Related papers: A Surface Hopping Gaussian Beam Method for High-Di…
State-space models have been successfully used for more than fifty years in different areas of science and engineering. We present a procedure for efficient variational Bayesian learning of nonlinear state-space models based on sparse…
In this paper, we propose a numerical method to solve the classic $L^2$-optimal transport problem. Our algorithm is based on use of multiple shooting, in combination with a continuation procedure, to solve the boundary value problem…
In this paper, we introduce a Gaussian process based moving horizon estimation (MHE) framework. The scheme is based on offline collected data and offline hyperparameter optimization. In particular, compared to standard MHE schemes, we…
Terrain analysis is critical for the practical ap- plication of ground mobile robots in real-world tasks, espe- cially in outdoor unstructured environments. In this paper, we propose a novel spatial-temporal traversability assessment…
This letter describes an incremental multimodal surface mapping methodology, which represents the environment as a continuous probabilistic model. This model enables high-resolution reconstruction while simultaneously compressing spatial…
A theoretical justification of the empirical surface hopping method for the laser-driven molecular dynamics is given utilizing the formalism of the exact factorization of the molecular wavefunction [Abedi et al., PRL $\textbf{105}$, 123002…
We present a dynamic subspace approach for efficiently approximating large-scale systems by learning time-continuous trajectories on the Grassmannian manifold. By parameterizing a low-dimensional basis as a geodesic path, the method allows…
Nonadiabatic dynamics methods are an essential tool for investigating photochemical processes. In the context of employing first principles electronic structure techniques, such simulations can be carried out in a practical manner using…
We propose a volumetric formulation for computing the Optimal Transport problem defined on surfaces in $\mathbb{R}^3$, found in disciplines like optics, computer graphics, and computational methodologies. Instead of directly tackling the…
We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…
Stochastic nonlinear dynamical systems can undergo rapid transitions relative to the change in their forcing, for example due to the occurrence of multiple equilibrium solutions for a specific interval of parameters. In this paper, we…
Sequential optimization methods are often confronted with the curse of dimensionality in high-dimensional spaces. Current approaches under the Gaussian process framework are still burdened by the computational complexity of tracking…
We propose a new Monte Carlo method for efficiently sampling trajectories with fixed initial and final conditions in a system with discrete degrees of freedom. The method can be applied to any stochastic process with local interactions,…
Many complex real world phenomena exhibit abrupt, intermittent or jumping behaviors, which are more suitable to be described by stochastic differential equations under non-Gaussian L\'evy noise. Among these complex phenomena, the most…
We consider the wave equation with highly oscillatory initial data, where there is uncertainty in the wave speed, initial phase and/or initial amplitude. To estimate quantities of interest related to the solution and their statistics, we…
To control how a robot moves, motion planning algorithms must compute paths in high-dimensional state spaces while accounting for physical constraints related to motors and joints, generating smooth and stable motions, avoiding obstacles,…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
Heterogeneous nature of the vehicular networks, which results from the co-existence of human-driven, semi-automated, and fully autonomous vehicles, is a challenging phenomenon toward the realization of the intelligent transportation systems…
We propose a real-time decision framework for multimodal freight dispatch through a system of hierarchical hubs, using a probabilistic model for transit times. Instead of assigning a fixed time to each transit, we advocate using historical…
We propose a principled algorithm for robust Bayesian filtering and smoothing in nonlinear stochastic dynamic systems when both the transition function and the measurement function are described by non-parametric Gaussian process (GP)…