Kraußhar, R.: Fock spaces, Landau operators and the time-harmo- nic Maxwell equations, Journal of Physics A: Mathematical and Theoretical 44 (2011)... Denis,Constales,Nelson,... - 《Journal of Physics A Mathematical & Theoretical》 被引量: 20发表: 2011年 Few-particle vortex cluster eq...
The primary focus of this paper is to address this issue. Recent studies have revealed the deep-rooted relationship between neural network structures and ordinal/partial differential equations (ODEs/PDEs)44,45,46,47,48,49. For example, Lu et al.45 bridged deep convolutional network architectures...
PDEs) that govern the system behaviors. These governing equations are conventionally obtained from rigorous first principles such as the conservation laws or knowledge-based phenomenological derivations. However, there remain many real-world complex
Harnessing data to discover the underlying governing laws or equations that describe the behavior of complex physical systems can significantly advance our modeling, simulation and understanding of such systems in various science and engineering disciplines. This work introduces a novel physics-informed deep...
In this paper, we focus specifically on equality-type constraints with the objective of minimizing the sum of squared residuals (SSR), and thus it is possible to use the well-known method of Lagrange multipliers. The Karush-Kuhn-Tucker (KKT) stationarity condition yields a system of equations ...
Give separate numbering to formulae and equations within appendices using formats such as Eq. (A.1), Eq. (A.2), etc. and in subsequent appendices, Eq. (B.1), Eq. (B. 2) etc. In a similar way, give separate numbering to tables and figures using formats such as Table A.1; Fig...
Furthermore, including the governing equations and physical facts in such methods is also another challenge, which entails either ignoring the physics or simplifying them using unrealistic data. To address such issues, physics informed machine learning methods have been developed which can integrate the...
In this paper, we describe these different parallel algorithms and report on computational experiments that we have conducted to evaluate their efficiency on parallel computers. The experiments used a testbed code that solves the nonlinear shallow water equations on a sphere; considerable care was ...
The Maxwell equations governing the behavior of light are solved by the multi-particle generalization of the Mie theory46. In short, the incident and scattered waves of each sphere are expanded in a series of vector spherical wavefunctions. Applying the vector translation–addition theorem and the...
This paper presents a physics-informed neural network (PINN) approach for monitoring the health of diesel engines. The aim is to evaluate the engine dynamics, identify unknown parameters in a “mean value” model, and anticipate maintenance requirements. The PINN model is applied to diesel engines...