Related papers: Gradient-informed basis adaptation for Legendre Ch…
Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational…
Model-based approaches bear great promise for decision making of agents interacting with the physical world. In the context of spatial environments, different types of problems such as localisation, mapping, navigation or autonomous…
Polynomial chaos methods have been extensively used to analyze systems in uncertainty quantification. Furthermore, several approaches exist to determine a low-dimensional approximation (or sparse approximation) for some quantity of interest…
Bayesian hierarchical models can provide efficient algorithms for finding sparse solutions to ill-posed inverse problems. The models typically comprise a conditionally Gaussian prior model for the unknown which is augmented by a generalized…
We derive and present explicit algorithms to facilitate streamlined computing for variational inference for models containing higher level random effects. Existing literature, such as Lee and Wand (2016), is such that streamlined…
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space. We define a novel geometric notion of exploration basis with low variance, called volumetric spanners, and give efficient algorithms…
We study generalized Hermite polynomials with rectangular matrix arguments arising in multivariate statistical analysis and the theory of zonal polynomials. We show that these are well-suited for expressing the Wiener-Ito chaos expansion of…
Variational Autoencoders (VAEs) have gained significant popularity among researchers as a powerful tool for understanding unknown distributions based on limited samples. This popularity stems partly from their impressive performance and…
Sparse polynomial chaos expansions (PCE) are a popular surrogate modelling method that takes advantage of the properties of PCE, the sparsity-of-effects principle, and powerful sparse regression solvers to approximate computer models with…
We explore quantum chaos diagnostics of variational circuit states at random parameters and study their correlation with the circuit expressibility and the optimization of control parameters. By measuring the operator spreading coefficient…
This paper presents a novel method for accelerating path planning tasks in unknown scenes with obstacles by utilizing Wasserstein Generative Adversarial Networks (WGANs) with Gradient Penalty (GP) to approximate the distribution of the free…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
Chaos presents complex dynamics arising from nonlinearity and a sensitivity to initial states. These characteristics suggest a depth of expressivity that underscores their potential for advanced computational applications. However,…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
This work suggests an interpolation-based stochastic collocation method for the non-intrusive and adaptive construction of sparse polynomial chaos expansions (PCEs). Unlike pseudo-spectral projection and regression-based stochastic…
Presence of a high-dimensional stochastic parameter space with discontinuities poses major computational challenges in analyzing and quantifying the effects of the uncertainties in a physical system. In this paper, we propose a stochastic…
In previous works, we have developed a new Malliavin calculus on the Poisson space based on the lent particle formula. The aim of this work is to prove that, on the Wiener space for the standard Ornstein-Uhlenbeck structure, we also have…
The large-scale integration of renewable energy sources introduces significant operational uncertainty into power systems. Although Polynomial Chaos Expansion (PCE) provides an efficient tool for uncertainty quantification (UQ) in power…
Based on the invariance principle of differential equations, a simple adaptive-feedback scheme is proposed to strictly synchronize almost all chaotic systems. Unlike the usual linear feedback, the variable feedback strength is automatically…
This article is an introductory review of random matrix theory (RMT) and its applications, with special focus on quantum chaos. Random matrices were first used by Wigner to understand the spectra of complex nuclei from a statistical…