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Computing atomic-scale properties of chemically disordered materials requires an efficient exploration of their vast configuration space. Traditional approaches such as Monte Carlo or Special Quasirandom Structures either entail sampling an…

The integration of autonomous vehicles into urban and highway environments necessitates the development of robust and adaptable behavior planning systems. This study presents an innovative approach to address this challenge by utilizing a…

Graph-based machine learning has seen an increased interest over the last decade with many connections to other fields of applied mathematics. Learning based on partial differential equations, such as the phase-field Allen-Cahn equation,…

High dimensional black-box optimization has broad applications but remains a challenging problem to solve. Given a set of samples $\{\vx_i, y_i\}$, building a global model (like Bayesian Optimization (BO)) suffers from the curse of…

Decision trees are renowned for their ability to achieve high predictive performance while remaining interpretable, especially on tabular data. Traditionally, they are constructed through recursive algorithms, where they partition the data…

Decision Tree (DT) Learning is a fundamental problem in Interpretable Machine Learning, yet it poses a formidable optimisation challenge. Practical algorithms have recently emerged, primarily leveraging Dynamic Programming and Branch &…

In big data analysis, a simple task such as linear regression can become very challenging as the variable dimension $p$ grows. As a result, variable screening is inevitable in many scientific studies. In recent years, randomized algorithms…

Topology Optimization (TO) provides a systematic approach for obtaining structure design with optimum performance of interest. However, the process requires numerical evaluation of objective function and constraints at each iteration, which…

Accurate static traffic assignment models are important tools for the assessment of strategic transportation policies. In this article we present a novel approach to partition road networks through network modularity to produce data-driven…

In this paper, we apply the Monte Carlo stochastic optimization (MOST) proposed by the authors to a deep learning of XOR gate and verify its effectiveness. Deep machine learning based on neural networks is one of the most important keywords…

There is an increasing need of continual learning in dynamic systems, such as the self-driving vehicle, the surveillance drone, and the robotic system. Such a system requires learning from the data stream, training the model to preserve…

Emerging applications of machine learning in numerous areas involve continuous gathering of and learning from streams of data. Real-time incorporation of streaming data into the learned models is essential for improved inference in these…

Machine Learning approaches like clustering methods deal with massive datasets that present an increasing challenge. We devise parallel algorithms to compute the Multi-Slice Clustering (MSC) for 3rd-order tensors. The MSC method is based on…

Efficient tabletop rearrangement planning seeks to find high-quality solutions while minimizing total cost. However, the task is challenging due to object dependencies and limited buffer space for temporary placements. The complexity…

Contextual Partitioning introduces an innovative approach to enhancing the architectural design of large-scale computational models through the dynamic segmentation of parameters into context-aware regions. This methodology emphasizes the…

Distributed computing excels at processing large scale data, but the communication cost for synchronizing the shared parameters may slow down the overall performance. Fortunately, the interactions between parameter and data in many problems…

The Steiner tree problem aims to determine a minimum edge-weighted tree that spans a given set of terminal vertices from a given graph. In the past decade, a considerable number of algorithms have been developed to solve this…

High dimensional and/or nonconvex optimization remains a challenging and important problem across a wide range of fields, such as machine learning, data assimilation, and partial differential equation (PDE) constrained optimization. Here we…

Dust properties, such as mass and porosity, impact planet formation directly. Understanding the time evolution of dust distribution across multiple properties requires numerical computation. However, available ways to calculate the…

Data-intensive platforms such as Hadoop and Spark are routinely used to process massive amounts of data residing on distributed file systems like HDFS. Increasing memory sizes and new hardware technologies (e.g., NVRAM, SSDs) have recently…