相关论文: Uncertainty quantification in a mechanical submode…

We present a provably safe sampling-based motion planning algorithm for robotic systems affected by random disturbances of unknown distribution. We consider systems with linear or linearizable dynamics evolving in workspace with…

With the rise of large radio interferometric telescopes, particularly the SKA, there is a growing demand for computationally efficient image reconstruction techniques. Existing reconstruction methods, such as the CLEAN algorithm or proximal…

Common measures of brain functional connectivity (FC) including covariance and correlation matrices are semi-positive definite (SPD) matrices residing on a cone-shape Riemannian manifold. Despite its remarkable success for Euclidean-valued…

Deep generative models provide a systematic way to learn nonlinear data distributions, through a set of latent variables and a nonlinear "generator" function that maps latent points into the input space. The nonlinearity of the generator…

Smart grids are crucial for meeting rising energy demands driven by global population growth and urbanization. By integrating renewable energy sources, they enhance efficiency, reliability, and sustainability. However, ensuring their…

Graph Neural Networks (GNN) provide a powerful framework that elegantly integrates Graph theory with Machine learning for modeling and analysis of networked data. We consider the problem of quantifying the uncertainty in predictions of GNN…

Obtaining reliable data describing local poverty metrics at a granularity that is informative to policy-makers requires expensive and logistically difficult surveys, particularly in the developing world. Not surprisingly, the poverty…

We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves…

We present a mathematically well founded approach for the synthetic modeling of turbulent flows using generative adversarial networks (GAN). Based on the analysis of chaotic, deterministic systems in terms of ergodicity, we outline a…

Generating samples given a specific label requires estimating conditional distributions. We derive a tractable upper bound of the Wasserstein distance between conditional distributions to lay the theoretical groundwork to learn conditional…

Generative adversarial networks (GANs) are a machine learning technique capable of producing high-quality synthetic images. In the field of materials science, when a crystallographic dataset includes inadequate or difficult-to-obtain…

We deconstruct the performance of GANs into three components: 1. Formulation: we propose a perturbation view of the population target of GANs. Building on this interpretation, we show that GANs can be viewed as a generalization of the…

Wasserstein distributionally robust optimization offers a framework for model fitting in machine learning under potential shifts in the data distribution. We study a regularized variant of this problem in which entropic smoothing produces a…

Generative adversarial networks (GANs) are designed with the help of min-max optimization problems that are solved with stochastic gradient-type algorithms which are known to be non-robust. In this work we revisit a non-adversarial method…

Wasserstein-GANs have been introduced to address the deficiencies of generative adversarial networks (GANs) regarding the problems of vanishing gradients and mode collapse during the training, leading to improved convergence behaviour and…

Generative adversarial networks (GAN) have recently been used for a design synthesis of mechanical shapes. A GAN sometimes outputs physically unreasonable shapes. For example, when a GAN model is trained to output airfoil shapes that…

Subgrid parameterizations of mesoscale eddies continue to be in demand for climate simulations. These subgrid parameterizations can be powerfully designed using physics and/or data-driven methods, with uncertainty quantification. For…

Generative adversarial networks, or GANs, commonly display unstable behavior during training. In this work, we develop a principled theoretical framework for understanding the stability of various types of GANs. In particular, we derive…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

Stochastic and conditional simulation methods have been effective towards producing realistic realizations and simulations of spatial numerical models that share equal probability of occurrence. Application of these methods are valuable…