Zobrazeno 1 - 10
of 924
pro vyhledávání: '"P. Offen"'
We construct new irreducible components in the discrete automorphic spectrum of symplectic groups. The construction lifts a cuspidal automorphic representation of $\mathrm{GL}_{2n}$ with a linear period to an irreducible component of the residual spe
Externí odkaz:
http://arxiv.org/abs/2410.10635
The depth of networks plays a crucial role in the effectiveness of deep learning. However, the memory requirement for backpropagation scales linearly with the number of layers, which leads to memory bottlenecks during training. Moreover, deep network
Externí odkaz:
http://arxiv.org/abs/2410.09537
Differential equations posed on quadratic matrix Lie groups arise in the context of classical mechanics and quantum dynamical systems. Lie group numerical integrators preserve the constants of motions defining the Lie group. Thus, they respect import
Externí odkaz:
http://arxiv.org/abs/2408.13043
Autor:
Offen, Christian
We introduce a method based on Gaussian process regression to identify discrete variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric
Externí odkaz:
http://arxiv.org/abs/2407.07642
Autor:
Offen, Christian
The article introduces a method to learn dynamical systems that are governed by Euler--Lagrange equations from data. The method is based on Gaussian process regression and identifies continuous or discrete Lagrangians and is, therefore, structure pre
Externí odkaz:
http://arxiv.org/abs/2404.19626
Autor:
Offen, Christian, Ober-Blöbaum, Sina
Publikováno v:
Chaos 34 (1), 013104 (2024)
We show how to learn discrete field theories from observational data of fields on a space-time lattice. For this, we train a neural network model of a discrete Lagrangian density such that the discrete Euler--Lagrange equations are consistent with th
Externí odkaz:
http://arxiv.org/abs/2308.05082
We prove the absolute convergence, functional equations and meromorphic continuation of local intertwining periods on parabolically induced representations of finite length for certain symmetric spaces over local fields of characteristic zero, includ
Externí odkaz:
http://arxiv.org/abs/2303.03663
Autor:
Offen, Christian, Ober-Blöbaum, Sina
Publikováno v:
Learning discrete Lagrangians for variational pdes from data and detection of travelling waves. In: Nielsen, F., Barbaresco, F. (eds.) Geometric Science of Information. vol. 14071, pp. 569-579, Springer Nature Switzerland, Cham (2023)
The article shows how to learn models of dynamical systems from data which are governed by an unknown variational PDE. Rather than employing reduction techniques, we learn a discrete field theory governed by a discrete Lagrangian density $L_d$ that i
Externí odkaz:
http://arxiv.org/abs/2302.08232
Publikováno v:
Chaos 33, 063115 (2023)
Recently, Hamiltonian neural networks (HNN) have been introduced to incorporate prior physical knowledge when learning the dynamical equations of Hamiltonian systems. Hereby, the symplectic system structure is preserved despite the data-driven modeli
Externí odkaz:
http://arxiv.org/abs/2301.07928
Autor:
Lishkova, Yana, Scherer, Paul, Ridderbusch, Steffen, Jamnik, Mateja, Liò, Pietro, Ober-Blöbaum, Sina, Offen, Christian
By one of the most fundamental principles in physics, a dynamical system will exhibit those motions which extremise an action functional. This leads to the formation of the Euler-Lagrange equations, which serve as a model of how the system will behav
Externí odkaz:
http://arxiv.org/abs/2211.10830