Allow more AD backends in optimization based solvers

[ErikQQY]

Fix #379

The previous implementation can't exploit the sparsity pattern of the loss function due to the value updates in loss function, this PR allows sparse AD in optimmization based internal solvers.

Before this PR:

With this PR:

[github-actions]

Benchmark Results

Click to check benchmark results

	master	d8aeb29...	master / d8aeb29...
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK2()	0.308 ± 0.02 s	0.32 ± 0.02 s	0.963 ± 0.086
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK3()	9.85 ± 0.33 ms	9.88 ± 0.5 ms	0.997 ± 0.06
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK4()	2.48 ± 0.095 ms	2.49 ± 0.07 ms	0.997 ± 0.047
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK5()	7.3 ± 1.8 ms	7.34 ± 1.8 ms	0.995 ± 0.35
Simple Pendulum/IIP/BoundaryValueDiffEqMIRK.MIRK6()	1.34 ± 0.34 ms	1.34 ± 0.097 ms	1 ± 0.27
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = false)	1.76 ± 0.99 ms	1.74 ± 0.98 ms	1.01 ± 0.8
Simple Pendulum/IIP/MultipleShooting(10, Tsit5; grid_coarsening = true)	2.93 ± 0.94 ms	2.94 ± 0.92 ms	0.998 ± 0.45
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.0705 ± 0.016 s	0.0706 ± 0.016 s	0.998 ± 0.32
Simple Pendulum/IIP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.0879 ± 0.028 s	0.0916 ± 0.029 s	0.959 ± 0.43
Simple Pendulum/IIP/Shooting(Tsit5())	0.237 ± 0.067 ms	0.237 ± 0.076 ms	0.999 ± 0.43
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK2()	0.462 ± 0.014 s	0.458 ± 0.0048 s	1.01 ± 0.031
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK3()	12.3 ± 6.2 ms	12.3 ± 5.7 ms	0.999 ± 0.68
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK4()	2.84 ± 0.2 ms	2.86 ± 0.15 ms	0.992 ± 0.087
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK5()	8.33 ± 1.2 ms	8.44 ± 1.2 ms	0.987 ± 0.2
Simple Pendulum/OOP/BoundaryValueDiffEqMIRK.MIRK6()	1.5 ± 0.24 ms	1.53 ± 0.23 ms	0.981 ± 0.21
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = false)	3.01 ± 3.2 ms	2.99 ± 3.2 ms	1.01 ± 1.5
Simple Pendulum/OOP/MultipleShooting(10, Tsit5; grid_coarsening = true)	5.18 ± 5.9 ms	5.15 ± 5.4 ms	1.01 ± 1.6
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = false)	0.114 ± 0.0059 s	0.111 ± 0.0068 s	1.03 ± 0.083
Simple Pendulum/OOP/MultipleShooting(100, Tsit5; grid_coarsening = true)	0.142 ± 0.061 s	0.148 ± 0.048 s	0.965 ± 0.52
Simple Pendulum/OOP/Shooting(Tsit5())	0.521 ± 0.31 ms	0.521 ± 0.28 ms	0.998 ± 0.8
time_to_load	4.31 ± 0.018 s	4.32 ± 0.012 s	0.997 ± 0.0049

### Benchmark Plots A plot of the benchmark results has been uploaded as an artifact to the workflow run for this PR. Go to "Actions"->"Benchmark a pull request"->[the most recent run]->"Artifacts" (at the bottom).