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Simulator imperfection, often known as model error, is ubiquitous in practical data assimilation problems. Despite the enormous efforts dedicated to addressing this problem, properly handling simulator imperfection in data assimilation…

Regression in supervised learning often requires the enforcement of constraints to ensure that the trained models are consistent with the underlying structures of the input and output data. This paper presents an iterative procedure to…

We propose an efficient algorithm for computing a common eigenvector of a finite set of square matrices. As an immediate consequence we obtain an algorithm for determining whether the matrices admit a simultaneous triangulation, and, if so,…

The simulation of large nonlinear dynamical systems, including systems generated by discretization of hyperbolic partial differential equations, can be computationally demanding. Such systems are important in both fluid and kinetic…

Many real-world problems can be naturally described by mathematical formulas. The task of finding formulas from a set of observed inputs and outputs is called symbolic regression. Recently, neural networks have been applied to symbolic…

Hard optimisation problems such as Boolean Satisfiability typically have long solving times and can usually be solved by many algorithms, although the performance can vary widely in practice. Research has shown that no single algorithm…

Machine learning pipelines that include a combinatorial optimization layer can give surprisingly efficient heuristics for difficult combinatorial optimization problems. Three questions remain open: which architecture should be used, how…

This paper presents a method for computing eigenvalues and eigenvectors for some types of nonlinear eigenvalue problems. The main idea is to approximate the functions involved in the eigenvalue problem by rational functions and then apply a…

Reinforcement Learning has emerged as a strong alternative to solve optimization tasks efficiently. The use of these algorithms highly depends on the feedback signals provided by the environment in charge of informing about how good (or…

The primary goal of motion planning is to generate safe and efficient trajectories for vehicles. Traditionally, motion planning models are trained using imitation learning to mimic the behavior of human experts. However, these models often…

User simulation is important for developing and evaluating human-centered AI, yet current student simulation in educational applications has significant limitations. Existing approaches focus on single learning experiences and do not…

We consider active learning under incentive compatibility constraints. The main application of our results is to economic experiments, in which a learner seeks to infer the parameters of a subject's preferences: for example their attitudes…

This work formulates the machine learning mechanism as a bi-level optimization problem. The inner level optimization loop entails minimizing a properly chosen loss function evaluated on the training data. This is nothing but the…

Many constraint satisfaction and optimisation problems can be solved effectively by encoding them as instances of the Boolean Satisfiability problem (SAT). However, even the simplest types of constraints have many encodings in the…

Neural models have achieved great success on machine reading comprehension (MRC), many of which typically consist of two components: an evidence extractor and an answer predictor. The former seeks the most relevant information from a…

Self-supervision has emerged as a propitious method for visual representation learning after the recent paradigm shift from handcrafted pretext tasks to instance-similarity based approaches. Most state-of-the-art methods enforce similarity…

Continual learning approaches help deep neural network models adapt and learn incrementally by trying to solve catastrophic forgetting. However, whether these existing approaches, applied traditionally to image-based tasks, work with the…

We explore the idea of integrating machine learning (ML) with high performance computing (HPC)-driven simulations to address challenges in using simulations to teach computational science and engineering courses. We demonstrate that a ML…

Ensembling a neural network is a widely recognized approach to enhance model performance, estimate uncertainty, and improve robustness in deep supervised learning. However, deep ensembles often come with high computational costs and memory…

Autonomous driving vehicles with self-learning capabilities are expected to evolve in complex environments to improve their ability to cope with different scenarios. However, most self-learning algorithms suffer from low learning efficiency…