Uncertainty quantification (UQ) methods play a pivotal role in reducing the impact of
uncertainties during both optimization and decision making processes. They have been …

Abstract Markov chain Monte Carlo (MCMC) algorithms are generally regarded as the gold
standard technique for Bayesian inference. They are theoretically well-understood and …

Over the last decade, neural networks have reached almost every field of science and
become a crucial part of various real world applications. Due to the increasing spread …

Score-based generative models (SGMs) have demonstrated remarkable synthesis quality.
SGMs rely on a diffusion process that gradually perturbs the data towards a tractable …

We propose a Bayesian physics-informed neural network (B-PINN) to solve both forward
and inverse nonlinear problems described by partial differential equations (PDEs) and noisy …

Machine learning develops rapidly, which has made many theoretical breakthroughs and is
widely applied in various fields. Optimization, as an important part of machine learning, has …

During the past five years the Bayesian deep learning community has developed
increasingly accurate and efficient approximate inference procedures that allow for …

Stochastic Gradient Descent with a constant learning rate (constant SGD) simulates a
Markov chain with a stationary distribution. With this perspective, we derive several new …

This paper proposes a new optimization algorithm called Entropy-SGD for training deep
neural networks that is motivated by the local geometry of the energy landscape. Local …

We investigate the dynamical and convergent properties of stochastic gradient descent
(SGD) applied to Deep Neural Networks (DNNs). Characterizing the relation between …