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We build on the dynamical systems approach to deep learning, where deep residual networks are idealized as continuous-time dynamical systems, from the approximation perspective. In particular, we establish general sufficient conditions for…
A fundamental requirement for intelligent systems is the ability to learn continuously under changing environments. However, models trained in this regime often suffer from catastrophic forgetting. Leveraging pre-trained models has recently…
The aim of this work is to develop general optimization methods for finite difference schemes used to approximate linear differential equations. The specific case of the transport equation is exposed. In particular, the minimization of the…
Metrics on the space of sets of trajectories are important for scientists in the field of computer vision, machine learning, robotics, and general artificial intelligence. However, existing notions of closeness between sets of trajectories…
Optimization of the last-mile delivery and first-mile pickup of parcels is integral to the logistics optimization pipeline as it entails both cost and resource efficiency and a heightened service quality. Such optimization requires accurate…
Supply chain management is an integrated approach for planning and controlling materials, information, and finances as they move in a process which begins from suppliers and ends with customers in forward approach. As distribution network…
The rapid expansion of online shopping has increased the demand for timely parcel delivery, compelling logistics service providers to enhance the efficiency, agility, and predictability of their hub networks. In order to solve the problem,…
We review our recent work in the area of autonomous materials research, highlighting the coupling of machine learning methods and models and more problem-aware modeling. We review the general Bayesian framework for closed-loop design…
Demand for fast and economical parcel deliveries in urban environments has risen considerably in recent years. A framework envisions efficient last-mile delivery in urban environments by leveraging a network of ride-sharing vehicles, where…
Operational consistent query answering (CQA) is a recent framework for CQA based on revised definitions of repairs, which are built by applying a sequence of operations (e.g., fact deletions) starting from an inconsistent database until we…
Resource balancing within complex transportation networks is one of the most important problems in real logistics domain. Traditional solutions on these problems leverage combinatorial optimization with demand and supply forecasting.…
Algorithms for continuous optimization problems have a rich history of design and innovation over the past several decades, in which mathematical analysis of their convergence and complexity properties plays a central role. Besides their…
In this paper we describe two bootstrap methods for massive data sets. Naive applications of common resampling methodology are often impractical for massive data sets due to computational burden and due to complex patterns of inhomogeneity.…
This paper describes a data-driven framework for approximate global optimization in which precomputed solutions to a sample of problems are retrieved and adapted during online use to solve novel problems. This approach has promise for…
We outline how modern likelihood theory, which provides essentially exact inferences in a variety of parametric statistical problems, may routinely be applied in practice. Although the likelihood procedures are based on analytical…
Designing and analyzing algorithms with provable performance guarantees enables efficient optimization problem solving in different application domains, e.g.\ communication networks, transportation, economics, and manufacturing. Despite the…
Sample average approximation (SAA) is a widely popular approach to data-driven decision-making under uncertainty. Under mild assumptions, SAA is both tractable and enjoys strong asymptotic performance guarantees. Similar guarantees,…
Connected and autonomous vehicles (CAVs) can reduce human errors in traffic accidents, increase road efficiency, and execute various tasks ranging from delivery to smart city surveillance. Reaping these benefits requires CAVs to…
In this paper, we propose an integrated dynamical model of Connected and Automated Vehicles (CAVs) which incorporates CAV technologies and a microscopic car-following model to improve safety, efficiency and convenience. We rigorously…
Many practical approximations in physics and engineering invoke a relatively long physical domain with a relatively thin cross-section. In this scenario we typically expect the system to have structures that vary slowly in the long…