toy_problems.Enzyme_ex1()

Simple air sea flux calculation and it's adjoint, obtained via Enzyme.

toy_problems.Enzyme_ex2()

• air sea flux calculation derived using standard bulk formulae algorithm.
• it's adjoint, obtained via Enzyme.

using ECCO
(f,f_ad,x)=toy_problems.Enzyme_ex2()
f(x...)
f_ad(x...)

toy_problems.Enzyme_ex3()

using ECCO
(f,f_ad,x,y)=toy_problems.Enzyme_ex3()
f(x,y)
f_ad(x,y)

toy_problems.Enzyme_ex4()

using ECCO
(f,f_ad,x,y)=toy_problems.Enzyme_ex4()
f(x,y)
f_ad(x,y)

toy_problems.ForwardDiff_ex1()

using ECCO
(x,adx)=toy_problems.ForwardDiff_ex1()

toy_problems.optim_ex1()

using ECCO
(f,x0,x1,result)=toy_problems.optim_ex1()

toy_problems.optim_ex2()

toy_problems.optim_ex3()

toy_problems.Zygote_ex1()

using ECCO
(x,adx)=Zygote_examples.Zygote_ex1()

forward_problem(M0=0.004; dt=1/12.0, nt=6*5000, dx = 1.0, nx = 30)

Simple, 1D mountain glacier model inspired from the book Fundamentals of Glacier Dynamics, by CJ van der Veen, and which was translated to Julia by S Gaikwad.

See https://sicopolis.readthedocs.io/en/latest/AD/tutorial_tapenade.html#mountain-glacier-model

V=glacier_model.forward_problem(0.002)

L63(; nt=10000)

See https://en.wikipedia.org/wiki/Lorenz_system

using ECCO, CairoMakie
x,y,z=Lorenz_models.L63()
lines(x,y,z)

L96(; N=5, F=8)

See https://en.wikipedia.org/wiki/Lorenz96model

using ECCO, CairoMakie
xyz=Lorenz_models.L96()
lines(xyz[1,:],xyz[2,:],xyz[end,:])

Budyko-Sellers Energy Balance Model

Parameter Choices

From B. Rose notebook :

R = 10^7 J/m2/K

From Walsh and Rackauckas :

• Figure 3. Equilibrium solutions (7) with albedo function (9) for five η-values. Note T∗ ηi (ηi) = Tc only for i = 2,5.
  • Parameters: Q = 343, A = 202, B = 1.9, C = 3.04, αw = 0.32, αs = 0.62, Tc =−10.
• Figure 9. Equilibrium solutions of (2) with albedo function (34). Solid: η= 0.1. Dashed: η= 0.25. Dash-Dot: η= 0.4.
  • Parameters: Q = 321,A = 167,B = 1.5,C = 2.25,M = 50,αw = 0.32,αi = 0.46,αs = 0.72,ρ= 0.35.

adjoint_demo(par=[Q])

• generate obs for cost function with fake_obs.
• call the_main_loop_cost and adthe_main_loop_cost
• return gradient check result

grdchk=adjoint_demo([Q])

dTdt_demo(par=[Q])

using ECCO, CairoMakie

(; Q, y) = Budyko_Sellers_models.params
Tsol,Tini,dTdt_ini,incr_t,incr=Budyko_Sellers_models.dTdt_demo(Q)

fig=Figure()
Axis(fig[1,1]); lines!(y,dTdt_ini)
Axis(fig[2,1]); lines!(y,Tini); lines!(y,Tsol,color=:red)
Axis(fig[3,1]); lines!(incr_t,incr)	
fig

dTdt_loop_optim()

Call the_main_loop and then Optim.optimize.

f,x0,x1,result=dTdt_loop_optim()

dTdt_solve_optim(Tobs)

Call dTdt_solve and then Optim.optimize (adjoint free).

f,x0,x1,result=dTdt_solve_optim(Tobs)

optim_demo(Q=Q; verbose=false)

Call dTdt_solve and then dTdt_solve_optim.

optim_demo()

optim_demo_loop()

Call dTdt_loop_optim.

the_main_loop(x; nt=10000)

Do nt time steps of dt*dTdt(result,Q=x).