Publications
Journal Article
A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems
Journal of Computational Physics 449 (2022): 110800.Status: Published
A new symmetric linearly implicit exponential integrator preserving polynomial invariants or Lyapunov functions for conservative or dissipative systems
A new symmetric linearly implicit exponential integrator that preserves the polynomial first integrals or the Lyapunov functions for the conservative and dissipative stiff equations, respectively, is proposed in this work. The method is tested by both oscillated ordinary differential equations and partial differential equations, e.g., an averaged system in wind-induced oscillation, the Fermi–Pasta–Ulam systems, and the polynomial pendulum oscillators. The numerical simulations confirm the conservative properties of the proposed method and demonstrate its good behavior in superior running speed when compared with fully implicit schemes for long-time simulations.
| Afilliation | Machine Learning |
| Project(s) | Department of Data Science and Knowledge Discovery |
| Publication Type | Journal Article |
| Year of Publication | 2022 |
| Journal | Journal of Computational Physics |
| Volume | 449 |
| Pagination | 110800 |
| Date Published | Jan-15-2022 |
| Publisher | Journal of Computational Physics |
| ISSN | 00219991 |
| URL | https://arxiv.org/abs/2104.12118 |
| DOI | 10.1016/j.jcp.2021.110800 |
Exploring Dynamic Metabolomics Data With Multiway Data Analysis: a Simulation Study
BMC Bioinformatics 23 (2022).Status: Published
Exploring Dynamic Metabolomics Data With Multiway Data Analysis: a Simulation Study
Background: Analysis of dynamic metabolomics data holds the promise to improve our understanding of underlying mechanisms in metabolism. For example, it may detect changes in metabolism due to the onset of a disease. Dynamic or time-resolved metabolomics data can be arranged as a three-way array with entries organized according to a subjects mode, a metabolites mode and a time mode. While such time-evolving multiway data sets are increasingly collected, revealing the underlying mechanisms and their dynamics from such data remains challenging. For such data, one of the complexities is the presence of a superposition of several sources of variation: induced variation (due to experimental conditions or inborn errors), individual variation, and measurement error. Multiway data analysis (also known as tensor factorizations) has been successfully used in data mining to find the underlying patterns in multiway data. In this paper, we study the use of multiway data analysis to reveal the underlying patterns and dynamics in time-resolved metabolomics data.
Results: We focus on simulated data arising from different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, and a human cholesterol model. We generate data with induced variation as well as individual variation. Systematic experiments are performed to demonstrate the advantages and limitations of multiway data analysis in analyzing such dynamic metabolomics data and their capacity to disentangle the different sources of variations. We choose to use simulations since we want to understand the capability of multiway data analysis methods which is facilitated by knowing the ground truth.
Conclusion: Our numerical experiments demonstrate that despite the increasing complexity of the studied dynamic metabolic models, tensor factorization methods CANDECOMP/PARAFAC(CP) and Parallel Profiles with Linear Dependences (Paralind) can disentangle the sources of variations and thereby reveal the underlying mechanisms and their dynamics.
| Afilliation | Machine Learning |
| Project(s) | Department of Data Science and Knowledge Discovery , TrACEr: Time-Aware ConstrainEd Multimodal Data Fusion |
| Publication Type | Journal Article |
| Year of Publication | 2022 |
| Journal | BMC Bioinformatics |
| Volume | 23 |
| Number | Article 31 |
| Date Published | 2022 |
| Publisher | Springer |
| DOI | 10.1186/s12859-021-04550-5 |
Talks, contributed
A new linearly implicit energy-preserving exponential method for conservative or dissipative systems.
In In Manifolds and Geometric Integration Colloquia, Norway, 2021.Status: Published
A new linearly implicit energy-preserving exponential method for conservative or dissipative systems.
In this work, we propose a linearly implicit exponential integrator that preserves the invariant or the Lyapunov functions for the conservative or dissipative systems by combining the idea of exponential integrators and discrete gradient methods. Numerical simulations are shown to confirm the conservative properties of the methods, and to demonstrate the efficiency of the methods when compared to other fully implicit schemes.
| Afilliation | Machine Learning |
| Project(s) | Department of Data Science and Knowledge Discovery |
| Publication Type | Talks, contributed |
| Year of Publication | 2021 |
| Location of Talk | In Manifolds and Geometric Integration Colloquia, Norway |
Exploring dynamic metabolomics data with multiway data analysis: A simulation study
In Virtual conference. SIAM Conference on Applications of Dynamical Systems, 2021.Status: Published
Exploring dynamic metabolomics data with multiway data analysis: A simulation study
Analysis of dynamic metabolomics data sets holds the promise to improve our understanding of the underlying mechanisms in human metabolism. That is crucial to detect the changes in the metabolism that can potentially lead to diseases. Dynamic metabolomics data has more than two axes of variation, i.e., samples, metabolites and time. While such time-evolving multi-way data sets are collected more and more in recent years, revealing the underlying mechanisms and their dynamics from such data remains challenging.
This talk will focus on a systematic study demonstrating the advantages and limitations of multi-way data analysis (also known as tensor factorizations) in terms of analyzing dynamic metabolomics data. We study different dynamic models of increasing complexity, i.e., a simple linear system, a yeast glycolysis model, a human cholesterol model, and generate data with different types of variation. Our numerical experiments demonstrate that despite the increasing complexity of the studied models, tensor factorization methods CANDECOMP/PARAFAC(CP) and PARAllel Profiles with LINear Dependences (PARALIND) can reveal the underlying mechanisms and their dynamics.
| Afilliation | Machine Learning |
| Project(s) | TrACEr: Time-Aware ConstrainEd Multimodal Data Fusion, Department of Data Science and Knowledge Discovery |
| Publication Type | Talks, contributed |
| Year of Publication | 2021 |
| Location of Talk | Virtual conference |
| Publisher | SIAM Conference on Applications of Dynamical Systems |