Ajit R. Jadhav's blog
The Machine Learning as an Expert System
1.
To cut a somewhat long story short, I think that I can ``see'' that Machine Learning (including Deep Learning) can actually be regarded as a rules-based expert system, albeit of a special kind.
I am sure that people must have written articles expressing this view. However, simple googling didn’t get me to any useful material.
I would deeply appreciate it if someone could please point out references in this direction. Thanks in advance.
2.
A preliminary document on my fresh new approach to QM
Hello, World
Here is a document that jots down, in a brief, point-wise manner, the elements of my new approach to understanding quantum mechanics.
Please note that the writing is very much at a preliminary stage. It is very much a work in progress. However, it does jot down many essential ideas.
I am uploading the document at iMechanica just to have an externally verifiable time-stamp to it. Further versions will also be posted at this thread.
Stress is defined as the quantity equal to ... what?
In introducing the very concept of the stress tensor to the beginning student, text-books always present only indirect relations involving the concept. Thus, you have the relations like "traction = (stress-transposed)(unit normal)" (i.e. Cauchy's formula, for uniform stress), or the relations for the coordinate transformations of the stress tensor, or the divergence theorem (for non-uniform stress). These are immediately followed or interspersed with alternative notations, and the rules for using them.
But what you never ever get to see, in text-books or references, is this: a *direct* definition of the stress tensor, i.e. an equation in which there is only the stress tensor on the left hand-side, and some expression involving some *other* quantities on right hand-side. Why? What possibly could be the conceptual and pedagogical advantages of giving a direct definition of this kind, and its physical meaning? I would like to ponder on these matters here, giving my answers to these and similar questions in the process.
Also remember Alcoa
Also remember Alcoa.
Yes I know about the [essentials of] QM!
Check out here [at my personal blog] [^] and the post before that.
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Have a happy holiday season!
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Sincerely,
--Ajit
A ``small'' but interesting riddle from the theory of vibrations
A ``small'' but interesting riddle from the basic theory of vibrations. Haven't run into it in any physics/classical mechanics text/reference.
Explicit vs. implicit FDM: Could you please suggest a reference?
The context is the finite difference modeling (FDM) of the transient diffusion equation (the linear one: $\dfrac{\partial T}{\partial t} = \alpha \dfrac{\partial^2 T}{\partial x^2}$).
Two approaches are available for modeling the evolution of $T$ in time: (i) explicit and (ii) implicit (e.g., the Crank-Nicolson method).
It was obvious to me that the explicit approach has a local (or compact) support whereas the implicit approach has a global support.
Expansion of a function into a basis set
Consider a ``neat'' function such as what an engineer is most likely to use in his typical theory/work. Such a function would typically be: (i) defined over a single finite interval, (ii) continuous throughout, and (iii) smooth enough. In other words, the sort of a function they used when they introduced the very idea of a graph of a function to you, back in high-school. ... Feel free to add any other qualifications you like, but note them explicitly, e.g., (iv) bounded throughout, and (v) periodic.
I am [still] confused about gradients, vectors, deformation gradient, etc.
I am creating this blog entry to have my confusions about gradients, vectors, and deformation gradient, etc., straightened out once (and hopefully for all time!) ... My confusions got exposed (even to me) while commenting on a thread started by Prof. Suo here [^]. In particular, I realized my confusions after writing this comment [^] there.