Related papers: Toolbox for analyzing finite two-state trajectorie…

Kinetic transport equations are notoriously difficult to simulate because of their complex multiscale behaviors and the need to numerically resolve a high dimensional probability density function. Past literature has focused on building…

The identification of states and parameters from noisy measurements of a dynamical system is of great practical significance and has received a lot of attention. Classically, this problem is expressed as optimization over a class of models.…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

Quantum-mechanical (QM) simulations, thanks to their predictive power, can provide significant insights into the nature and dynamics of defects such as vacancies, dislocations and grain boundaries. These considerations are essential in the…

We propose a methodology to address two analysis problems concerning complex systems, namely bounding state functionals of stochastic differential equations (SDEs) and verifying set avoidance of systems described by partial differential…

Test-time scaling has emerged as a prominent research direction in machine learning, enabling models to enhance their expressive capabilities during inference.Transformers, renowned for striking a delicate balance between efficiency and…

Implementing an autonomous vehicle that is able to output feasible, smooth and efficient trajectories is a long-standing challenge. Several approaches have been considered, roughly falling under two categories: rule-based and learning-based…

For quadrotor trajectory planning, describing a polynomial trajectory through coefficients and end-derivatives both enjoy their own convenience in energy minimization. We name them double descriptions of polynomial trajectories. The…

The contemporary scientific landscape is characterized by a "curse of dimensionality," where our capacity to collect high-dimensional network data frequently outstrips our ability to computationally simulate or intuitively comprehend the…

The two-layer quasi-geostrophic equations (2QGE) serve as a simplified model for simulating wind-driven, stratified ocean flows. However, their numerical simulation remains computationally expensive due to the need for high-resolution…

While the ground-state problem for the random-field Ising model is polynomial, and can be solved using a number of well-known algorithms for maximum flow or graph cut, the analogue random-field Potts model corresponds to a multi-terminal…

Temporal Difference (TD) algorithms are widely used in Deep Reinforcement Learning (RL). Their performance is heavily influenced by the size of the neural network. While in supervised learning, the regime of over-parameterization and its…

When solving the time-dependent radiative transport equation (RTE), implicit time discretization is often employed for its robustness and stability. This results in a sequence of steady-state RTEs with identical cross-sections but varying…

In this contribution we present an accelerated optimization-based approach for combined state and parameter reduction of a parametrized linear control system which is then used as a surrogate model in a Bayesian inverse setting. Following…

Quantum computing is an advancing area of research in which computer hardware and algorithms are developed to take advantage of quantum mechanical phenomena. In recent studies, quantum algorithms have shown promise in solving linear systems…

A framework is proposed to generate a phenomenological model that extracts the essence of a dynamical system (DS) with large degrees of freedom using machine learning. For a given microscopic DS, the optimum transformation to a small number…

Microtransit offers opportunities to enhance urban mobility by combining the reliability of public transit and the flexibility of ride-sharing. This paper optimizes the design and operations of a deviated fixed-route microtransit system…

Models that balance accuracy against computational costs are advantageous when designing dynamic systems with optimization studies, as several hundred predictive function evaluations might be necessary to identify the optimal solution. The…

Dynamic Mode Decomposition (DMD) and its variants, such as extended DMD (EDMD), are broadly used to fit simple linear models to dynamical systems known from observable data. As DMD methods work well in several situations but perform poorly…

Distortion Risk Measures (DRMs) capture risk preferences in decision-making and serve as general criteria for managing uncertainty. This paper proposes gradient descent algorithms for DRM optimization based on two dual representations: the…