GaussianSINDy (GPSINDy)

Discovering Equations of Motion from Data

Research Notes

Aug 18, 2023

Somi:

• try planar car dynamics
  • can use box car dynamics (driven by rear wheel axle from Estimation)

Aug 17, 2023

My own thoughts:

• Added headers to Xi matrix, easy to tell what is what now
• Try unicycle dynamics again, but in simulation. Then try Jake's car data again
• motivating examples? Use homework problems from Estimation, read more papers on robotics and use same style

Aug 16, 2023

Adam:

• said same thing as Somi: motivating example
  • give persuasive argument why SINDy is bad and we want to use GPSINDy instead
  • why having a good/better model is important
  • application areas: dynamics fudginess causes issues
  • safety applications

Aug 11, 2023

• use double pendulum hardware data *ONGOING
• fix validation script and plotting *DONE
• start writing: update the methods section *ONGOING
• try MeanLin with beta transpose *DONE (still doesn't work?)

paper:

• motivate the problem diagram: have a robot or satellite where we want to learn the dynamics, think about where modeling is useful
• show SINDy is bad
• plot 1: motivating example (something with a robot)
• save data, figure out best plot later

Aug 6, 2023

Double Pendulum Chaotic dataset:

• https://ibm.github.io/double-pendulum-chaotic-dataset/
• Extract and save data to folder test/double-pendulum-chaotic/

July 28

• (suggestion) For step 2: implement the mean function from Adam's white board as the mean function
  • subtract Theta(x)*xi from training points dx_noise

submit paper:

• learned models have uncertainty
• can take learned models with uncertainties into parametric form
• experiments, learn dynamics
• treat uncertainty of the learned system as disturbance on data

this weekend:

• try on real data

my idea:

• kalman filter GP-SINDy? condition learned model on new data?

July 27

David:

• implement the picture you took with your phone (GP-SINDy-GP-SINDy etc)
• create nice plot from Lasse (fig 3) *DONE
• table it: actually implement LASSO
• write problem in a way to say that we used coordinate descent (with separate primal variables)
• say that we stacked unknown variables (xi coefficients and sigma hyperparameters) into 1 unknown vector
• and then say we used coordinate descent to split unknown into 2 split variables
• and then do that thing that we wrote on the white board
• try on Jake's data, just see how it looks *DONE (it looks terrible with SINDy alone)

deadline:

• nicer to have journal
• decide later

email Chante about work ending Aug 4 email her again about lunch reimbursement she is responsive

July 26

Somi:

1. smooth dx_noise with x_noise as training inputs --> dx_GP
   • smooth x with t first --> x_GP (SE kernel)
   • smooth dx with x --> dx_GP (SE kernel)
   • try diff kernel? SE *DONE
   • set up kernel to be function of x *DONE
2. plug in dx_GP and x_noise into SINDy, good plots? *DONE
3. fix ADMM stuff, only update hyperparameters at the start *DONE
4. compare SINDy and GPSINDy *DONE

July 24-28

Somi: (2)

• try Matern52 kernel within SINDy-GP-ADMM (and maybe Matern32 kernel)

David: (4)

• table it for now: figure right way to do sparsity, soft thresholding? hard thresholding?

• iterate: GP --> SINDy --> GP --> SINDy --> repeat

  • GP takes in (t,x) as input, outputs smoothed x
  • Coefficients * function library to generate dx ?

• (tangential) try SINDy with soft thresholding

• create pull request, merge into main

        # new dx 
        # dx_new = Θx * Ξ_gpsindy 
  
        # combine dx_noise and dx_new 
        # dx_combine = ... ? 
  
        # dx_GP2 = post_dist_M52I( t, t_test, dx_new ) 
        # Ξ_gpsindy2 = SINDy_test( x_GP, dx_GP2, λ ) 
  

Adam: (1) --> GPs

• standardize x, add noise --> GP --> derivative of GP *set up GP dx = f(x)
• set up kernel to be function of x *DONE

Yue: (3) --> l1 norm min, ADMM

• remove relative tolerances for ADMM *DONE
• SINDy, keep it the way it is
• don't change hyperparameters every step for ADMM (do not change objective function at every iteration), maybe let ADMM run for 1000 iterations and then update hyperparameters *DONE
• try taking out log(det(Ky)) of obj fn *DONE

Junette:

• just do Jake's car data *DONE SET UP SANDBOX

July 17-21

• look into sparsity: increase lambda, compare gpsindy and sindy
• decrease samples and increase noise, gpsindy works better?
• use GP to smooth data and use as input into sindy

fixed kernel?

• input should be time, not x or dx as previously specified in the paper?

June 19, 2023

• put predator_prey plot into function in utils.jl
• added metrics to end of predator_prey_test.jl (just opnorm) for truth vs. sindy vs. gpsindy
• also tried just turning off one small coefficient for sindy per David's suggestion - it makes trajectory propagate much differently
• now just put everything that you've found into a latex document ... and run more experiments