[HTML][HTML] Physics-informed machine learning: a comprehensive review on applications in anomaly detection and condition monitoring

Y Wu, B Sicard, SA Gadsden - Expert Systems with Applications, 2024 - Elsevier
Condition monitoring plays a vital role in ensuring the reliability and optimal performance of
various engineering systems. Traditional methods for condition monitoring rely on physics …

Partial differential equations meet deep neural networks: A survey

S Huang, W Feng, C Tang, J Lv - ar** points of agent-based models
G Fabiani, N Evangelou, T Cui, JM Bello-Rivas… - Nature …, 2024 - nature.com
We present a machine learning framework bridging manifold learning, neural networks,
Gaussian processes, and Equation-Free multiscale approach, for the construction of …

A framework for machine learning of model error in dynamical systems

M Levine, A Stuart - Communications of the American Mathematical Society, 2022 - ams.org
The development of data-informed predictive models for dynamical systems is of
widespread interest in many disciplines. We present a unifying framework for blending …

Leveraging viscous Hamilton–Jacobi PDEs for uncertainty quantification in scientific machine learning

Z Zou, T Meng, P Chen, J Darbon… - SIAM/ASA Journal on …, 2024 - SIAM
Uncertainty quantification (UQ) in scientific machine learning (SciML) combines the powerful
predictive power of SciML with methods for quantifying the reliability of the learned models …

Machine learning for elliptic pdes: Fast rate generalization bound, neural scaling law and minimax optimality

Y Lu, H Chen, J Lu, L Ying, J Blanchet - arxiv preprint arxiv:2110.06897, 2021 - arxiv.org
In this paper, we study the statistical limits of deep learning techniques for solving elliptic
partial differential equations (PDEs) from random samples using the Deep Ritz Method …