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Found 10 papers, 0 papers with code
Critical Sampling for Robust Evolution Operator Learning of Unknown Dynamical Systems
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?
Deep-OSG: Deep Learning of Operators in Semigroup
It is a sequel to the previous flow map learning (FML) works [T. Qin, K. Wu, and D. Xiu, J. Comput.
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
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
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
A novel correction algorithm is proposed for multi-class classification problems with corrupted training data.
Data-Driven Deep Learning of Partial Differential Equations in Modal Space
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
We present a numerical approach for approximating unknown Hamiltonian systems using observation data.
Data Driven Governing Equations Approximation Using Deep Neural Networks
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
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
We present an explicit construction for feedforward neural network (FNN), which provides a piecewise constant approximation for multivariate functions.
