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Piyush Grover's user avatar
Piyush Grover's user avatar
Piyush Grover's user avatar
Piyush Grover
  • Member for 11 years, 11 months
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Importance of integral equations
Anothe example of memory: dynamics of an inertial spherical passive particle in fluid flow: arxiv.org/abs/1310.2450
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Importance of integral equations
A big subfield in PDEs is a that of non-local equations: in time and especially in space. These equations are integro-differential. web.ma.utexas.edu/mediawiki/index.php/…
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Theoretical results on neural networks
Too broad. Every ML conference of past 10 years has tens of such results.
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Reference request: Optimal controls can be assumed to take values in a convex set
Title of your post is misleading.Your post says that the $\text{reachable sets}$ form a convex set when control is in a compact set.
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Method of characteristics and explicit formula for an IBVP for the transport equation
What do you want to prove ? Can't you just substitute and check ?
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Neural networks over gadgets other than $\mathbb{R}$
You can do operator inference, i.e. learn nonlinear operators between $L_2$ functions, google "Physics informed neural networks". Here's the first paper:sciencedirect.com/science/article/pii/S0021999118307125
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What are desirable properties that data should satisfy to reasonably use the dynamic mode decomposition?
To make this a mathematics question, you should define what you mean by reasonable.
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Existence of a continuous ergodic dynamical system for a given distribution?
You will probably need a absolutely continuous measure w.r.t to Lebesgue.
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Solution of Riccati system of ODEs
Is there any context to this question ? Where did you get them from ?
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