Scheduled for completion at the end of 2008, Anton is built with the aim of doing millisecond simulations. In contrast with approaches like Folding@Home, they are interested in a single trajectory. Folding@Home patches together many small trajectories that are more feasible on a regular desktop PC. Their initial configuration will have 512 nodes.

Many of the ideas implemented in their software simulation engine Desmond were developed with Anton in mind. For long range electrostatic interactions, they use a method called k-space Gaussian split Ewald, reducing the computational burden from O(n^2) to O(n log(n)). Another advantage is that the same kernel is used for force interpolation and spreading saving real estate on the chip.

As any molecular dynamics aficionado knows, about 90% of the computational time is spent in computing non-bonded forces. With this is mind, they’ve done everything possible to speed up the process devoting much of the ASIC space. One of their ideas that struck me was the explicit computation between all pairs and then to go back subtract correction terms. This leads to a clear separation in the accounting between what particles are required for what forces – a major win for scalability.

They get major speedups by building a specialized hardware datapath and control logic tuned for common molecular dynamics communication patterns. They even have dedicated support to accumulate forces for reducing latency. I was previously excited by the addition of the dot product instruction haddps to recent generations of processors. Anton does dot products in hardware. Dot products can be used everytime you’d want to “squish” a vector.

Anton does all computation in fixed point arithmetic, which is faster and more accurate for the same silicon area (their claim.) Molecular dynamics is expensive in computation and communication, but not so much in memory. All of their data for a 25,000 particle system fits in L1 cache.

One of the courses in Engineering at SFU (ENSC 250) deals with designing a RISC processor from the ground up. I vaguely remember building branch prediction logic in VHDL, not really knowing if I’d ever use that knowledge again. If only I’d known…

Anyways, I’m missing out on some of the finer details of their technology. Go read the paper for the real deal.

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I came across a paper on the pre-print archive: “Introduction to protein folding for physicists.” Proteins are polymers of amino acids and the sequence of these amino acids completely determine the native three dimensional structure. The human genome project gives us the sequences of all proteins in the human body. In theory it should be possible to study diseases like Alzheimer’s that are caused by the misfolding. Right?

Unfortunately, the combinatorial nature of the problem makes it impossible to do a brute force search. This paper is a decent introduction to the vocabulary of molecular biologists. The abstract:

[...] we provide an exhaustive account of the reasons underlying the protein folding problem enormous relevance and summarize the present-day sta- tus of the methods aimed to solving it. We also provide an introduction to the particular structure of these biological heteropolymers, and we phys- ically define the problem stating the assumptions behind this (commonly implicit) definition. [...]

The author recognizes the inadequacies of implicit solvent models. He also asks a key question: is kinetic information important for determining which minima is chosen. This was a similar question that I had while doing my docking project. Most docking algorithms right now only use static information.

References:

• Introduction to protein folding for physicists, by Pablo Echenique. arXiv:0705.1845v1 [physics.bio-ph]

• Picture courtesy of Wikipedia

and is traditionally derived from the Taylor expansion of sine and cosine. In this paper, the author generalizes the Euler identity to matrices. He does this by introducing a complex matrix, known as the imaginary unit matrix

Just like , .

He then proves the Euler identity for these matrices as:

for all real x.

In constrained molecular dynamics simulations using some of the most popular molecular dynamics codes, calculation of the velocities of constrained particles is based solely on the differences in particle positions during two successive time steps. This creates a numerical instability that the authors’ show to be significant in a typical single-precision floating-point simulation. They describe a simple modification that eliminates this source of instability and demonstrate that this change substantially reduces the energy drift of a sample single-precision NVE simulation.

The paper is really short (2 pages) and describes recipes for modifying constraint algorithms SHAKE, RATTLE and SETTLE. Below is a graph of the energy drift in double-precision, single-precision and modified versions of GROMACS and Desmond (that’s D.E. Shaw’s MD engine.) They simulated a 30A cube of 901 water molecules with periodic boundary conditions for one nanosecond with a one femtosecond timestep. See how bad single-precision GROMACS is for NVE simulations?

One of the papers nominated for the best paper award at Supercomputing 06 is titled “Scalable Algorithms for Molecular Dynamics Simulations on Commodity Clusters” from the DE Shaw Research group. If your standard of a modern molecular dynamics code is Computer Simulations of Liquids, then this paper is definitely worth a look. I’ve summarized the innovations below:

Midpoint method

Published earlier this year in the Journal of Chemical Physics, this is a parallelizing algorithm which is a hybrid between spatial decompositions and force decompositions. The major innovation of this method is the reduced communication bandwidth, which can be a problem when you scale simulations to hundreds of computers.

Bitwise Time Reversibility

One of the most important requirements for an integrator solving Newton’s equations of motion is symplecticity. One way to check to check for this is by running your integrator in negative time. Doing so should return the system to the initial state. Though not an absolute requirement, this is a nice thing to have for minimizing the energy drift, which ultimately leads to a more realistic simulation. These guys have an integrator that does this.

Constraints in single precision

To reduce high frequency motions (like vibrations of Carbon-Hydrogen bonds for example), simulations typically make use of constraints to hold bond lengths or atom velocities fixed. Typical codes RATTLE and SHAKE need to be done in double precision for accuracy and to maintain energy conservation. This paper talks about the use of an (unpublished) algorithm that is stable in single precision.

Normalized local coordinates

Instead of representing coordinates in an absolute global frame, these guys normalize coordinates. This gives them more precision (due to operations done on floating points of the same magnitudes.) It also makes handling periodic boundary conditions simple. Another advantage they mention is that doing pressure control is time reversible.

Interpolation schemes

Personally, I think this is the cornerstone of the paper. The paper mentions that instead of interactions being a function of distance between the particles, they compute it as a function of . The advantage is that the same set of polynomial coefficients can be used for computing both forces and energies.

SIMD instructions

I’m just mentioning this for completeness. As far as I know, every high performance engine makes use of these instructions. In fact, GROMACS has hand tuned kernels written using these instructions. In theory, this makes your code four times faster.

In conclusion, I was pretty impressed with the quality of work and the innovations these guys have brought to the community. Download the paper here.