A robust framework for identification of PDEs from noisy data

Z Zhang, Y Liu - Journal of Computational Physics, 2021 - Elsevier
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 …

Parsimony-enhanced sparse Bayesian learning for robust discovery of partial differential equations

Z Zhang, Y Liu - Mechanical Systems and Signal Processing, 2022 - Elsevier
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 …

System identification through Lipschitz regularized deep neural networks

E Negrini, G Citti, L Capogna - Journal of Computational Physics, 2021 - Elsevier
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 …

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 …

Recent advance in machine learning for partial differential equation

KC Cheung, S See - CCF Transactions on High Performance Computing, 2021 - Springer
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 …

Physics-informed identification of PDEs with LASSO regression, examples of groundwater-related equations

Y Zhan, Z Guo, B Yan, K Chen, Z Chang, V Babovic… - Journal of …, 2024 - Elsevier
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 …

The uniqueness problem of physical law learning

P Scholl, A Bacho, H Boche… - ICASSP 2023-2023 IEEE …, 2023 - ieeexplore.ieee.org
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 …

Robust identifiability for symbolic recovery of differential equations

H Hauger, P Scholl, G Kutyniok - arxiv preprint arxiv:2410.09938, 2024 - arxiv.org
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 …

Robust data-driven discovery of partial differential equations under uncertainties

Z Zhang, Y Liu - arxiv preprint arxiv:2102.06504, 2021 - arxiv.org
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 …

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 …