This paper reviews the mathematical foundation of the importance sampling technique and
discusses two general classes of methods to construct the importance sampling density (or …

In this work we propose a deep adaptive sampling (DAS-PINNs) method for solving partial
differential equations (PDEs), where deep neural networks are utilized to approximate the …

In this paper we present an adaptive deep density approximation strategy based on KRnet
(ADDA-KR) for solving the steady-state Fokker-Planck (FP) equations. FP equations are …

In this work, we introduce a flow based machine learning approach called reaction
coordinate (RC) flow for the discovery of low-dimensional kinetic models of molecular …

In this work, we propose an adaptive learning approach based on temporal normalizing
flows for solving time-dependent Fokker-Planck (TFP) equations. It is well known that …

Estimation of spatially-varying parameters for computationally expensive forward models
governed by partial differential equations (PDEs) is addressed. A novel multiscale Bayesian …

In this work, we propose an end-to-end adaptive sampling framework based on deep neural
networks and the moving mesh method (MMPDE-Net), which can adaptively generate new …

In this work we propose a deep adaptive sampling (DAS) method for solving partial
differential equations (PDEs), where deep neural networks are utilized to approximate the …

Surrogate modeling is of great practical significance for parametric differential equation
systems. In contrast to classical numerical methods, using physics-informed deep learning …

In this paper we consider adaptive deep neural network approximation for stochastic
dynamical systems. Based on the continuity equation associated with the stochastic …