3 ms·
This algorithms is obviously used in solving the n-body problem (references to gravity fields and electric fields in the article). I have a question. Although
by cgufus 6y ago
This algorithms is obviously used in solving the n-body problem (references to gravity fields and electric fields in the article).
I have a question. Although the article clearly states that this is not an epidemiological problem, I wonder about the following: gravity and electric fields are 1/r^2 type problems. I imagine that disease transmission depending on distance is a rather different thing, such as "high in immediate vicinity to the other point and then falling off quickly".
Do we know if the algorithm is accurate enough for this kind of "field"? Is it in general enough accurate or only for 1/r^2 type fields?
- throwlaplace 6y ago1/r^2 fields are the gradients of 1/r potentials (not all efields are 1/r^2 btw). What is the potential in the case of disease transmission? disease transmission can be modeled as a stochastic process and you can dig up a relationship to similar type methods (basis methods for solving odes) through the feynman-kac formula.
- andyljones 6y agoShort answer: yes, the underlying black-box fast multipole method will be very accurate with just a small number of Chebyshev coefficients. The main requirement is the kernel is reasonably smooth away from the origin. Here's a toy example, 100 sources and points over a 10x10 square and a 1/(1 + d^2) kernel: https://colab.research.google.com/drive/1F5rGIPxI8RI9tYJ4RSv85xdlfyEFT6Mk https://colab.research.google.com/drive/1F5rGIPxI8RI9tYJ4RSv... Here, it gets 1e-8 residual variance. Exactly which kernel to use for disease transmission is an open question, but IIRC the Imperial model used something like 1/(1 + d^(3/2)) based on fits to data.