Math

Browse all posts in the Math category.

31 to 36 of 82

03NOV 2023
Math
Limits of the stabilization of a networked hyperbolic system with a circle
Limits of the stabilization of a networked hyperbolic system with a circle 1 Introduction In this post, we discuss the exponential stability of a networked hyperbolic system with a circle. In many applications, the graphs of these networks contain cycles, such as pipeline networks for gas transportation (see, for example, [1]). In [[2], Page 197], […]
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29SEP 2023
Math
Stability of hyperbolic systems with non-symmetric partial dissipation
Stability of hyperbolic systems with non-symmetric partial dissipation Introduction In this post, we report new results for -components linear hyperbolic systems in of the type The unknown () depends on the time variable and on the space variable , is a symmetric matrix and is a semidefinite positive matrix such that . System (1) […]
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11AUG 2023
Math
Neural ODEs for interpolation and transport: From tight to shallow
Neural ODEs for interpolation and transport: From tight to shallow Introduction We consider in our work residual neural networks (ResNets) which take the form for some initial input . The states are the output after each layers, with being the final output. The depth of the neural network is the number of layers , and […]
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04AUG 2023
Hub
Combined convection and diffusion in a network. A numerical analysis
Combined convection and diffusion in a network. A numerical analysis. The problem: a contaminant in a network of water pipes Imagine that there is a network of pipes full of water. The water is flowing from some source nodes (say, some water plants) to some destination nodes (say, people’s homes). A contaminant is present in […]
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12JUL 2023
Hub
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach
The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach Motivation This post shows the source code from the paper “The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach”. (See reference below) We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for […]The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach Motivation This post shows the source code from the paper “The ADMM-PINNs Algorithmic Framework for Nonsmooth PDE-Constrained Optimization: A Deep Learning Approach”. (See reference below) We study the combination of the alternating direction method of multipliers (ADMM) with physics-informed neural networks (PINNs) for […]
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03JUL 2023
Hub
Reinforcement learning as a new perspective into controlling physical systems
Reinforcement learning as a new perspective into controlling physical systems Introduction Optimal control addresses the problem of bringing a system from an initial state to a target state, like a satellite that we want to send into orbit using the least possible amount of fuel. Since the last century, mathematics has helped develop powerful numerical […]
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