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The solution of computational fluid dynamics problems is one of the most computationally hard tasks, especially in the case of complex geometries and turbulent flow regimes. We propose to use Tensor Train (TT) methods, which possess…

Combinatorial optimization problems play a central role in computer science with many real world applications. A number of relevant problems remain computationally difficult to solve as they lie in the NP-hard complexity class. We present a…

Accurately evaluating configurational integrals for dense solids remains a central and difficult challenge in the statistical mechanics of condensed systems. Here, we present a novel tensor network approach that reformulates the…

Unmanned Aerial Vehicles (UAVs) in Wireless Power Transfer (WPT)-assisted Internet of Things (IoT) systems face the following challenges: limited resources and suboptimal trajectory planning. Reinforcement learning-based trajectory planning…

In this work, we develop an optimization framework for problems whose solutions are well-approximated by Hierarchical Tucker (HT) tensors, an efficient structured tensor format based on recursive subspace factorizations. By exploiting the…

In designing stellarators, any design decision ultimately comes with a trade-off. Improvements in particle confinement, for instance, may increase the burden on engineers to build more complex coils, and the tightening of financial…

Finding the Time-Optimal Parameterization of a Path (TOPP) subject to second-order constraints (e.g. acceleration, torque, contact stability, etc.) is an important and well-studied problem in robotics. In comparison, TOPP subject to…

Black-box optimization methods play an important role in many fields of computational simulation. In particular, such methods are often used in the design and modelling of biological systems, including proteins and their complexes with…

With the advances in data acquisition technology, tensor objects are collected in a variety of applications including multimedia, medical and hyperspectral imaging. As the dimensionality of tensor objects is usually very high,…

Additive models can be used for interpretable machine learning for their clarity and simplicity. However, In the classical models for high-order data, the vectorization operation disrupts the data structure, which may lead to degenerated…

Remote sensing image registration is valuable for image-based navigation system despite posing many challenges. As the search space of registration is usually non-convex, the optimization algorithm, which aims to search the best…

Spatiotemporal traffic time series, such as traffic speed data, collected from sensing systems are often incomplete, with considerable corruption and large amounts of missing values. A vast amount of data conceals implicit data structures,…

Software engineering presents complex, multi-step challenges for Large Language Models (LLMs), requiring reasoning over large codebases and coordinated tool use. The difficulty of these tasks is exemplified by benchmarks like SWE-bench,…

In this paper we present a new GPU-oriented mesh optimization method based on high-order finite elements. Our approach relies on node movement with fixed topology, through the Target-Matrix Optimization Paradigm (TMOP) and uses a global…

Computational catalysis is playing an increasingly significant role in the design of catalysts across a wide range of applications. A common task for many computational methods is the need to accurately compute the adsorption energy for an…

Efficient observer design and accurate sensor fusion are key in state estimation. This work proposes an optimization-based methodology, termed Trajectory Based Optimization Design (TBOD), allowing the user to easily design observers for…

Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…

We develop both first and second order numerical optimization methods to solve non-smooth optimization problems featuring a shared sparsity penalty, constrained by differential equations with uncertainty. To alleviate the curse of…

Designing high-entropy alloys (HEAs) that are both mechanically hard and possess soft magnetic properties is inherently challenging, as a trade-off is needed for mechanical and magnetic properties. In this study, we optimize HEA…

In this paper, we present a brief review and introduction to Quadratic Unconstrained D-ary Optimization (QUDO), Tensor Quadratic Unconstrained D-ary Optimization (T-QUDO) and Higher-Order Unconstrained Binary Optimization (HOBO)…