We already gave an inch and the government took a mile. Closing down state parks and playgrounds. Making it illegal to play with the kids next door.
I was probably pro tracking app a month or two ago, but the draconian measures taken by some governments (Michigan, Wisconsin) has changed my mind. Its going to lead to abuse abuse abuse abuse.
We should move this conversation to email (as I will check that more frequently and will be more likely to get back to it). See email in my profile.
Active subspace comes from the uncertainty quantification community. If you assume all your parameters are Gaussian, then the sensitivity matrix is directly correlated to the probability density functions. I find it easier to think in terms of the sensitivity matrix, but useful to realize the sensitivity matrix to approximate (complex) probability distributions.
My though was that if you were optimizing have a huge parameter space theta = [theta1, ... thetam] then you could reduce the parameter space by only looking at theta_reduce = [theta | d loss/d theta > threshold] or you could look at active subspaces and change the parameter space to xi = [xi1, ... xi_m] where x_i = SUM a_j theta_j.
xi_i could be given by the largest eigenvectors of the sensitivity matrix S_ij = d^2 loss/dtheta_i dtheta_j
Wouldn't it be nice if hacker news supported latex.
I haven't done any work here, but I suspect I will be doing some of this towards the end of summer.
I keep coming back to bother you :). One of the newer tricks to make parameter fitting less expensive which has recently been developed is active subspaces. I thought you might be interested in playing around with it.
Most of the research is being done out at the Colorado school of mines by Paul Constantine. The basic idea is that you reduce your parameter space to the eigenvectors of the sensitivity matrix with the largest eigenvalues. Some of the work I have seen in constitutive modeling (and UQ) has effectively reduced parameters spaces of a couple hundred DOF to about 5-6.
Thanks! I am pretty sure nobody does direct optimization on the mesh quality because it is hefty. I did come across a PhD thesis which was doing it for fluid structures interactions and his conclusion was it was inferior to other techniques. I have a few tricks which will hopefully make the problem more tractable.
I use FEMAP at my day job have found Laplacian smoothing and FEMAPs other built in tools have been wanting.
I am currently thinking that my goal is to try and use reinforcement learning to build high quality meshes. In order to do that you need a loss function and if you are building a loss function you might as well wrap an optimizer around it.
What library are you using for automatic differentiation. I am working on building code to optimize (and later build) high quality finite element meshes for structural analysis. For the initial proof of concept, I am simply doing finite differences, but would prefer to eventually add AD. I am unsure which packages are suitable (currently all numpy and scipy).
I was probably pro tracking app a month or two ago, but the draconian measures taken by some governments (Michigan, Wisconsin) has changed my mind. Its going to lead to abuse abuse abuse abuse.