# Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data

@article{Xu2021DeeplearningBD, title={Deep-learning based discovery of partial differential equations in integral form from sparse and noisy data}, author={Hao Xu and Dongxiao Zhang and Nanzhe Wang}, journal={J. Comput. Phys.}, year={2021}, volume={445}, pages={110592} }

## 10 Citations

### Robust discovery of partial differential equations in complex situations

- Computer SciencePhysical Review Research
- 2021

Results prove that the proposed R-DLGA is able to calculate derivatives accurately with the optimization of PINN and possesses surprising robustness to complex situations, including sparse data with high noise, high-order derivatives, and shock waves.

### Bayesian Deep Learning for Partial Differential Equation Parameter Discovery with Sparse and Noisy Data

- Computer ScienceJournal of Computational Physics: X
- 2022

### Combining physics-based and data-driven techniques for reliable hybrid analysis and modeling using the corrective source term approach

- Computer ScienceApplied Soft Computing
- 2022

This work demonstrates how a hybrid approach combining the best of PBM and DDM can result in models which can outperform them both, and demonstrates the method’s superior performance in terms of accuracy, and generalizability.

### Solution of diffusivity equations with local sources/sinks and surrogate modeling using weak form Theory-guided Neural Network

- Computer ScienceAdvances in Water Resources
- 2021

### Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data

- Materials ScienceArXiv
- 2021

Deep-Learning Discovers Macroscopic Governing Equations for Viscous Gravity Currents from Microscopic Simulation Data and finds macroscopic rules for viscous gravity currents from microscopic simulation data.

### Data‐Driven Discovery of Soil Moisture Flow Governing Equation: A Sparse Regression Framework

- Computer ScienceWater Resources Research
- 2022

This study provides a new perspective for deriving soil moisture flow governing equations from a data‐driven sparse regression framework based on a homogeneous soil assumption and discovers the time‐dependent nonlinear soil moistureflow equation from only volumetric water content observations.

### A novel corrective-source term approach to modeling unknown physics in aluminum extraction process

- Computer Science
- 2022

This work investigates the Corrective Source Term Approach (CoSTA), which uses a data-driven model to correct a misspeciﬁed physics-based model, and demonstrates that the method improves both accuracy and predictive stability, yielding an overall more trustworthy model.

### Integration of knowledge and data in machine learning

- Computer ScienceArXiv
- 2022

A closed loop of knowledge generation and usage are formed by combining knowledge embedding with knowledge discovery, which can improve the robustness and accuracy of models and uncover previously unknown scientiﬁc principles.

### Data-driven bond-based peridynamics with nonlocal influence function for crack propagation

- PhysicsEngineering Fracture Mechanics
- 2022

### Data-driven and physical-based identification of partial differential equations for multivariable system

- MathematicsTheoretical and Applied Mechanics Letters
- 2022

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