Related papers: Transforming physics-informed machine learning to …
Numerical methods such as finite element have been flourishing in the past decades for modeling solid mechanics problems via solving governing partial differential equations (PDEs). A salient aspect that distinguishes these numerical…
Physics-informed Machine Learning has recently become attractive for learning physical parameters and features from simulation and observation data. However, most existing methods do not ensure that the physics, such as balance laws (e.g.,…
Variational inequalities are widely applied in mechanical engineering, fluid penetration, transportation, and other fields. In this paper, a Deep Ritz method based on Physics-Informed Neural Networks (PINNs) is proposed to enhance the…
Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear…
Electromagnetic (EM) imaging is widely applied in sensing for security, biomedicine, geophysics, and various industries. It is an ill-posed inverse problem whose solution is usually computationally expensive. Machine learning (ML)…
Predictive Physics has been historically based upon the development of mathematical models that describe the evolution of a system under certain external stimuli and constraints. The structure of such mathematical models relies on a set of…
Modeling stiff partial differential equations (PDEs) with sharp gradients remains a significant challenge for scientific machine learning. While Physics-Informed Neural Networks (PINNs) struggle with spectral bias and slow training times,…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
Most noninvasive imaging techniques utilize electromagnetic or acoustic waves originating from multiple locations and directions to identify hidden geometrical structures. Surprisingly, it is also possible to image hidden voids and…
Relying on either deep models or physical models are two mainstream approaches for solving inverse sample reconstruction problems in programmable illumination computational microscopy. Solutions based on physical models possess strong…
Coupling physics with machine learning models has shown great potential for solving fluid dynamics problems governed by partial differential equations. However, conventional methods, such as physics-informed neural networks, often suffer…
This work proposes a solution for the problem of training physics-informed networks under partial integro-differential equations. These equations require an infinite or a large number of neural evaluations to construct a single residual for…
Spinodal metamaterials, with architectures inspired by natural phase-separation processes, have presented a significant alternative to periodic and symmetric morphologies when designing mechanical metamaterials with extreme performance.…
The work is a continuation of a paper by Iskhakov A.S. and Dinh N.T. "Physics-integrated machine learning: embedding a neural network in the Navier-Stokes equations". Part I // arXiv:2008.10509 (2020) [1]. The proposed in [1]…
The convergence of cross-modal adversarial learning and physics-driven methods represents a cutting-edge direction for tackling challenges in complex multi-modal tasks and scientific computing. This review focuses on systematically…
We introduce a manifold-based framework for addressing optimization problems with equality and inequality constraints found in robotics. Our approach transforms the original problem into an unconstrained optimization problem directly on the…
In an era increasingly focused on green computing and explainable AI, revisiting traditional approaches in theoretical and phenomenological particle physics is paramount. This project evaluates various machine learning (ML)…
Physics-constrained data-driven computing is an emerging hybrid approach that integrates universal physical laws with data-driven models of experimental data for scientific computing. A new data-driven simulation approach coupled with a…
Manifold optimization is ubiquitous in computational and applied mathematics, statistics, engineering, machine learning, physics, chemistry and etc. One of the main challenges usually is the non-convexity of the manifold constraints. By…
This paper introduces, for the first time to our knowledge, physics-informed neural networks to accurately estimate the AC-OPF result and delivers rigorous guarantees about their performance. Power system operators, along with several other…