Zobrazeno 1 - 10
of 253
pro vyhledávání: '"37M15"'
Autor:
Stern, Ari, Viviani, Milo
Runge-Kutta methods are affine equivariant: applying a method before or after an affine change of variables yields the same numerical trajectory. However, for some applications, one would like to perform numerical integration after a quadratic change
Externí odkaz:
http://arxiv.org/abs/2411.12634
We present a novel methodology for convex optimization algorithm design using ideas from electric RLC circuits. Given an optimization problem, the first stage of the methodology is to design an appropriate electric circuit whose continuous-time dynam
Externí odkaz:
http://arxiv.org/abs/2411.02573
We study a universal approximation property of ODENet and ResNet. The ODENet is a map from an initial value to the final value of an ODE system in a finite interval. It is considered a mathematical model of a ResNet-type deep learning system. We cons
Externí odkaz:
http://arxiv.org/abs/2410.16709
An integrator for a class of stochastic Lie-Poisson systems driven by Stratonovich noise is developed. The integrator is suited for Lie-Poisson systems that also admit an isospectral formulation, which enables scalability to high-dimensional systems.
Externí odkaz:
http://arxiv.org/abs/2408.16701
Growing demands in the semiconductor industry necessitate increasingly stringent requirements on throughput and positioning accuracy of lithographic equipment. Meeting these demands involves employing highly aggressive motion profiles, which introduc
Externí odkaz:
http://arxiv.org/abs/2408.03642
Machine learning techniques have recently been of great interest for solving differential equations. Training these models is classically a data-fitting task, but knowledge of the expression of the differential equation can be used to supplement the
Externí odkaz:
http://arxiv.org/abs/2407.18057
Structure-preserving particle methods have recently been proposed for a class of nonlinear continuity equations, including aggregation-diffusion equation in [J. Carrillo, K. Craig, F. Patacchini, Calc. Var., 58 (2019), pp. 53] and the Landau equation
Externí odkaz:
http://arxiv.org/abs/2407.00533
Matrix evolution equations occur in many applications, such as dynamical Lyapunov/Sylvester systems or Riccati equations in optimization and stochastic control, machine learning or data assimilation. In many cases, their tightest stability condition
Externí odkaz:
http://arxiv.org/abs/2406.13761
Let $\tau: I=[0, 1]\to [0, 1]$ be a piecewise convex map with countably infinite number of branches. In \cite{GIR}, the existence of absolutely continuous invariant measure (ACIM) $\mu$ for $\tau$ and the exactness of the system $(\tau, \mu)$ has bee
Externí odkaz:
http://arxiv.org/abs/2405.02729
Autor:
Mañosa, Víctor, Pantazi, Chara
In this work we investigate the set of cubic Hamiltonian vector fields for which their associated Kahan-Hirota-Kimura maps preserve the original Hamiltonian function. We analyze these fields in $\mathbb{R}^2$ and $\mathbb{R}^4$. We also study a famil
Externí odkaz:
http://arxiv.org/abs/2405.01321