This post is going to summarize the advanced reserach of reservoir computing based on various designs and implementations, the paper “Recent advances in physical reservoir computing: A review”1 dated in 2019 has a great summary for the research field, however it is a bit outdated, this post is going to follow the structure of the article but will add new updates to this article to gain beter understanding of the research field of reservoir computing.
sequenceDiagram
participant web as Web Browser
participant blog as Blog Service
participant account as Account Service
participant mail as Mail Service
participant db as Storage
Note over web,db: The user must be logged in to submit blog posts
web->>+account: Logs in using credentials
account->>db: Query stored accounts
db->>account: Respond with query result
alt Credentials not found
account->>web: Invalid credentials
else Credentials found
account->>-web: Successfully logged in
Note over web,db: When the user is authenticated, they can now submit new posts
web->>+blog: Submit new post
blog->>db: Store post data
par Notifications
blog--)mail: Send mail to blog subscribers
blog--)db: Store in-site notifications
and Response
blog-->>-web: Successfully posted
end
end\begin{align*}
\underbrace{\mathbf{x}(t)_{N\times1}}_{\substack{\text{Reservoir}\\\text{State }t}} &= \left(1-\alpha\right)\cdot \mathbf{x}(t-1)+\alpha \cdot f \left(\overbrace{\mathbf{W}_{in}}^{N\times M} \mathbf{u}(t)_{N\times 1} +\overbrace{\mathbf{W}_{res}}^{N\times N} \mathbf{x}(t-1)_{N\times 1} \right)\\[1em]
\underbrace{\mathbf{x}(t)_{N\times1}}_{\substack{\text{Reservoir}\\\text{State }t\\\text{Residual ESN}}} &=\alpha\cdot \underbrace{\mathbf{O}}_{\substack{\text{Random}\\\text{Orthogonal}\\N\times N}}\mathbf{x}(t-1)+\beta\cdot f \left(\overbrace{\mathbf{W}_{in}}^{N\times M} \mathbf{u}(t)_{N\times 1} +\overbrace{\mathbf{W}_{res}}^{N\times N} \mathbf{x}(t-1)_{N\times 1} \right)\\
\mathbf{y}(t)_{(M+N)\times 1} &= g\left( \overbrace{\mathbf{W}_{out}}^{(M+N)\times (M+N)} \begin{bmatrix} \mathbf{x}(t) \\\mathbf{u}(t) \\\mathbf{u}(t-1)\\\mathbf{u}(t-2)\\\mathbf{u}(t-m+1)\end{bmatrix}_{(m\cdot M+N)\times 1} \right)
\end{align*}\underset{\mathbf{W}_{out}}{\text{argmax}}\left\|\mathbf{y}(t)-\mathbf{z}\right\|^{2}https://arxiv.org/abs/2012.02974
https://ieeexplore.ieee.org/document/9966815
S_{t}, A_{t}, r_{t}, \mathbf{x}(t-1)https://ieeexplore.ieee.org/abstract/document/11014312
https://www.esann.org/sites/default/files/proceedings/2023/ES2023-112.pdf
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