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Found 19 papers, 1 papers with code
Modeling Unknown Stochastic Dynamical System via Autoencoder
We present a numerical method to learn an accurate predictive model for an unknown stochastic dynamical system from its trajectory data.
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
Flow map learning (FML), in conjunction with deep neural networks (DNNs), has shown promises for data driven modeling of unknown dynamical systems.
Learning Stochastic Dynamical System via Flow Map Operator
Termed stochastic flow map learning (sFML), the new framework is an extension of flow map learning (FML) that was developed for learning deterministic dynamical systems.
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence
Recent work has focused on data-driven learning of the evolution of unknown systems via deep neural networks (DNNs), with the goal of conducting long term prediction of the dynamics of the unknown system.
Deep Learning of Chaotic Systems from Partially-Observed Data
A distinct feature of chaotic systems is that even the smallest perturbations will lead to large (albeit bounded) deviations in the solution trajectories.
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning
In the proposed ensemble averaging method, multiple models are independently trained and model predictions are averaged at each time step.
Modeling unknown dynamical systems with hidden parameters
We present a data-driven numerical approach for modeling unknown dynamical systems with missing/hidden parameters.
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.
Data-driven learning of non-autonomous systems
To circumvent the difficulty presented by the non-autonomous nature of the system, our method transforms the solution state into piecewise integration of the system over a discrete set of time instances.
Learning reduced systems via deep neural networks with memory
We then use a set of numerical examples to demonstrate the effectiveness of our method.
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.
On generalized residue network for deep learning of unknown dynamical systems
When an existing coarse model is not available, we present numerical strategies for fast creation of coarse models, to be used in conjunction with the generalized ResNet.
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.
Reducing Parameter Space for Neural Network Training
For neural networks (NNs) with rectified linear unit (ReLU) or binary activation functions, we show that their training can be accomplished in a reduced parameter space.
