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07/20/2023
Flow Map Learning for Unknown Dynamical Systems: Overview, Implementation, and Benchmarks
Flow map learning (FML), in conjunction with deep neural networks (DNNs)...
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05/05/2023
Learning Stochastic Dynamical System via Flow Map Operator
We present a numerical framework for learning unknown stochastic dynamic...
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06/03/2022
Learning Fine Scale Dynamics from Coarse Observations via Inner Recurrence
Recent work has focused on data-driven learning of the evolution of unkn...
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03/07/2022
Robust Modeling of Unknown Dynamical Systems via Ensemble Averaged Learning
Recent work has focused on data-driven learning of the evolution of unkn...
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02/03/2022
Modeling unknown dynamical systems with hidden parameters
We present a data-driven numerical approach for modeling unknown dynamic...
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06/07/2021
Deep Neural Network Modeling of Unknown Partial Differential Equations in Nodal Space
We present a numerical framework for deep neural network (DNN) modeling ...
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06/02/2020
Data-driven learning of non-autonomous systems
We present a numerical framework for recovering unknown non-autonomous d...
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03/20/2020
Learning reduced systems via deep neural networks with memory
We present a general numerical approach for constructing governing equat...
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03/05/2020
Methods to Recover Unknown Processes in Partial Differential Equations Using Data
We study the problem of identifying unknown processes embedded in time-d...
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02/11/2020
A Non-Intrusive Correction Algorithm for Classification Problems with Corrupted Data
A novel correction algorithm is proposed for multi-class classification ...
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01/23/2020
On generalized residue network for deep learning of unknown dynamical systems
We present a general numerical approach for learning unknown dynamical s...
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10/15/2019
A neural network approach for uncertainty quantification for time-dependent problems with random parameters
In this work we propose a numerical framework for uncertainty quantifica...
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10/15/2019
Data-Driven Deep Learning of Partial Differential Equations in Modal Space
We present a framework for recovering/approximating unknown time-depende...
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05/24/2019
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data
We present a numerical approach for approximating unknown Hamiltonian sy...
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11/13/2018
Data Driven Governing Equations Approximation Using Deep Neural Networks
We present a numerical framework for approximating unknown governing equ...
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09/24/2018
Numerical Aspects for Approximating Governing Equations Using Data
We present effective numerical algorithms for locally recovering unknown...
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08/22/2018
An Explicit Neural Network Construction for Piecewise Constant Function Approximation
We present an explicit construction for feedforward neural network (FNN)...
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05/22/2018