Search Results for author:
Found 11 papers, 2 papers with code
Deep adaptive sampling for surrogate modeling without labeled data
In this work, we present a deep adaptive sampling method for surrogate modeling ($\text{DAS}^2$), where we generalize the deep adaptive sampling (DAS) method [62] [Tang, Wan and Yang, 2023] to build surrogate models for low-regularity parametric differential equations.
Adaptive importance sampling for Deep Ritz
The first step is solving the PDEs using the Deep Ritz method by minimizing an associated variational loss discretized by the collocation points in the training set.
Adversarial Adaptive Sampling: Unify PINN and Optimal Transport for the Approximation of PDEs
The key idea is to use a deep generative model to adjust random samples in the training set such that the residual induced by the approximate PDE solution can maintain a smooth profile when it is being minimized.
Bounded KRnet and its applications to density estimation and approximation
In this paper, we develop an invertible mapping, called B-KRnet, on a bounded domain and apply it to density estimation/approximation for data or the solutions of PDEs such as the Fokker-Planck equation and the Keller-Segel equation.
Dimension-reduced KRnet maps for high-dimensional Bayesian inverse problems
We present a dimension-reduced KRnet map approach (DR-KRnet) for high-dimensional Bayesian inverse problems, which is based on an explicit construction of a map that pushes forward the prior measure to the posterior measure in the latent space.
Adaptive deep density approximation for fractional Fokker-Planck equations
To this end, we represent the solution with an explicit PDF model induced by a flow-based deep generative model, simplified KRnet, which constructs a transport map from a simple distribution to the target distribution.
DAS-PINNs: A deep adaptive sampling method for solving high-dimensional partial differential equations
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 solutions of PDEs and deep generative models are employed to generate new collocation points that refine the training set.
Augmented KRnet for density estimation and approximation
In the augmented KRnet, a fully nonlinear update is achieved in two iterations.
Adaptive deep density approximation for Fokker-Planck equations
In this paper we present an adaptive deep density approximation strategy based on KRnet (ADDA-KR) for solving the steady-state Fokker-Planck (F-P) equations.
VAE-KRnet and its applications to variational Bayes
VAE is used as a dimension reduction technique to capture the latent space, and KRnet is used to model the distribution of the latent variable.
Coupling the reduced-order model and the generative model for an importance sampling estimator
An effective technique to reduce the variance reduction is importance sampling, where we employ the generative model to estimate the distribution of the data from the reduced-order model and use it for the change of measure in the importance sampling estimator.
