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We adapt the alternating linearization method for proximal decomposition to structured regularization problems, in particular, to the generalized lasso problems. The method is related to two well-known operator splitting methods, the…

Probabilistic sampling methods have become very popular to solve single-shot path planning problems. Rapidly-exploring Random Trees (RRTs) in particular have been shown to be efficient in solving high dimensional problems. Even though…

The availability of the Global Positioning System (GPS) trajectory data is increasing along with the availability of different GPS receivers and with the increasing use of various mobility services. GPS trajectory is an important data…

We use convex relaxation techniques to provide a sequence of solutions to the matrix completion problem. Using the nuclear norm as a regularizer, we provide simple and very efficient algorithms for minimizing the reconstruction error…

The reduced basis method (RBM) empowers repeated and rapid evaluation of parametrized partial differential equations through an offline-online decomposition, a.k.a. a learning-execution process. A key feature of the method is a greedy…

In this paper we propose a novel methodology that allows to design, in a purely data-based fashion and for linear single-input and single-output systems, both robustly stable and performing control systems for tracking piecewise constant…

The density matrix renormalization group (DMRG) algorithm is a popular alternating minimization scheme for solving high-dimensional optimization problems in the tensor train format. Classical DMRG, however, is based on sequential…

Conformal prediction is a statistical tool for producing prediction regions of machine learning models that are valid with high probability. However, applying conformal prediction to time series data leads to conservative prediction…

Reinforcement learning (RL) algorithms for real-world robotic applications need a data-efficient learning process and the ability to handle complex, unknown dynamical systems. These requirements are handled well by model-based and…

As predictive models are increasingly being deployed in high-stakes decision making (e.g., loan approvals), there has been growing interest in post hoc techniques which provide recourse to affected individuals. These techniques generate…

Recent progress in randomized motion planners has led to the development of a new class of sampling-based algorithms that provide asymptotic optimality guarantees, notably the RRT* and the PRM* algorithms. Careful analysis reveals that the…

X-ray ptychography is one of the versatile techniques for nanometer resolution imaging. The magnitude of the diffraction patterns is recorded on a detector and the phase of the diffraction patterns is estimated using phase retrieval…

Path following and lateral stability are crucial issues for autonomous vehicles. Moreover, these problems increase in complexity when handling articulated heavy-duty vehicles due to their poor manoeuvrability, large sizes and mass…

Parameter regularization or allocation methods are effective in overcoming catastrophic forgetting in lifelong learning. However, they solve all tasks in a sequence uniformly and ignore the differences in the learning difficulty of…

Parallel computing is omnipresent in today's scientific computer landscape, starting at multicore processors in desktop computers up to massively parallel clusters. While domain decomposition methods have a long tradition in computational…

Reinforcement Learning with Verifiable Rewards (RLVR)-based post-training of Large Language Models (LLMs) has been shown to improve accuracy on reasoning tasks and continues to attract significant attention. Existing RLVR methods, however,…

Density functional theory calculations use a significant fraction of current supercomputing time. The resources required scale with the problem size, internal workings of the code and the number of iterations to convergence, the latter…

In continual learning, the primary challenge is to learn new information without forgetting old knowledge. A common solution addresses this trade-off through regularization, penalizing changes to parameters critical for previous tasks. In…

Verification is crucial for effective mathematical reasoning. We present a new temporal consistency method where verifiers iteratively refine their judgments based on the previous assessment. Unlike one-round verification or multi-model…

Complying with traffic rules is challenging for automated vehicles, as numerous rules need to be considered simultaneously. If a planned trajectory violates traffic rules, it is common to replan a new trajectory from scratch. We instead…