Tag: equations
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Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels
Error Analysis of Generalized Langevin Equations with Approximated Memory Kernels arXiv:2512.10256v1 Announce Type: new Abstract: We analyze prediction error in stochastic dynamical systems with memory, focusing on generalized Langevin equations (GLEs) formulated as stochastic Volterra equations. We establish that, under a strongly convex potential, trajectory discrepancies decay at a rate determined by the decay of…
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Discovering equations from data: symbolic regression in dynamical systems
Discovering equations from data: symbolic regression in dynamical systems arXiv:2508.20257v1 Announce Type: cross Abstract: The process of discovering equations from data lies at the heart of physics and in many other areas of research, including mathematical ecology and epidemiology. Recently, machine learning methods known as symbolic regression have automated this process. As several methods are…
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A generative modeling / Physics-Informed Neural Network approach to random differential equations
A generative modeling / Physics-Informed Neural Network approach to random differential equations arXiv:2507.01687v1 Announce Type: new Abstract: The integration of Scientific Machine Learning (SciML) techniques with uncertainty quantification (UQ) represents a rapidly evolving frontier in computational science. This work advances Physics-Informed Neural Networks (PINNs) by incorporating probabilistic frameworks to effectively model uncertainty in complex systems.…
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Reinforcement Learning with PDEs
Reinforcement Learning with PDEs Previously we discussed applying reinforcement learning to Ordinary Differential Equations (ODEs) by integrating ODEs within gymnasium. ODEs are a powerful tool that can describe a wide range of systems but are limited to a single variable. Partial Differential Equations (PDEs) are differential equations involving derivatives of multiple variables that can cover…