CREEK: Multi-Domain Methods & Case Studies

• CREEK is a multifaceted framework spanning Galactic archaeology’s chemo-dynamical clustering, distributed systems replication, and stochastic geometric graphs.
• In Galactic archaeology, CREEK leverages Siamese and Graph Neural Networks to fuse chemical abundances with orbital dynamics, enabling the discovery of stellar halo substructures.
• In distributed systems, Creek uses a two-phase broadcast (timestamp and CAB) to balance speculative execution with final consistency, achieving up to 2.5× lower latency.

CREEK denotes several distinct technical constructs and study objects in contemporary research. In Galactic archaeology it is the acronym “Clustering with gRaph nEural nEtworK”, a deep chemo-dynamical pipeline for recovering stellar halo substructures. In distributed systems, Creek is a low-latency mixed-consistency transactional replication scheme. In stochastic geometry, creek-crossing graphs are a family of geometric graphs generated by point processes. The term also appears in numerous place-based case studies, including Maules Creek, Mud Creek, Cedar Creek, Chelsea Creek, Nacetinsky creek, Nassawadox Creek, Imnavait Creek, and Hat Creek (Berni et al., 10 Jul 2025, Kobus et al., 2019, Rousselle, 2015).

1. CREEK in Galactic archaeology

In astrophysics, CREEK is a deep clustering method designed to identify accreted stellar structures in the Milky Way halo by combining chemistry and dynamics rather than relying on dynamics alone. Its motivation is that stellar streams, merger remnants, and related halo structures can lose dynamical coherence through tidal stripping, Galactic-plane passages, and phase mixing, whereas stellar abundances remain comparatively persistent. The method therefore uses dynamics to define star-to-star relations and chemistry to define the features that are clustered (Berni et al., 10 Jul 2025).

The thesis formulation introduced CREEK as a pipeline operating on halo stars from APOGEE and Gaia-ESO, with orbital actions used for kinematic similarity and selected abundances used for chemical representation. The later APOGEE-focused implementation used APOGEE DR17 abundances, Gaia DR3 astrometry, Bailer-Jones distances, and AGAMA orbital quantities in the McMillan potential, with a final halo sample of 3548 stars selected using $|v_{\rm tot}| > 220\ {\rm km\,s^{-1}}$ and $[\mathrm{Fe/H}] < -1$ (Berni, 2024, Berni et al., 10 Jul 2025).

A central design principle is that chemistry and dynamics are not treated symmetrically. The method clusters mainly in chemical space while using orbital information to define graph connectivity. In the APOGEE implementation, the final graph node features were only two standardized chemical dimensions,

$$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$

whereas the dynamical input to the Siamese stage was the standardized action triplet $(J_R, J_\phi, J_Z)$ (Berni et al., 10 Jul 2025).

2. Pipeline, training strategy, and empirical results

CREEK proceeds in four stages. First, halo stars are selected and their orbital actions computed. Second, a Siamese Neural Network is trained on known globular-cluster pairs to predict whether two stars are dynamically associated. Third, the predicted high-probability links define an undirected graph whose nodes carry chemical-abundance features. Fourth, a Graph Neural Network autoencoder learns a latent chemo-dynamical representation, and OPTICS is applied to that latent space to extract dense groups (Berni, 2024, Berni et al., 10 Jul 2025).

The APOGEE implementation trained the Siamese network on 2250 intra-cluster pairs and 2250 inter-cluster pairs, using three hidden layers of 32, 64, and 128 neurons with ReLU activations and a Sigmoid output

$\sigma(x) = \frac{1}{1+e^{-x}}.$

The reported validation accuracy was 0.99. Edges were then created for star pairs satisfying $P_{ij} \ge 0.8$. The graph autoencoder explored several architectures and selected a configuration with layers of 300, 100, and 5 neurons; the latent space was standardized before OPTICS, with a main globular-cluster configuration of $\xi = 0.001$ and $\text{min\_sample} = 7$ (Berni et al., 10 Jul 2025).

The recovery metrics for benchmark globular clusters were

$$H = \frac{\text{Number of cluster stars included in group}}{\text{Number of stars in group}}, \qquad C = \frac{\text{Number of cluster stars included in group}}{\text{Number of stars in cluster}}.$$

Using the relaxed criterion $H \ge 0.3$ and $[\mathrm{Fe/H}] < -1$0, the APOGEE study reported recovery of 8 out of 10 globular clusters with at least 10 APOGEE members, i.e. about 80%. It also re-identified several known stellar streams, repeatedly split Gaia-Enceladus-Sausage into two chemo-energetic sub-groups, and proposed a new retrograde candidate structure, Arnus I (Berni et al., 10 Jul 2025).

The thesis version extended the framework to Gaia-ESO. There the final abundance choices differed, using $[\mathrm{Fe/H}] < -1$1 rather than APOGEE’s $[\mathrm{Fe/H}] < -1$2. This suggests that CREEK was conceived as a survey-adaptive framework rather than a fixed feature prescription (Berni, 2024).

3. Creek as a mixed-consistency transactional replication scheme

In distributed systems, Creek is a low-latency, eventually consistent replication scheme that also supports strongly consistent operations akin to ACID transactions. Operations may have arbitrary deterministic semantics. The system totally orders all operations, but does so with two broadcast mechanisms: a timestamp-based mechanism for tentative ordering and speculative execution, and Conditional Atomic Broadcast (CAB) for finalizing the order of strong operations when distributed consensus can be solved (Kobus et al., 2019).

Creek distinguishes weak and strong operations. Weak operations are executed immediately and returned without inter-replica coordination, yielding eventual consistency in the paper’s sense of fluctuating eventual consistency. Strong operations are also executed speculatively, but their stable response is returned only after CAB fixes their final order. The execution of strong operations also stabilizes the order of causally related weak operations, because a strong operation carries a causal context and, upon commit, moves those weak operations from the tentative list into the committed prefix (Kobus et al., 2019).

Replica state is organized around two ordered lists, committed and tentative, and execution follows their concatenation. Creek uses rollback and reexecution when the speculative order differs from the final order. To make this practical, the implementation uses multiversion concurrency control, maintaining multiple immutable versions and validating dependencies so that only operations affected by an ordering change need to be reexecuted (Kobus et al., 2019).

In the TPC-C benchmark, Creek was reported to offer up to 2.5 times lower latency in returning client responses than the state-of-the-art speculative SMR scheme, while maintaining speculative-execution accuracy of 92–100%. In the main five-replica evaluation, weak tentative latency was about 0.5 ms, strong tentative latency about 0.1 ms, and strong stable latency about 0.8–1.2 ms, with maximum throughput around 32.5k tx/s (Kobus et al., 2019).

4. Creek-crossing graphs in stochastic geometry

In stochastic geometry, creek-crossing graphs form a family of deterministic geometric graphs built on a locally finite point configuration $[\mathrm{Fe/H}] < -1$3. For integer $[\mathrm{Fe/H}] < -1$4, the creek-crossing graph $[\mathrm{Fe/H}] < -1$5 connects distinct points $[\mathrm{Fe/H}] < -1$6 iff there do not exist

$[\mathrm{Fe/H}] < -1$7

such that

$[\mathrm{Fe/H}] < -1$8

Equivalently, $[\mathrm{Fe/H}] < -1$9 is retained only when one cannot move from $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$0 to $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$1 in at most $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$2 strictly shorter hops (Rousselle, 2015).

The paper explicitly identifies $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$3 with the relative neighborhood graph, and $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$4 with the Euclidean minimum spanning forest. It also states the inclusion relations

$$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$5

so creek-crossing graphs are treated as sparse subgraphs of the Gabriel graph and Delaunay triangulation (Rousselle, 2015).

The main probabilistic result is an annealed invariance principle for the simple continuous-time random walk on $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$6 under strong assumptions on the underlying stationary point process, including isotropy, finite-range dependence, and void/deviation conditions. The rescaled walk

$$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$7

converges weakly in $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$8-probability to a nondegenerate Brownian motion $$x_i = \big([\mathrm{M/H}]_i,\ [\alpha/\mathrm{M}]_i\big),$$9 with

$(J_R, J_\phi, J_Z)$0

The result is proved for several point processes, including homogeneous Poisson, Matérn cluster, and Matérn hardcore processes (Rousselle, 2015).

5. Creek-named empirical case studies

A large part of the research record uses “creek” not as a method name but as a geographically specific benchmark or field site.

Creek/site	Research context	Role or reported result
Maules Creek	3D conditional GAN generation	Reservoir/aquifer-scale test case conditioned to a centered single well; 1024 conditioned 3D realizations in 8 hours on one GPU; exact well matching and an elliptical conditioning influence (Mosser et al., 2018)
Mud Creek	Landslide forecasting from InSAR networks	Multilayer modularity detected the failure zone roughly 400 days before collapse, and community persistence rose about 56 days before the 2017 failure (Desai et al., 2022)
Cedar Creek	Nitrogen-induced hysteresis in grassland biodiversity	ODE model used to explain persistence of a low-diversity exotic-dominated state after N addition ceased, via litter-mediated bistability and hysteresis (Meyer et al., 2022)
Chelsea Creek	Situated data physicalization and environmental justice	“Chemicals in the Creek” translated EPA water-permit violations from 2013 to 2017 into a creek-based lantern installation co-designed with GreenRoots and ECO (Perovich et al., 2020)
Nacetinsky creek	Multivariate Gaussian change-point inference	Bivariate and trivariate analyses detected a significant increase in log-transformed monthly water discharges, with $(J_R, J_\phi, J_Z)$1, i.e. a change after 1964 (Fotopoulos et al., 2010)
Nassawadox Creek	Estuarine fecal coliform transport and decay	Combined observed FC distributions, modeled transit time, and an analytical framework to estimate an average removal rate of $(J_R, J_\phi, J_Z)$2 (Du et al., 2020)
Imnavait Creek	Permafrost thermal hydrology	Observation-informed modeling showed the creek-feeding supra-permafrost aquifer became broader, deeper, and longer active from 1981 to 2020 (Mukherjee et al., 22 Dec 2025)
Hat Creek	Spectrum-sharing protection for radio astronomy	Proposed SAS neighborhood distances for HCRO of 112 km for category A and 144 km for category B devices (Papadopoulos et al., 2023)

Across these papers, creek-named sites function as concrete calibration and validation settings rather than merely descriptive geography. Maules Creek is a reservoir-scale proof-of-concept for conditioned 3D generation; Mud Creek is a hindcast test for spatiotemporal warning signals; Cedar Creek anchors a hysteresis theory; Nassawadox and Imnavait Creek ground physically based hydrologic inference; Hat Creek is an engineering target for dynamic protection-area design (Mosser et al., 2018, Desai et al., 2022, Meyer et al., 2022, Du et al., 2020, Mukherjee et al., 22 Dec 2025, Papadopoulos et al., 2023).

6. Cross-domain patterns

A recurring pattern in the cited literature is methodological coupling. The Galactic-archaeology CREEK combines chemistry and dynamics in a graph-based latent representation. The transactional Creek system combines timestamp-based speculation with CAB-based finalization. The Maules Creek GAN workflow combines a hard-data content term with a discriminator-based perceptual term. The Mud Creek study combines topographic susceptibility and InSAR-derived deformation in multilayer edge weights. The Nassawadox Creek method combines observations, hydrodynamic transit time, and an analytical decay model (Berni et al., 10 Jul 2025, Kobus et al., 2019, Mosser et al., 2018, Desai et al., 2022, Du et al., 2020).

Another common feature is the use of partial or noisy information as an organizing constraint. CREEK in Galactic archaeology is trained on known globular clusters and then generalized to streams and field stars. Creek in distributed systems allows tentative execution before final agreement. Maules Creek conditioning begins from sparse one-dimensional well data. Mud Creek forecasting uses 6–24 day InSAR revisit intervals and extracts a warning-like signal from changing community persistence rather than from raw displacement alone. This suggests that “CREEK,” across otherwise unrelated literatures, is repeatedly associated with frameworks that preserve structure while operating under incomplete observability (Berni et al., 10 Jul 2025, Kobus et al., 2019, Mosser et al., 2018, Desai et al., 2022).

The term therefore has no single disciplinary meaning. In current arXiv-linked usage, it names a chemo-dynamical clustering pipeline, a mixed-consistency replication protocol, a graph class, and a set of place-based benchmark systems spanning reservoir modeling, landslide forecasting, ecosystem theory, hydrology, environmental justice, radio-spectrum engineering, and Arctic permafrost science (Berni et al., 10 Jul 2025, Kobus et al., 2019, Rousselle, 2015).