewed interest in discrete element method (DEM) modeling of frictional contact. Force…
Tensor train (TT) decomposition has drawn people's attention due to its powerful representation ability and performance stability in high-order tensors. In this paper, we propose a novel approach to recover the missing entries of incomplete…
The tensor train (TT) rank has received increasing attention in tensor completion due to its ability to capture the global correlation of high-order tensors ($\textrm{order} >3$). For third order visual data, direct TT rank minimization has…
We present a quantum feature-selection framework based on a higher-order unconstrained binary optimization (HUBO) formulation that explicitly incorporates multivariate dependencies beyond standard quadratic encodings. In contrast to…
The Travelling Salesman Problem (TSP) is an important combinatorial optimisation problem, and is usually solved on a quantum computer using a Quadratic Unconstrained Binary Optimisation (QUBO) formulation or a Higher Order Binary…
Molecular adsorption is the first important step of many surface-mediated chemical processes, from catalysis to tribology. This phenomenon is controlled by physical/chemical interactions, which can be accurately described by first…
Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…
We investigate the application of tensor-train (TT) algorithms to multigroup thermal radiation transport (i.e., photon radiation transport). The TT framework enables simulations at discretizations that might otherwise be computationally…
Using entropy as a measure of heterogeneity to guide optimization has emerged as a crucial research direction in Reinforcement Learning for LLMs. However, existing methods typically treat it as a discrete filter or post-hoc regulator rather…
As consequences of disruptions in railway traffic affect passenger experience/satisfaction, appropriate rerouting and/or rescheduling is necessary. These problems are known to be NP-hard, given the numerous restrictions of traffic nature.…