7 papers
A perfectly matched layer approach for the spectral split-step Padé method
Daniel Walsken, Matthias Ehrhardt, Pavel Petrov
The split-step-Padé (SSP) method is widely used to model wave phenomena in various applications, including radio physics, optics and acoustics. In this method, the propagator of th…
A Spectral Split-Step Padé Method for Guided Wave Propagation
Daniel Walsken, Pavel Petrov, Matthias Ehrhardt
In this study, a Fourier-based, split-step Padé (SSP) method for solving the parabolic wave equation with applications in guided wave propagation in ocean acoustics is presented. T…
Port-Hamiltonian Neural Networks: From Theory to Simulation of Interconnected Stochastic Systems
Luca Di Persio, Matthias Ehrhardt, Youness Outaleb +1
This work introduces a new framework integrating port-Hamiltonian systems (PHS) and neural network architectures. This framework bridges the gap between deterministic and stochasti…
A finite element-based machine learning model for hydro-mechanical analysis of swelling behavior in clay-sulfate rocks
Reza Taherdangkoo, Mostafa Mollaali, Matthias Ehrhardt +4
The hydro-mechanical behavior of clay-sulfate rocks, especially their swelling properties, poses significant challenges in geotechnical engineering. This study presents a hybrid co…
A Space Mapping approach for the calibration of financial models with the application to the Heston model
Anna Clevenhaus, Claudia Totzeck, Matthias Ehrhardt
We present a novel approach for parameter calibration of the Heston model for pricing an Asian put option, namely space mapping. Since few parameters of the Heston model can be dir…
Absorbing Boundary Conditions for Variable Potential Schrödinger Equations via Titchmarsh-Weyl Theory
Matthias Ehrhardt, Chunxiong Zheng
We propose a novel approach to simulate the solution of the time-dependent Schrödinger equation with a general variable potential. The key idea is to approximate the Titchmarsh-Wey…
Integrating Port-Hamiltonian Systems with Neural Networks: From Deterministic to Stochastic Frameworks
Luca Di Persio, Matthias Ehrhardt, Sofia Rizzotto
This article presents an innovative approach to integrating port-Hamiltonian systems with neural network architectures, transitioning from deterministic to stochastic models. The s…