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Compressive sensing has become a powerful addition to uncertainty quantification in recent years. This paper identifies new bases for random variables through linear mappings such that the representation of the quantity of interest is more…

Machine learning (ML) surrogate models are increasingly used in engineering analysis and design to replace computationally expensive simulation models, significantly reducing computational cost and accelerating decision-making processes.…

A perturbative technique, the low-temperature expansion, is developed for matrix models of random surfaces. It can be applied to models with arbitrary target spaces, including ones with c>1. As a simple illustration, the series is worked…

New computational technique based on the symbolic description utilizing kneading invariants is used for explorations of parametric chaos in a two exemplary systems with the Lorenz attractor: a normal model from mathematics, and a laser…

A Bayesian multivariate model with a structured covariance matrix for multi-way nested data is proposed. This flexible modeling framework allows for positive and for negative associations among clustered observations, and generalizes the…

Classical methods in robot motion planning, such as sampling-based and optimization-based methods, often struggle with scalability towards higher-dimensional state spaces and complex environments. Diffusion models, known for their…

We propose a scalable variational Bayes method for statistical inference for a single or low-dimensional subset of the coordinates of a high-dimensional parameter in sparse linear regression. Our approach relies on assigning a mean-field…

Let $\K$ be a field and $(f_1, \ldots, f_n)\subset \K[X_1, \ldots, X_n]$ be a sequence of quasi-homogeneous polynomials of respective weighted degrees $(d_1, \ldots, d_n)$ w.r.t a system of weights $(w_{1},\dots,w_{n})$. Such systems are…

The surrogate model-based uncertainty quantification method has drawn much attention in many engineering fields. Polynomial chaos expansion (PCE) and deep learning (DL) are powerful methods for building a surrogate model. However, PCE needs…

A probabilistic performance-oriented controller design approach based on polynomial chaos expansion and optimization is proposed for flight dynamic systems. Unlike robust control techniques where uncertainties are conservatively handled,…

Hierarchical Bayesian models are increasingly used in large, inhomogeneous complex network dynamical systems by modeling parameters as draws from a hyperparameter-governed distribution. However, theoretical guarantees for these estimates as…

We propose a methodology that combines generative latent diffusion models with physics-informed machine learning to generate solutions of parametric partial differential equations (PDEs) conditioned on partial observations, which includes,…

We describe the results of analytic calculations and computer simulations of adaptive predictors (predictive agents) responding to an evolving chaotic environment and to one another. Our simulations are designed to quantify adaptation and…

In this work, we combine the idea of data-driven polynomial chaos expansions with the weighted least-square approach to solve uncertainty quantification (UQ) problems. The idea of data-driven polynomial chaos is to use statistical moments…

This paper is the second in a series of two, and describes the current state of the art in modelling and prediction of chaotic time series. Sampled data from deterministic non-linear systems may look stochastic when analysed with linear…

We propose an algorithmic framework, that employs active subspace techniques, for scalable global optimization of functions with low effective dimension (also referred to as low-rank functions). This proposal replaces the original…

The Polynomial Chaos Expansion (PCE) technique recovers a finite second order random variable exploiting suitable linear combinations of orthogonal polynomials which are functions of a given stochas- tic quantity {\xi}, hence acting as a…

We extend stochastic basis adaptation and spatial domain decomposition methods to solve time varying stochastic partial differential equations (SPDEs) with a large number of input random parameters. Stochastic basis adaptation allows the…

Recent advances in the estimation of deep directed graphical models and recurrent networks let us contribute to the removal of a blind spot in the area of probabilistc modelling of time series. The proposed methods i) can infer distributed…

Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…