Add UODE Lotka-Volterra notebook

[markusheinonen]

• Observe both prey and predator (H=I_2) at dt=0.2 (150 points)
• Laplace(0, 0.005) prior for SINDy-like sparsity on Theta
• SVI config: lr=1e-3, cov_rescaling=2.0, lr_decay=0.5, 2000 steps
• Correctly recovers xy interaction coefficients (Frobenius err ~0.077)
• Includes debug CLI script for systematic experiments

[mattlevine22]

Was able to get this notebook to run "perfectly" in #155 .

To get things to work better

1. Use ContinuousTimeEnKF instead of EKF, as EnKF is more numerically robust
2. Revert to simple ADAM with lr=1e-3 and 4000 epochs. At 1000 epochs, things are pretty close, and by 4000 epochs, the answer has fully sparsified
3. There are some bugs when trying to do MAP-Predictive Filter here...observe that svi_result.params['Theta_auto_loc] != Theta_inferred`

Instead of predictive_filter = Predictive(data_conditioned_model, params=svi_result.params, num_samples=1), do
predictive_filter = Predictive(data_conditioned_model, params=guide.median(svi_result.params), num_samples=1)

[DanWaxman]

I also just updated this in lieu of #135

[mattlevine22]

Now that it is working (mostly by using EnKF and running ADAM for longer), we should think about where to put this example.

1. Should this go in Docs as a deep dive? Or should It be in the dynestyx-examples repo?

• I like the idea of us having a reimplementation of "Universal ODEs" in our repo (to show that most of the popular methods can be set up easily in Dynestyx)

2. Do we want to keep the debugging script / put it in dynestyx-examples?

[DanWaxman]

1. Should this go in Docs as a deep dive? Or should It be in the `dynestyx-examples` repo?

Hmm I think this is a good open question. I think there are two choices for how we use dynestyx-examples: (1) have every example there; (2) keep minimal examples (e.g., that implement mainstream ideas in a single notebook) in dynestyx, and delegate more complex multi-file case studies to dynestyx-examples. I lean more towards (2), in which case we may still consider this a "deep dive."

In any case, I think it's a low-cost decision, it's easy to revert this later.

2. Do we want to keep the debugging script / put it in dynestyx-examples?

I would get rid of the debugging script if we keep it in dynestyx, and keep it if we put it in dynestyx-examples. I don't want duplicated code across repos, though.

[DanWaxman]

Just got this to be working again and fixed some text/formatting issues. I think it makes sense to add to our deep dives for now, so I deleted the debug script and added this to our docs site nav. LGTM. Since I just made a bunch of changes, I think it's best if Matt does a quick review of this before merging. Thanks @markusheinonen!!

[mattlevine22]

@copilot Do a thorough check of the Jupyter notebook and please provide a bulleted list of how to fix the exposition to match the code (there are many discrepancies). For example, we code H=jnp.eye(state_dim) but write about partial observations and H = [1 0] in the exposition (also learning rate and cov_rescaling are not used in the code anymore).

[Copilot]

@copilot Do a thorough check of the Jupyter notebook and please provide a bulleted list of how to fix the exposition to match the code (there are many discrepancies). For example, we code `H=jnp.eye(s...

Addressed in 3bfc01a.

• Updated the intro and configuration table to match the current setup: both species observed, H = I_2, \Delta t = 0.2, and the explicit initial-state prior/covariance.
• Corrected the prior descriptions to match the code: Theta ~ Laplace(0, 0.005), sigma_x ~ LogNormal(log 0.05, 1.0), sigma_y ~ HalfNormal(0.5).
• Replaced stale EKF wording with EnKF wording in the marginal-likelihood, inference, filtering, and phase-space sections, plus the filtered-trajectory plot title.
• Removed stale exposition about cov_rescaling, learning-rate decay, and optax, and replaced it with the actual optimizer settings: ADAM with lr=1e-3 for 4000 SVI steps.
• Updated the SVI text to reflect the current MAP readout path via guide.median(svi_result.params).

[mattlevine22]

Looks good, thanks! Fixed the text so it matches what was done (no LR schedule, no cov_rescaling, full observations, EnKF not EKF).

Tried to get copilot to do it, but that was a big mistake lol.

[DanWaxman]

Haha thanks Matt!! I tried but I guess I missed some of them… and thanks again for drafting it, Markus!

…

On Tue, Jun 2, 2026 at 5:50 PM Matt Levine ***@***.***> wrote: ***@***.**** approved this pull request. Looks good, thanks! Fixed the text so it matches what was done (no LR schedule, no cov_rescaling, full observations, EnKF not EKF). Tried to get copilot to do it, but that was a big mistake lol. — Reply to this email directly, view it on GitHub <#153?email_source=notifications&email_token=AC2DPOOIEVNR2VTUDZZO5VL455D33A5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBRGM4DQNZQHA4KM4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJLDGN5XXIZLSL5RWY2LDNM#pullrequestreview-4413887088>, or unsubscribe <https://github.com/notifications/unsubscribe-auth/AC2DPOKXCCGLMTMQUH7O25L455D33AVCNFSM6AAAAACWXAA2F2VHI2DSMVQWIX3LMV43YUDVNRWFEZLROVSXG5CSMV3GSZLXHM2DIMJTHA4DOMBYHA> . Triage notifications, keep track of coding agent tasks and review pull requests on the go with GitHub Mobile for iOS <https://github.com/notifications/mobile/ios/AC2DPOJ7Y5S3CZV3XMSW3G3455D33A5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBRGM4DQNZQHA4KM4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJKTGN5XXIZLSL5UW64Y> and Android <https://github.com/notifications/mobile/android/AC2DPONJVXLPNGATN4AIHVD455D33A5CNFSNUABKM5UWIORPF5TWS5BNNB2WEL2QOVWGYUTFOF2WK43UKJSXM2LFO4XTINBRGM4DQNZQHA4KM4TFMFZW63VHMNXW23LFNZ2KKZLWMVXHJLTGN5XXIZLSL5QW4ZDSN5UWI>. Download it today! You are receiving this because you commented.Message ID: ***@***.***>