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A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise

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Titel: A Data Driven Approach for Resolving Time-dependent Differential Equations with Noise
Autoren: Liu, Donglin, Sopasakis, Alexandros
Weitere Verfasser: 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
Quelle: IFAC-PapersOnLine System Identification and Data-Driven Modeling. 59(6):379-384
Schlagwörter: Natural Sciences, Mathematical Sciences, Mathematical Analysis, Naturvetenskap, Matematik, Matematisk analys
Beschreibung: 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.
Zugangs-URL: https://doi.org/10.1016/j.ifacol.2025.07.175
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  Data: <searchLink fieldCode="AR" term="%22Liu%2C+Donglin%22">Liu, Donglin</searchLink><br /><searchLink fieldCode="AR" term="%22Sopasakis%2C+Alexandros%22">Sopasakis, Alexandros</searchLink>
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  Data: 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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