22 citations · 45 across the 14 of their papers we have counts for
19 papers
SIPHy: Sparse identification of port-Hamiltonian systems from noisy data
Håkon Noren Myhr, Sølve Eidnes, J. Nathan Kutz
We propose sparse identification of port-Hamiltonian systems (SIPHy), enabling structure-preserving symbolic regression from noisy trajectory observations. The method applies to po…
Learning partially observed systems with neural Hamiltonian ordinary differential equations
Sunniva Meltzer, Sølve Eidnes, Alexander Johannes Stasik
When learning dynamical systems from data, embedding physical structure can constrain the solution space and improve generalization, but many physics-informed models assume access…
Derivative-free discrete gradient methods
Håkon Noren Myhr, Sølve Eidnes
Discrete gradient methods are a class of numerical integrators producing solutions with exact preservation of first integrals of ordinary differential equations. In this paper, we…
Machine learning in wastewater treatment: insights from modelling a pilot denitrification reactor
Eivind Bøhn, Sølve Eidnes, Kjell Rune Jonassen
Wastewater treatment plants are increasingly recognized as promising candidates for machine learning applications, due to their societal importance and high availability of data. H…
Analysis of Full-scale Riser Responses in Field Conditions Based on Gaussian Mixture Model
Jie Wu, Sølve Eidnes, Jingzhe Jin +5
Offshore slender marine structures experience complex and combined load conditions from waves, current and vessel motions that may result in both wave frequency and vortex shedding…
Recency-Weighted Temporally-Segmented Ensemble for Time-Series Modeling
Pål V. Johnsen, Eivind Bøhn, Sølve Eidnes +2
Time-series modeling in process industries faces the challenge of dealing with complex, multi-faceted, and evolving data characteristics. Conventional single model approaches often…
Learning Dynamical Systems from Noisy Data with Inverse-Explicit Integrators
Håkon Noren, Sølve Eidnes, Elena Celledoni
We introduce the mean inverse integrator (MII), a novel approach to increase the accuracy when training neural networks to approximate vector fields of dynamical systems from noisy…
Pseudo-Hamiltonian system identification
Sigurd Holmsen, Sølve Eidnes, Signe Riemer-Sørensen
Identifying the underlying dynamics of physical systems can be challenging when only provided with observational data. In this work, we consider systems that can be modelled as fir…
Pseudo-Hamiltonian neural networks for learning partial differential equations
Sølve Eidnes, Kjetil Olsen Lye
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend…
Pseudo-Hamiltonian Neural Networks with State-Dependent External Forces
Sølve Eidnes, Alexander J. Stasik, Camilla Sterud +2
Hybrid machine learning based on Hamiltonian formulations has recently been successfully demonstrated for simple mechanical systems, both energy conserving and not energy conservin…
Order theory for discrete gradient methods
Sølve Eidnes
The discrete gradient methods are integrators designed to preserve invariants of ordinary differential equations. From a formal series expansion of a subclass of these methods, we…
Linearly implicit local and global energy-preserving methods for PDEs with a cubic Hamiltonian
Sølve Eidnes, Lu Li
We present linearly implicit methods that preserve discrete approximations to local and global energy conservation laws for multi-symplectic PDEs with cubic invariants. The methods…
Linearly implicit structure-preserving schemes for Hamiltonian systems
Sølve Eidnes, Lu Li, Shun Sato
Kahan's method and a two-step generalization of the discrete gradient method are both linearly implicit methods that can preserve a modified energy for Hamiltonian systems with a c…
Energy preserving methods on Riemannian manifolds
Elena Celledoni, Sølve Eidnes, Brynjulf Owren +1
The energy preserving discrete gradient methods are generalized to finite-dimensional Riemannian manifolds by definition of a discrete approximation to the Riemannian gradient, a r…
Dissipative numerical schemes on Riemannian manifolds with applications to gradient flows
Elena Celledoni, Sølve Eidnes, Brynjulf Owren +1
This paper concerns an extension of discrete gradient methods to finite-dimensional Riemannian manifolds termed discrete Riemannian gradients, and their application to dissipative…
Energy preserving moving mesh methods applied to the BBM equation
Sølve Eidnes, Torbjørn Ringholm
Energy preserving numerical methods for a certain class of PDEs are derived, applying the partition of unity method. The methods are extended to also be applicable in combination w…
Shape analysis on Lie groups and homogeneous spaces
Elena Celledoni, Sølve Eidnes, Markus Eslitzbichler +1
In this paper we are concerned with the approach to shape analysis based on the so called Square Root Velocity Transform (SRVT). We propose a generalisation of the SRVT from Euclid…
Shape analysis on homogeneous spaces: a generalised SRVT framework
Elena Celledoni, Sølve Eidnes, Alexander Schmeding
Shape analysis is ubiquitous in problems of pattern and object recognition and has developed considerably in the last decade. The use of shapes is natural in applications where one…
Adaptive Energy Preserving Methods for Partial Differential Equations
Sølve Eidnes, Brynjulf Owren, Torbjørn Ringholm
A method for constructing first integral preserving numerical schemes for time-dependent partial differential equations on non-uniform grids is presented. The method can be used wi…