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Sophisticated trajectory prediction models that effectively mimic team dynamics have many potential uses for sports coaches, broadcasters and spectators. However, through experiments on soccer data we found that it can be surprisingly…
In this paper, we introduce a novel approach for autonomous driving trajectory generation by harnessing the complementary strengths of diffusion probabilistic models (a.k.a., diffusion models) and transformers. Our proposed framework,…
We study smooth, caustic-free, chaotic semiclassical dynamics on two-dimensional phase space and find that the dynamics can be approached by an iterative procedure which constructs an approximation to the exact long-time semiclassical…
We study model-based learning of finite-window policies in tabular partially observable Markov decision processes (POMDPs). A common approach to learning under partial observability is to approximate unbounded history dependencies using…
Projection-based model reduction has become a popular approach to reduce the cost associated with integrating large-scale dynamical systems so they can be used in many-query settings such as optimization and uncertainty quantification. For…
Mixed observable Markov decision processes (MOMDPs) are a modeling framework for autonomous systems described by both fully and partially observable states. In this work, we study the problem of synthesizing a control policy for MOMDPs that…
A mean-field model to describe electron transfer processes in ion-molecule collisions at the $\hbar =0$ level is presented and applied to collisions involving water and ammonia molecules. Multicenter model potentials account for the…
In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…
We propose a homotopy continuation method called FLUX for approximating complicated probability density functions. It is based on progressive processing for smoothly morphing a given density into the desired one. Distributed ordinary…
In this paper, we consider a strongly convex finite-sum minimization problem over a decentralized network and propose a communication-efficient decentralized Newton's method for solving it. We first apply dynamic average consensus (DAC) so…
We present an application of our new theoretical formulation of quantum dynamics, moment propagation theory (MPT) (Boyer et al., J. Chem. Phys. 160, 064113 (2024)), for employing machine-learning techniques to simulate the quantum dynamics…
The emergence of new nanoporous materials, based e.g. on 2D materials, offers new avenues for water filtration and energy. There is accordingly a need to investigate the molecular mechanisms at the root of the advanced performances of these…
Classical theory for quasi-Newton schemes has focused on smooth deterministic unconstrained optimization while recent forays into stochastic convex optimization have largely resided in smooth, unconstrained, and strongly convex regimes.…
Optimization-based methods are widely used for computing fast, diverse solutions for complex tasks such as collision-free movement or planning in the presence of contacts. However, most of these methods require enforcing non-penetration…
The main contribution of this paper is a novel method for planning globally optimal trajectories for dynamical systems subject to polygonal constraints. The proposed method is a hybrid trajectory planning approach, which combines graph…
In stochastic systems, numerically sampling the relevant trajectories for the estimation of the large deviation statistics of time-extensive observables requires overcoming their exponential (in space and time) scarcity. The optimal way to…
We present a method for the approximate propagation of mean and covariance of a probability distribution through ordinary differential equations (ODE) with discontinous right-hand side. For piecewise affine systems, a normalization of the…
The features of the quasi-static analysis of multiconductor transmission lines by the method of moments are described. Comparison of their efficiency of methods for adaptive mesh refinement is carried out on the example of calculating…
The Weak-form Estimation of Non-linear Dynamics (WENDy) framework is a recently developed approach for parameter estimation and inference of systems of ordinary differential equations (ODEs). Prior work demonstrated WENDy to be robust,…
In this paper, we propose a novel approximation strategy for time-dependent hyperbolic systems of conservation laws for the Euler system of gas dynamics that aims to represent the dynamics of strong interacting discontinuities. The goal of…