Search Results for author: Kailiang Wu

Found 8 papers, 0 papers with code

Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space

no code implementations7 Jun 2021 Zhen Chen, Victor Churchill, Kailiang Wu, Dongbin Xiu

Consequently, a trained DNN defines a predictive model for the underlying unknown PDE over structureless grids.

Methods to Recover Unknown Processes in Partial Differential Equations Using Data

no code implementations5 Mar 2020 Zhen Chen, Kailiang Wu, Dongbin Xiu

Various numerical examples are then presented to demonstrate the performance and properties of the numerical methods.

A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data

no code implementations11 Feb 2020 Jun Hou, Tong Qin, Kailiang Wu, Dongbin Xiu

A novel correction algorithm is proposed for multi-class classification problems with corrupted training data.

Classification General Classification +1

Data-Driven Deep Learning of Partial Differential Equations in Modal Space

no code implementations15 Oct 2019 Kailiang Wu, Dongbin Xiu

The evolution operator of the PDE, defined in infinite-dimensional space, maps the solution from a current time to a future time and completely characterizes the solution evolution of the underlying unknown PDE.

Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data

no code implementations24 May 2019 Kailiang Wu, Tong Qin, Dongbin Xiu

We present a numerical approach for approximating unknown Hamiltonian systems using observation data.

Data Driven Governing Equations Approximation Using Deep Neural Networks

no code implementations13 Nov 2018 Tong Qin, Kailiang Wu, Dongbin Xiu

We demonstrate that the ResNet block can be considered as a one-step method that is exact in temporal integration.

Numerical Aspects for Approximating Governing Equations Using Data

no code implementations24 Sep 2018 Kailiang Wu, Dongbin Xiu

We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data.

An Explicit Neural Network Construction for Piecewise Constant Function Approximation

no code implementations22 Aug 2018 Kailiang Wu, Dongbin Xiu

We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions.

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