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Reference Request: Getting from introductory PDEs to kinetic models, non-local aggregation, and mean field...
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My background is in statistics/machine learning though I have been looking more and more at differential equation models to better understand the dynamics of social and economic systems. It seems like a lot of the contemporary work in PDEs focuses on finding PDEs to model the aggregation of lower level interactions between agents. In other words kinetic models like the Fokker-Planck equation are used to model criminal activity, non-local aggregation is used to model swarming behavior, and mean field game theory is used to look at the emergence of bubbles in financial markets.
I have studied the basics of PDEs, including the standard heat equation, wave equation, poisson equation, etc., at the level of Strauss. I also have a decent background in analysis through measure theory.
My question is trying to understand the set of books to work through to get from my current basic understanding of PDEs towards understanding and ultimately being able to model phenomena using these "aggregation" type phenomena mentioned above.
The problem I have run into in reading many of the papers on say kinetic models or mean field games, is that the audience for that work generally already understands how those models work. So it is difficult to learn from those types of work.
So I was trying to understand how much focus I should put on learning the functional analysis stuff first? What are the best sources for understanding the intuition behind these aggregation approaches, before launching into the mathematically rigorous theory and losing sight of the underlying intuition. Are there any good course syllabi that cover this topic--I did not find any?
Does anyone have some suggestions on how to work from basic PDE theory towards these more interesting contemporary applications?
Please let me know if I need to be more specific in my question.
ordinary-differential-equations reference-request pde physics
asked Jan 31 at 22:31
krishnabkrishnab
464415
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add a comment |
$begingroup$
My background is in statistics/machine learning though I have been looking more and more at differential equation models to better understand the dynamics of social and economic systems. It seems like a lot of the contemporary work in PDEs focuses on finding PDEs to model the aggregation of lower level interactions between agents. In other words kinetic models like the Fokker-Planck equation are used to model criminal activity, non-local aggregation is used to model swarming behavior, and mean field game theory is used to look at the emergence of bubbles in financial markets.
I have studied the basics of PDEs, including the standard heat equation, wave equation, poisson equation, etc., at the level of Strauss. I also have a decent background in analysis through measure theory.
My question is trying to understand the set of books to work through to get from my current basic understanding of PDEs towards understanding and ultimately being able to model phenomena using these "aggregation" type phenomena mentioned above.
The problem I have run into in reading many of the papers on say kinetic models or mean field games, is that the audience for that work generally already understands how those models work. So it is difficult to learn from those types of work.
So I was trying to understand how much focus I should put on learning the functional analysis stuff first? What are the best sources for understanding the intuition behind these aggregation approaches, before launching into the mathematically rigorous theory and losing sight of the underlying intuition. Are there any good course syllabi that cover this topic--I did not find any?
Does anyone have some suggestions on how to work from basic PDE theory towards these more interesting contemporary applications?
Please let me know if I need to be more specific in my question.
ordinary-differential-equations reference-request pde physics
asked Jan 31 at 22:31
krishnabkrishnab
464415
$endgroup$
add a comment |
$begingroup$
My background is in statistics/machine learning though I have been looking more and more at differential equation models to better understand the dynamics of social and economic systems. It seems like a lot of the contemporary work in PDEs focuses on finding PDEs to model the aggregation of lower level interactions between agents. In other words kinetic models like the Fokker-Planck equation are used to model criminal activity, non-local aggregation is used to model swarming behavior, and mean field game theory is used to look at the emergence of bubbles in financial markets.
I have studied the basics of PDEs, including the standard heat equation, wave equation, poisson equation, etc., at the level of Strauss. I also have a decent background in analysis through measure theory.
My question is trying to understand the set of books to work through to get from my current basic understanding of PDEs towards understanding and ultimately being able to model phenomena using these "aggregation" type phenomena mentioned above.
The problem I have run into in reading many of the papers on say kinetic models or mean field games, is that the audience for that work generally already understands how those models work. So it is difficult to learn from those types of work.
So I was trying to understand how much focus I should put on learning the functional analysis stuff first? What are the best sources for understanding the intuition behind these aggregation approaches, before launching into the mathematically rigorous theory and losing sight of the underlying intuition. Are there any good course syllabi that cover this topic--I did not find any?
Does anyone have some suggestions on how to work from basic PDE theory towards these more interesting contemporary applications?
Please let me know if I need to be more specific in my question.
ordinary-differential-equations reference-request pde physics
asked Jan 31 at 22:31
krishnabkrishnab
464415
$endgroup$
My background is in statistics/machine learning though I have been looking more and more at differential equation models to better understand the dynamics of social and economic systems. It seems like a lot of the contemporary work in PDEs focuses on finding PDEs to model the aggregation of lower level interactions between agents. In other words kinetic models like the Fokker-Planck equation are used to model criminal activity, non-local aggregation is used to model swarming behavior, and mean field game theory is used to look at the emergence of bubbles in financial markets.
I have studied the basics of PDEs, including the standard heat equation, wave equation, poisson equation, etc., at the level of Strauss. I also have a decent background in analysis through measure theory.
My question is trying to understand the set of books to work through to get from my current basic understanding of PDEs towards understanding and ultimately being able to model phenomena using these "aggregation" type phenomena mentioned above.
The problem I have run into in reading many of the papers on say kinetic models or mean field games, is that the audience for that work generally already understands how those models work. So it is difficult to learn from those types of work.
So I was trying to understand how much focus I should put on learning the functional analysis stuff first? What are the best sources for understanding the intuition behind these aggregation approaches, before launching into the mathematically rigorous theory and losing sight of the underlying intuition. Are there any good course syllabi that cover this topic--I did not find any?
Does anyone have some suggestions on how to work from basic PDE theory towards these more interesting contemporary applications?
Please let me know if I need to be more specific in my question.
ordinary-differential-equations reference-request pde physics
ordinary-differential-equations reference-request pde physics
asked Jan 31 at 22:31
krishnabkrishnab
464415
asked Jan 31 at 22:31
krishnabkrishnab
464415
edited Jan 31 at 23:03
krishnab
asked Jan 31 at 22:31
krishnabkrishnab
464415
asked Jan 31 at 22:31
krishnabkrishnab
464415
asked Jan 31 at 22:31
krishnabkrishnab
464415
464415
add a comment |
add a comment |
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