1 code implementation • 15 May 2024 • Junfeng Chen, Kailiang Wu
Operator learning for Partial Differential Equations (PDEs) is rapidly emerging as a promising approach for surrogate modeling of intricate systems.
no code implementations • 15 Apr 2023 • Ce Zhang, Kailiang Wu, Zhihai He
Given an unknown dynamical system, what is the minimum number of samples needed for effective learning of its governing laws and accurate prediction of its future evolution behavior, and how to select these critical samples?
no code implementations • 7 Feb 2023 • Junfeng Chen, Kailiang Wu
It is a sequel to the previous flow map learning (FML) works [T. Qin, K. Wu, and D. Xiu, J. Comput.
no code implementations • 7 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.
no code implementations • 5 Mar 2020 • Zhen Chen, Kailiang Wu, Dongbin Xiu
Various numerical examples are then presented to demonstrate the performance and properties of the numerical methods.
no code implementations • 11 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.
no code implementations • 15 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.
no code implementations • 24 May 2019 • Kailiang Wu, Tong Qin, Dongbin Xiu
We present a numerical approach for approximating unknown Hamiltonian systems using observation data.
no code implementations • 13 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.
no code implementations • 24 Sep 2018 • Kailiang Wu, Dongbin Xiu
We present effective numerical algorithms for locally recovering unknown governing differential equations from measurement data.
no code implementations • 22 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.