A robust framework for identification of PDEs from noisy data
Robust physics (eg, governing equations and laws) discovery is of great interest for many
engineering fields and explainable machine learning. A critical challenge compared with …
engineering fields and explainable machine learning. A critical challenge compared with …
Parsimony-enhanced sparse Bayesian learning for robust discovery of partial differential equations
Robust physics discovery is of great interest for many scientific and engineering fields.
Inspired by the principle that a representative model is the simplest one among all possible …
Inspired by the principle that a representative model is the simplest one among all possible …
System identification through Lipschitz regularized deep neural networks
In this paper we use neural networks to learn governing equations from data. Specifically we
reconstruct the right-hand side of a system of ODEs x˙(t)= f (t, x (t)) directly from observed …
reconstruct the right-hand side of a system of ODEs x˙(t)= f (t, x (t)) directly from observed …
A solution method for differential equations based on Taylor PINN
Y Zhang, M Wang, F Zhang, Z Chen - IEEE Access, 2023 - ieeexplore.ieee.org
Based on deep neural network, elliptic partial differential equations in complex regions are
solved. Accurate and effective strategies and numerical methods for elliptic partial …
solved. Accurate and effective strategies and numerical methods for elliptic partial …
Recent advance in machine learning for partial differential equation
Abstract Machine learning method has been applied to solve different kind of problems in
different areas due to the great success in several tasks such as computer vision, natural …
different areas due to the great success in several tasks such as computer vision, natural …
Physics-informed identification of PDEs with LASSO regression, examples of groundwater-related equations
In recent years, the application of machine learning methods in the derivation of physical
governing equations has gained significant attention. This has become increasingly relevant …
governing equations has gained significant attention. This has become increasingly relevant …
The uniqueness problem of physical law learning
Physical law learning is the ambiguous attempt at automating the derivation of governing
equations with the use of machine learning techniques. This paper shall serve as a first step …
equations with the use of machine learning techniques. This paper shall serve as a first step …
Robust identifiability for symbolic recovery of differential equations
Recent advancements in machine learning have transformed the discovery of physical laws,
moving from manual derivation to data-driven methods that simultaneously learn both the …
moving from manual derivation to data-driven methods that simultaneously learn both the …
Robust data-driven discovery of partial differential equations under uncertainties
Robust physics (eg, governing equations and laws) discovery is of great interest for many
engineering fields and explainable machine learning. A critical challenge compared with …
engineering fields and explainable machine learning. A critical challenge compared with …
Wavelet neural networks functional approximation and application
A Zeglaoui, A Ben Mabrouk… - International Journal of …, 2022 - World Scientific
Approximation theory constitutes a useful field that is related to quasi all other fields, in both
theoretical and applied sciences. In approximation theory, the aim is generally to construct …
theoretical and applied sciences. In approximation theory, the aim is generally to construct …