>0.2.0 feature list

[patrick-kidger]

Creating a list of potential features that may be nice to have, but aren't necessarily a priority right now.

• [x] Double backward w/ adjoint (#49)
• [x] Stratonovich adjoint support for additive/scalar/diagonal noise.
• [x] Continuous integration.
• [x] Fix speed performance regression (compared to v0.1.1, the CPU-only example is 3 times as slow as before for v0.2.1) (#86)
• [ ] autogenerated documentation
• [ ] Add Milstein for general noise, using Levy area approximation.
• [x] Allow an f_and_g function on SDEs, that computes drift+diffusion simultaneously. (#84)

Tests:

• [ ] Write tests for full Levy area.
• [ ] Write tests for sdeint actually approximating the analytical solution...
• [ ] Write tests that logqp is computing the thing it's supposed to compute.
• [ ] Fix BI doesn't pass tests when alpha=1e-2 issue. Very likely, something is wrong.

Maybe?

• [ ] Derivative-using Stratonovich Milstein w/ scalar noise doesn't look like it's getting the right weak/strong convergence behaviour. (Curved line on log-log plot).
• [ ] Use batch-vjp to compute dg_ga, if and when batch-vjp ever becomes available.
• [ ] Add static tensors as an input to sdeint, sdeint_adjoint
• [ ] C++ BInterval/BPath (to discuss) (If we do this, then #54 is relevant)

[jparkhill]

My number one desired feature is antithetic sampling as an option for sdeint. It's pretty cumbersome to achieve this without editing the package by changing the BrownianInterval's W.

[patrick-kidger]

I've not filled in every detail, but I'd have thought something like this should work:

class AntitheticBrownian(BaseBrownian):
   def __init__(self, bm):
       self.bm = bm

    def __call__(self, ta, tb):
        return -self.bm(ta, tb)

bm = BrownianInterval(...)
ys = torchsde(bm=bm, ...)

abm = AntitheticBrownian(bm)
ays = torchsde(bm=abm, ...)

ys = torch.cat([ys, ays])

Does this approach fail / am I missing something / are you trying to achieve something beyond this?

[jparkhill]

Does work, but it's still much uglier than it needs to be vs sdeint(...,antithetic=True). For innumerable financial applications of this library, this type of option is... priceless ;p Here's a filled in version in case anyone else is following along:

ts = tch.linspace(0,1.,365)
ntraj = 1000
bm = torchsde.BrownianInterval(ts[0], ts[-1], size=(ntraj,sde.brownian_size), levy_area_approximation='space-time')
ys_ = torchsde.sdeint(sde,sde.y0(ntraj=ntraj), ts, bm=bm)
class AntitheticBrownian(torchsde.BrownianInterval):
    def __init__(self, t0, t1, size, bm):
        super(AntitheticBrownian, self).__init__(t0,t1,size, levy_area_approximation='space-time')
        self.bm = bm
    def __call__(self, ta, tb=None, return_U=False, return_A=False):
        Z = self.bm(ta, tb, return_U, return_A)
        if return_U:
            if return_A:
                return -Z[0], Z[1], Z[2]
            else:
                return -Z[0], Z[1]
        else:
            if return_A:
                return -Z[0], Z[1]
            else:
                return -Z
abm = AntitheticBrownian(ts[0], ts[-1], (ntraj,sde.brownian_size), bm)
ays = torchsde.sdeint(sde,sde.y0(ntraj=ntraj), ts, bm=abm)
ys = torch.cat([ys_, ays],1)```