De Lellis, C.,Székelyhidi, L. Jr.: High dimensionality and h-principle in PDE.Bull. Am. Math. Soc. (N.S.),54(2), 247–282, 2017 Eyink, G.L.: Energy dissipation without viscosity in ideal hydrodynamics. I. Four
Due to the mega high dimensionality nature of datasets, data dimension reduction has drawn special attention for such type of data analysis. Data Reduction can be viewed as preprocessing step which removes distracting variance from the datasets so that clustering, classifiers can estimators perform ...
A key difficulty is that, without appropriate constraints, the high dimensionality of the data makes the model search space far too large for any purely data-driven approach to be tractable. In principle, machine learning can be used to construct suitable models (e.g., nonlinear partial ...
Solving high-dimensional optimal control problems and corresponding Hamilton–Jacobi PDEs are important but challenging problems in control engineering. In this paper, we propose two abstract neural network architectures which are, respectively, used to compute the value function and the optimal control fo...
We introduce an entirely new class of high-order methods for computational fluid dynamics based on the Gaussian process (GP) family of stochastic functions
Introduction Emerging implantable biomedical systems need to transmit large amounts of data through skin/tissue to achieve high accuracy measurements, high dimensionality and real-time control of complex prosthetic devices like brain machine interfaces [1–3]. These systems require wireless biotelemetry ...
While neural networks grapple with the curse of dimensionality as problems become more complex, PINNs strive to resolve PDEs and their inversion challenges in domains characterized by intricate geometries and high dimensions, where numerical simulations are notably challenging. PINNs have produced compelling...
The study of forward–backward stochastic differential equations (FBSDEs) originates from the optimal control problem, and the main objective is to study how to reach the desired goal under the given conditions. Pardoux et al. [2] proposed the general stochastic maximum principle, which, under ...
In addition, this method can effectively detect points near sharp edges without additional processing. In addition, Yao et al. exploited dimensionality reduction technology to generate 2D data by extracting the first and the second principal components of the original data with minor information loss....
A Dimensionality Reduction-Based Multi-Step Clustering Method for Robust Vessel Trajectory Analysis. Sensors 2017, 17, 1792. [CrossRef] [PubMed] 33. Guangyun, Z.; Xiuping, J.; Jiankun, H. Superpixel-based graphical model for remote sensing image mapping. IEEE Trans. Geosci. Remote Sens. ...