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Motion prediction plays an important role in autonomous driving. This study presents LMFormer, a lane-aware transformer network for trajectory prediction tasks. In contrast to previous studies, our work provides a simple mechanism to…

For the challenging task of modeling multivariate time series, we propose a new class of models that use dependent Mat\'ern processes to capture the underlying structure of data, explain their interdependencies, and predict their unknown…

Overparameterized transformer networks have obtained state of the art results in various natural language processing tasks, such as machine translation, language modeling, and question answering. These models contain hundreds of millions of…

We describe a new framework for fitting jump models to a sequence of data. The key idea is to alternate between minimizing a loss function to fit multiple model parameters, and minimizing a discrete loss function to determine which set of…

Structured reduced-order modeling is a central component in the computer-aided design of control systems in which cheap-to-evaluate low-dimensional models with physically meaningful internal structures are computed. In this work, we develop…

A novel general framework is proposed in this paper for dimension reduction in regression to fill the gap between linear and fully nonlinear dimension reduction. The main idea is to transform first each of the raw predictors monotonically,…

Model order reduction techniques simplify high-dimensional dynamical systems by deriving lower-dimensional models that retain essential system characteristics. These techniques are crucial for the controller design of complex systems while…

The use of machine learning algorithms to predict behaviors of complex systems is booming. However, the key to an effective use of machine learning tools in multi-physics problems, including combustion, is to couple them to physical and…

Data-driven reduced order models (ROMs) recently emerged as powerful tool for the solution of inverse scattering problems. The main drawback of this approach is that it was limited to the measurement arrays with reciprocally collocated…

We present a novel projection-based model reduction framework for parametric linear time-invariant systems that allows interpolating the transfer function at a given frequency point along parameter-dependent curves as opposed to the…

Transformer-based foundation models have emerged as a dominant paradigm in time series analysis, offering unprecedented capabilities in tasks such as forecasting, anomaly detection, classification, trend analysis and many more time series…

This paper introduces decentralized and modular neural network framework designed to enhance the scalability, interpretability, and performance of artificial intelligence (AI) systems. At the heart of this framework is a dynamic switch…

Many engineering processes can be accurately modelled using partial differential equations (PDEs), but high dimensionality and non-convexity of the resulting systems pose limitations on their efficient optimisation. In this work, a model…

Sorting is a fundamental operation of all computer systems, having been a long-standing significant research topic. Beyond the problem formulation of traditional sorting algorithms, we consider sorting problems for more abstract yet…

Transformers have reshaped machine learning by utilizing attention mechanisms to capture complex patterns in large datasets, leading to significant improvements in performance. This success has contributed to the belief that "bigger means…

We consider the reduction of parametric families of linear dynamical systems having an affine parameter dependence that differ from one another by a low-rank variation in the state matrix. Usual approaches for parametric model reduction…

We consider stability analysis of constrained switching linear systems in which the dynamics is unknown and whose switching signal is constrained by an automaton. We propose a data-driven Lyapunov framework for providing probabilistic…

This paper develops a new framework, called modular regression, to utilize auxiliary information -- such as variables other than the original features or additional data sets -- in the training process of linear models. At a high level, our…

The paper develops a second-order time-domain moment matching framework for the structure-preserving model reduction of second-order dynamical systems of high dimension, avoiding the first-order double-sized equivalent system. The moments…

Transformer architectures, capable of capturing sequential dependencies in the history of user interactions, have become the dominant approach in sequential recommender systems. Despite their success, such models consider sequence elements…