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pro vyhledávání: '"Lorin, Emmanuel"'
Autor:
Khan, Mashhood, Lorin, Emmanuel
In this note, we establish some connections between standard (data-driven) neural network-based solvers for PDE and eigenvalue problems developed on one side in the applied mathematics and engineering communities (e.g. Deep-Ritz and Physics Informed
Externí odkaz:
http://arxiv.org/abs/2410.09177
Autor:
Lorin, Emmanuel, Novruzi, Arian
In this paper we develop a non-diffusive neural network (NDNN) algorithm for accurately solving weak solutions to hyperbolic conservation laws. The principle is to construct these weak solutions by computing smooth local solutions in subdomains bound
Externí odkaz:
http://arxiv.org/abs/2405.15559
Autor:
Lorin, Emmanuel, Yang, Xu
We propose to compute the time-dependent Dirac equation using physics-informed neural networks (PINNs), a new powerful tool in scientific machine learning avoiding the use of approximate derivatives of differential operators. PINNs search solutions i
Externí odkaz:
http://arxiv.org/abs/2204.02959
Autor:
Lorin, Emmanuel, Yang, Xu
This paper develops a physics-informed neural network (PINN) based on the Schwarz waveform relaxation (SWR) method for solving local and nonlocal advection-diffusion-reaction equations. Specifically, we derive the formulation by constructing subdomai
Externí odkaz:
http://arxiv.org/abs/2111.02559
Autor:
Lorin, Emmanuel, Yang, Xu
Publikováno v:
In Applied Numerical Mathematics May 2024 199:85-104
Publikováno v:
In Communications in Nonlinear Science and Numerical Simulation February 2024 129
Pseudospectral numerical schemes for solving the Dirac equation in general static curved space are derived using a pseudodifferential representation of the Dirac equation along with a simple Fourier-basis technique. Owing to the presence of non-const
Externí odkaz:
http://arxiv.org/abs/1909.02894
Autor:
Lorin, Emmanuel, Yang, Xu
Publikováno v:
In Journal of Computational Physics 15 January 2023 473
Autor:
Lorin, Emmanuel, Yang, Xu
Publikováno v:
In Computer Physics Communications November 2022 280