A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise
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| Title: | A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise |
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| Authors: | Liu, Donglin, Sopasakis, Alexandros |
| Contributors: | Lund University, Faculty of Science, Centre for Mathematical Sciences, Mathematics (Faculty of Engineering), Lunds universitet, Naturvetenskapliga fakulteten, Matematikcentrum, Matematik LTH, Originator, Lund University, Lunds universitet, Originator |
| Source: | IFAC-PapersOnLine System Identification and Data-Driven Modeling. 59(6):379-384 |
| Subject Terms: | Natural Sciences, Mathematical Sciences, Mathematical Analysis, Naturvetenskap, Matematik, Matematisk analys |
| Description: | We propose data-driven surrogate models to solve systems of time-dependent differential equations coupled with noise. Using a feedforward neural network, we separately learn the noise and solution, tackling approximations across regimes with bifurcations and rare events. Focusing on irregular data generated by a stochastic noise model on a one-dimensional spatial lattice coupled to a differential equation, we examine two profiles: the periodic complex Ginzburg-Landau equation and a saddle bifurcation equation exhibiting rare events. This coupling introduces conditional data, enabling solutions to reach new states while posing challenges for accurately learning the underlying dynamics. |
| Access URL: | https://doi.org/10.1016/j.ifacol.2025.07.175 |
| Database: | SwePub |
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Nájsť tento článok vo Web of Science | Abstract: | We propose data-driven surrogate models to solve systems of time-dependent differential equations coupled with noise. Using a feedforward neural network, we separately learn the noise and solution, tackling approximations across regimes with bifurcations and rare events. Focusing on irregular data generated by a stochastic noise model on a one-dimensional spatial lattice coupled to a differential equation, we examine two profiles: the periodic complex Ginzburg-Landau equation and a saddle bifurcation equation exhibiting rare events. This coupling introduces conditional data, enabling solutions to reach new states while posing challenges for accurately learning the underlying dynamics. |
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| ISSN: | 24058971 24058963 |
| DOI: | 10.1016/j.ifacol.2025.07.175 |