yousef/Global search for high order explicit Runge-Kutta methods

Progress

  • Yousef tried looking for 13-stages 9th order ERK with Baron, but the solver did not converge after running for a couple of days. Yousef had tried previously to submit jobs that run baron code but it didn’t work.

  • Yousef contacted Octeract Engine’s developers in mid-January (for the third time) to get their trial version but got no response. It would be nice to try another global solver that may perform better and more efficiently than Baron.

Jan-29

Action Items

  • Set an appointment with the IBEX team to figure out how to submit a job to the cluster (Done, we’ll meet Thursday, Feb 2nd).

Feb 5th

  • Was able to find sixth order seven stages ERK, confirming that baron is able to find optimal 6th order ERK method.

  • Still Unable to submit jobs in ibex to run GAMs remotely (simple codes) due to permission access error which I couldn’t resolve. Met today with the ibex guys and they told me to open a ticket. I did.

  • Once figured out, I’ll submit multiple jobs looking for 9th-order ERK using both the sparse structure of A and the slacking formulations. I’ll leave this project aside for the next couple of weeks and work on the CHJ instead.

Feb 7th

I successfully submitted the following jobs

JOBID PARTITION     NAME     USER ST       TIME  NODES NODELIST(REASON)

          23665275     batch job_ERK1 alamriym  R       0:00      1 (Priority).  ===  ERK1510 MAX TOL

          23665274     batch job_ERK1 alamriym  R       0:00      1 (Priority).  ===  ERK1710

          23665273     batch job_ERK1 alamriym  R       0:00      1 (Priority).  ===  ERK1610

          23665272     batch job_ERK1 alamriym  R       0:00      1 (Priority).    ===  ERK1510

          23665210     batch job_ERK1 alamriym R       0:00      1 (Priority)     ===   ERK139 MAX TOL

          23665207     batch job_ERK1 alamriym  R       1:06      1 cn509-11-l  === ERK139

          23665208     batch job_ERK1 alamriym  R       1:06      1 cn509-10-r  === ERK149

          23665209     batch job_ERK1 alamriym  R       1:06      1 cn509-09-l. === ERK159

Feb 11

  • I tried setting up the optimization problem for finding high-order ERK and using the sparse structure for A (the scripts above). The output by BARON was that the problem is infeasible.

  • I tried the other formulation that adds constraints for the ERK structure. The code is still running.

Feb 16

  • I think the solver declared the problem infeasible because I added bounds on the values for the coefficients a’s and b’s to be between -10 and 10. I remember experiencing similar issues previously. I re-ran these scripts without this bound for ERK9 and ERK10.

  • The 9th order ERK method by Verner is in this paper ( https://epubs.siam.org/doi/pdf/10.1137/0715051 ). It is an 8(9) pair with 16 stages (not 15, what I thought)

Mar 1st

  • The only solution that was obtained is ERK169 (i.e., same as Verner’s), but accuracy is around 1e-6. I was not able to improve it

  • The other codes for 9th and 10th order methods did not converge.