Neural State-Dependent Delay Differential Equations
| Autor: | Monsel, Thibault, Semeraro, Onofrio, Mathelin, Lionel, Charpiat, Guillaume |
|---|---|
| Přispěvatelé: | DAtascience, trAnsition, Fluid instability, contrOl, Turbulence (DATAFLOT), Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Mécanique-Energétique (M.-E.), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), TAckling the Underspecified (TAU), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), ANR-20-CE23-0025,SPEED,Simulation de systèmes d'EDP de la Physique par apprentissage profond(2020) |
| Jazyk: | angličtina |
| Rok vydání: | 2023 |
| Předmět: |
FOS: Computer and information sciences
Delay Neural Networks Continuous-depth models Computer Science - Artificial Intelligence Neural Ordinary Differential Equations [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Physical Modelling Dynamical Systems (math.DS) Delay Differential Equations Dynamical Systems [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI] Artificial Intelligence (cs.AI) [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG] Discontinuities Delay Differential Equations Delay Differential Equations Neural Networks Discontinuities Neural Ordinary Differential Equations NODE Physical Modelling Dynamical Systems Numerical Integration Continuous-depth models Software DDE solver Differential Equations [NLIN.NLIN-CD]Nonlinear Sciences [physics]/Chaotic Dynamics [nlin.CD] FOS: Mathematics DDE solver Mathematics - Dynamical Systems Numerical Integration NODE Software |
| Popis: | Discontinuities and delayed terms are encountered in the governing equations of a large class of problems ranging from physics, engineering, medicine to economics. These systems are impossible to be properly modelled and simulated with standard Ordinary Differential Equations (ODE), or any data-driven approximation including Neural Ordinary Differential Equations (NODE). To circumvent this issue, latent variables are typically introduced to solve the dynamics of the system in a higher dimensional space and obtain the solution as a projection to the original space. However, this solution lacks physical interpretability. In contrast, Delay Differential Equations (DDEs) and their data-driven, approximated counterparts naturally appear as good candidates to characterize such complicated systems. In this work we revisit the recently proposed Neural DDE by introducing Neural State-Dependent DDE (SDDDE), a general and flexible framework featuring multiple and state-dependent delays. The developed framework is auto-differentiable and runs efficiently on multiple backends. We show that our method is competitive and outperforms other continuous-class models on a wide variety of delayed dynamical systems. |
| Databáze: | OpenAIRE |
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