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A general memristor-based partial differential equation solver (rochester.edu)
47 points by godelmachine 7 months ago | hide | past | web | favorite | 12 comments



Not the original paper but this explains in detail how this works. http://www2.ece.rochester.edu/~xiguo/gomac15.pdf

I would guess they are solving PDEs using systems of linear equations. The approximate solutions to these linear equations are found via the analog linear solvers.


Thanks, we changed the URL to that from http://www.nature.com/articles/s41928-018-0100-6 since the latter is behind a paywall without workarounds. (This is explained at https://news.ycombinator.com/newsfaq.html and https://news.ycombinator.com/item?id=10178989).


With respect (I didn't downvote you), there is a workaround: sci-hub (I checked that it is available there).

For others who want a comparison; the two papers are very different: the Nature paper uses entirely analog techniques to achieve high precision results while the newly-linked article is a mixed-precision approach. That is, the newly-linked article only uses analog to obtain a low-precision estimate which is fed back to a digital computing algorithm to produce the final high-precision result. The hope is that the overall time to solution is still faster because you do not need (hopefully eventually slower) digital computation to achieve the low-accuracy result. I am not an expert in this particular hardware field (I do applied math so I am used to solving the problems they do here in digital computers), but here is what the authors of the Nature article say:

> Recent theoretical and experimental studies have used memristor (including phase-change memory) arrays to generate an initial, low-precision guess (seed), and rely on an integrated high-precision digital solver to produce the required high-precision solutions from the seed solution. Such types of accelerators are certainly beneficial, as they reduce the number of iterations required by the digital solver. Determining whether memristor-based hardware can be used to directly perform high-precision computing tasks, however, will enable a better understanding of how broadly memristive hardware can be applied. Such knowledge will help pave the way to build more general memristor-based computing platforms, instead of special-purpose accelerators.


I have done graduate computational physics (Multigrid and such) So im familiar with the "digital" side of this but certainly not familiar with almost any analog computations. (beyond those trivial op-amp integrators)


FWIW, here's the university press release about the initially submitted article (although I'd guess it'd best to now ask /u/goedelmachine to submit it as a new story, this one is too confused already): https://news.umich.edu/memory-processing-unit-could-bring-me...


Can you mark the PDF? It crashed my browser.


Right, the innovation is in using storage-compute collocation to allow common data operations to be structured into the way the storage arrays are set up. The paper is really about doing sparse linear algebra in hardware not PDEs (but of course after discretization that is all PDEs are--linear algebra).


The title is incorrect. It's not a general partial differential equation solver. The paper doesn't even claim it to be. The issue is that not all, not even most, PDEs can be discretized to a linear system of equations. Normally these need to be discretized to either a nonlinear rootfinding problem G(x)=0 find x, or a stiff ODE (normally solved by an implicit method, but not necessarily).

However, both of those problems do include a subproblem which is solving linear systems (when the ODE is solved implicitly), and so PDE solvers which take these routes will generally be able to be accelerated by an improved linear equation solver. Thus it's not an be all and end all algorithm, but when combined with the tools that exist for PDEs in something like PETSc or Julia then this can be used to give a more efficient algorithm for most PDEs (though there are still other PDEs where linear solving is entirely avoided, for example with exponential integrators or Runge-Kutta Chebyshev methods, which can be more efficient depending on the problem).


The link was changed from the original Nature article which has the original title. The new link is unrelated.

You're correct that the innovation is really about sparse linear algebra (though not just solvers) done in hardware. However the advantages are exploited not just by way of solving linear systems for implicit time-stepping. They implemented a Jacobi iteration in hardware for solving a system arising from discretization of the Poisson equation, but they also used an efficient forward-map of the coefficient matrix to do explicit time-stepping for a wave solver. So they solve both a time-independent and time-dependent problem, but neither with implicit time-stepping (though there appears to be no technical limitation here, it's just what they focused on).


Why isn't this PDF marked? Aren't they usually marked?

It even has a .pdf extension.

Accessibility fail.


PDF

This crashed my browser.


Should this be flagged due to the paywall?




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