hp finite element methods
Penguin learning project
The project uses 342 complete Palmer penguin records: 240 training-pool and 102 held-out rows. The selected training rows determine feature scaling and model parameters. Source CSV
This project trains weights with softmax, unlike the homepage lab, which uses nearest species averages. Same penguin measurements; different classification methods. Predictions can differ.
PDE and stochastic processes · Describe differential equations and stochastic representations.
PDE and quantum models are not operations on these penguin measurements.
Consider this concept alongside the project; its source assumptions may differ. These observations do not prove a theorem.
Input: 12 × 2; Held-out evaluation: 102 · #58 · 40.6 mm, 193 mm. Known answer: Adélie; Prediction: Adélie · [≈0.7383, ≈0.2444, ≈0.01737].
Used in these source sections: 3.2 Simple pieces, many layers
In hp finite elements, h describes mesh size and p describes polynomial degree used on elements.
The source compares neural-network approximation rates with those methods.
Source formula example
illustration · This evaluates one degree-two polynomial; it does not solve a finite element problem or establish a rate.
Symbols
- A mesh-size parameter.
- Polynomial degree.
Source formula example
This source example uses its own inputs and assumptions. Editing it does not change the project.
Edit a value or the code, then run the example. This is a finite demonstration, not a proof of the paper’s theorem.
This example’s data flow
Code changed. Reset to restore this example’s data flow.
Initial values in code
h=0.5p=2x=0.25
Calculated here
Result expression: { h, p, x, polynomial }
polynomial=x * xUses:x
Returns
h- 0.5
p- 2
x- 0.25
polynomial- 0.0625
Read numbers from input and return the result. JavaScript basics.
Result
Technical statement
The numerical values are invented. This evaluates one degree-two polynomial; it does not solve a finite element problem or establish a rate.
Source: Inline notation