[Trilinos-Users] [EXTERNAL] Would Trilinos be suitable for this project?

[Salinger, Andrew]

Van,

You sure have an interesting problem. It is hard to tell from this if
there is any low-hanging fruit that Trilinos could help with. I was
glad to hear you are already using analytic derivatives and Newton solve.
Here are ideas from a quick read ― most would require more extensive
collaborations.

* Parallelization of sparse matrix solve (if it becomes significant cost)
  is an easy piece to replace
* Adjoint gradients ― integrate the mismatch backwards instead of the
  sensitivities forward. If you are integrating forward sensitivities for
  20 quantities x 72 levels along each path, the adjoint approach could
  lead to a huge savings. (Can ask our seismic inversion team.)
* Automatic differentiation ― would have saved on coding of Jacobians
  and sensitivities. May not be useful now if these are already correct
  and the equations aren’t changing, but a Huge development cost savings
  when calculating derivatives when the model changes regularly.
* Multi-integrations: if sets of the integrals follow the same path,
  then a single integration with multiple right-hand sides could lead to
  efficiencies. Sounds like each integral might have a unique path because
  of frequency-dependent parameters.
* Optimization alg: perhaps Dakota or ROL have algorithms that could
  reduce the iterations needed to converge.
* Bayesian calibration: instead of inverting for a single best-guess of
  all the parameters that minimize the mismatch, invert for probability
  functions for them. For instance, the data might constrain some of the
  quantities (temperature) very tightly about the optimum while others
  (some trace species) might be able to vary widely without impacting
  the data fit significantly. This can add 1000x to the computational
  cost. (This is accessible through Dakota.)
* Are there opportunities to learn from previous runs to accelerate
  convergence? Such as re-using preconditioners or recycling Krylov
subspaces.
* Reduced order modeling: can you construct a reduced basis for your
unknowns if they have a consistent correlation?

Andy



On 10/5/15, 4:54 PM, "Trilinos-Users on behalf of W Van Snyder"
<trilinos-users-bounces at trilinos.org on behalf of
van.snyder at sbcglobal.net> wrote:

>I work with an instrument called the Microwave Limb Sounder that was
>launched on the NASA EOS Aura satellite in 2004:
>
>http://mls.jpl.nasa.gov
>
>It's a passive microwave spectro-radiometer with an antenna that's aimed
>at the Earth's limb, and scans in the orbit plane from about 100km above
>the limb to the surface, every 26 seconds.  There are 148 integration
>periods per scan, and about 1000 spectrometer channels, for a total of
>about 500 million measurements per day.
>
>The quantities of interest are temperature, relative humidity,
>geopotential height, ice-water content, and the concentrations of minor
>constituents of the atmosphere, especially but not limited to those
>related to pollution or ozone depletion, altogether about 20 quantities.
>Estimates of these quantities are computed on 3500 profiles in the orbit
>plane, at 72 pressure levels, giving about 5 million results each day.
>
>The mathematical problem consists firstly in integrating the clear-sky
>non-scattering radiative transfer equation along a path through the
>atmosphere:
>
>dI/ds + alpha I = alpha B
>
>where s is path length, I is radiative intensity, alpha = sum beta_k f_k
>is the absorption cross section, beta_k is the absorption coefficient of
>the k'th chemical species, f_k is its volume mixing ratio, and B is the
>Planck black-body radiation function; beta_k and B depend upon
>temperature; f_k does not.  Derivatives of this equation with respect to
>f_k and temperature at the points in the profiles are also integrated on
>the same path.
>
>These equations are integrated from deep space, through the atmosphere,
>to the antenna, at several frequencies, typically far more frequencies
>than the number of channels.  The results are averaged using the
>laboratory-measured channel response functions, giving power estimates
>for each channel, and derivatives with respect to temperatures and
>mixing ratios.  The integration paths are determined by the number of
>pressure surfaces in the solution, not by the number of integration
>periods and their respective antenna pointings.  The solutions (and
>derivatives) are then convolved with the antenna response function to
>produce model estimates of the instrument response, and derivatives
>thereof.  The derivatives form a sparse Jacobian matrix.
>
>The quantities of interest are then computed using a Newton iteration to
>calculate a zero (in the least-squares sense) of the difference between
>the measured and modeled instrument response, subject to variation of
>mixing ratios and temperatures at the points in the profiles.
>
>The parallelization strategy is very simple:  350 instances of the
>program are launched, each one on a different core of a small cluster.
>Each one gets a chunk of 20 scans of the antenna.  Each chunk begins ten
>scans after the previous one, and overlaps five scans with the previous
>chunk and five with the next chunk.  The instances do not communicate
>with each other.  Linear algebra is not parallelized.  Each instance
>spends a few minutes communicating with a master to get its assignment,
>spends fifteen hours computing on its own, and then spends a few minutes
>communicating its results to the master.
>
>The program is of modest size by today's standards (350,000 lines), but
>its structure is tied rigidly to the viewing and reporting geometry:
>vertical scans in the orbit plane, and evenly-spaced vertical profiles
>in the orbit plane.  We are considering a newer instrument that will
>have a more general viewing geometry, and necessarily wish to provide
>more general reporting geometries.  We are trying to determine whether
>we should modify the existing program, or start over.
>
>Is this the sort of problem that might fit well into the trilinos
>framework?
>
>Thanks,
>Van Snyder
>van.snyder at jpl.nasa.gov
>
>
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