Related papers: Generative modeling with low-rank Wasserstein poly…
This paper introduces Tree-based Polynomial Chaos Expansion (Tree-PCE), a novel surrogate modeling technique designed to efficiently approximate complex numerical models exhibiting nonlinearities and discontinuities. Tree-PCE combines the…
Wasserstein barycenter, built on the theory of optimal transport, provides a powerful framework to aggregate probability distributions, and it has increasingly attracted great attention within the machine learning community. However, it…
Wasserstein GANs with Gradient Penalty (WGAN-GP) are a very popular method for training generative models to produce high quality synthetic data. While WGAN-GP were initially developed to calculate the Wasserstein 1 distance between…
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.…
Machine learning interatomic potentials are revolutionizing large-scale, accurate atomistic modelling in material science and chemistry. Many potentials use atomic cluster expansion or equivariant message passing frameworks. Such frameworks…
We present a novel multiscale framework for analyzing sequences of probability measures in Wasserstein spaces over Euclidean domains. Exploiting the intrinsic geometry of optimal transport, we construct a multiscale transform applicable to…
We consider the optimization problem of minimizing a functional defined over a family of probability distributions, where the objective functional is assumed to possess a variational form. Such a distributional optimization problem arises…
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
A novel and efficient algorithm based on the Wiener chaos expansion is proposed for the stochastic Maxwell equations driven by Wiener process. The proposed algorithm can reduce the original stochastic system to the deterministic case and…
This paper introduces a new generalized polynomial chaos expansion (PCE) comprising multivariate Hermite orthogonal polynomials in dependent Gaussian random variables. The second-moment properties of Hermite polynomials reveal a weakly…
The paper presents a novel methodology to build surrogate models of complicated functions by an active learning-based sequential decomposition of the input random space and construction of localized polynomial chaos expansions, referred to…
Dimensionally decomposed generalized polynomial chaos expansion (DD-GPCE) efficiently performs forward uncertainty quantification (UQ) in complex engineering systems with high-dimensional random inputs of arbitrary distributions. However,…
This paper introduces an efficient sparse recovery approach for Polynomial Chaos (PC) expansions, which promotes the sparsity by breaking the dimensionality of the problem. The proposed algorithm incrementally explores sub-dimensional…
This article is a continuation of our first work \cite{chaudruraynal:frikha}. We here establish some new quantitative estimates for propagation of chaos of non-linear stochastic differential equations in the sense of McKean-Vlasov. We…
Many scientific systems, such as cellular populations or economic cohorts, are naturally described by probability distributions that evolve over time. Predicting how such a system would have evolved under different forces or initial…
Surrogate modelling techniques have opened up new possibilities to overcome the limitations of computationally intensive numerical models in various areas of engineering and science. However, while fundamental in many engineering…
The ability to model relational information using machine learning has driven advancements across various domains, from medicine to social science. While graph representation learning has become mainstream over the past decade, representing…
Data consisting of time-indexed distributions of cross-sectional or intraday returns have been extensively studied in finance, and provide one example in which the data atoms consist of serially dependent probability distributions.…
Anomaly detection plays a pivotal role in numerous real-world scenarios, such as industrial automation and manufacturing intelligence. Recently, variational inference-based anomaly analysis has attracted researchers' and developers'…
Generative autoencoders learn compact latent representations of data distributions through jointly optimized encoder--decoder pairs. In particular, Wasserstein autoencoders (WAEs) minimize a relaxed optimal transport (OT) objective, where…