Prof. John Gustafson on Interval Methods

[David G Hough at validgh]

Posted on behalf of Prof. Gustafson who is away from email at the moment:



From: John Gustafson <gusaameslab.gov>
Date: Sat, 08 May 1999 12:57:37 -0500

To Whom It May Concern:

As the result of the publication of my article in CS&E on the need for
verifiable computing, I have been contacted by William Walster.
Dr. Walster has brought me up-to-date on his efforts to introduce
some innovative and potentially very important technology to the
computer industry.

I have reviewed Dr. Walster's research work through his web site
posting, and found it eye-opening.  I had no idea interval
arithmetic--and verifiable computing in general--had come so
far.  This kind of thing is like the difference between chemistry
and alchemistry.  With respect to the largest government procurements
like those for the ASCI program, this technology should be mandatory.
The ASCI participants HAVE to do it if they want to make credible
pronouncements about nuclear weapon stewardship.  There will still be
people who say not all the relevant physics is in the models, but that's
still a much smaller criticism than not being able to establish firm
results for the physics that _is_ being modeled.

I used to work in the marketing department when I was at FPS.  Like
many computer companies, FPS had a somewhat adversarial relationship
between its engineering visionaries and its marketing executives.
I say this because I had a foot in both camps, and I understand how
an engineering-driven idea like "interval arithmetic" seems radical
when the marketing department sees that almost no one is presently selling
computers because they have this feature.  Before FPS fell into financial
disarray, we had stumbled on the work on interval arithmetic publicized
by Miranker and Kulisch, and we were in the process of developing a hardware
product for verifiable computing that could have saved the company by
giving it a unique product that a certain part of the marketplace would
insist on owning... once they realized it were technically possible:  A
computer for simulation that can guarantee its answers.

I believe that interval arithmetic could do as much for scientific
computing as the graphical user interface has done for personal computing.
It is that different.  It is that revolutionary.  Like the graphical
user interface, it was a technology that had existed for many years in
a research setting but had been ignored by industry.  All it took was
one major vendor willing to make the leap, and after the usual reluctance
and "paradigm shift" inertia, everyone followed suit.  That's exactly what
could happen with interval arithmetic.

I am in contact with Dr. Gil Weigand, who is in charge of the ASCI program.
Years ago, upon learning of the program, I asked him, "Have you ever
heard of interval arithmetic?"  He had not; he belonged to the school
of thought that you make computer simulations more accurate by getting
more and more FLOPS in the design until it seems like it's enough.
Since then, I understand Dr. Walster has approached Weigand and found
him more educated and more receptive to the idea that interval arithmetic,
in hardware and software, might be crucial to the primary mission of
ASCI: to simulate something without the possibilty of confirmation by
physical experiments.

It does not take a lot of imagination to see what might happen if the
next major ASCI procurement rests heavily on interval arithmetic and
verifiable computing techniques.  Companies that use structural
analysis (possibly the largest consumer of floating-point arithmetic
cycles) would soon insist that the buildings, bridges, machine parts,
etc. that they design be tested using only verifiable methods.  Financial
modelers would demand to know the range of uncertainty in their
predictions.  Weather and climate prediction, another source of large
federal computer procurements, would be able to state a firm interval
instead of the guesses.  This does not even touch on the advances
in _optimization_ that Walster has made... the ability to guarantee
where the solution of an optimization problem does and does not exist
in a computer program with a vast number of variables.

In short, the people who presently buy computers to predict physical
behavior will in many cases take certainty over peak speed if the choice
is offered to them.  When the technology of interval arithmetic
(and Walster's approach in particular) becomes commercially available,
I'll be among those lining up to purchase it.

Sincerely,

Dr. John L. Gustafson
Computational Scientist
Ames Laboratory - USDOE