LensingFlow: Automated Gravitational Lensing Analysis

• LensingFlow is an automated framework for gravitational lensing analyses that integrates advanced parameter estimation pipelines and scalable job management to efficiently process large astrophysical datasets.
• It employs a multi-stage workflow with low latency filtering and full Bayesian analysis to reduce computational expense by up to 85% while robustly detecting various lensing regimes.
• Its modular design and integration with systems like Asimov and CBCFlow ensure horizontal scalability, reproducibility, and extensibility for multimessenger astrophysical applications.

LensingFlow denotes a class of methodologies and frameworks that systematically model, detect, and analyze gravitational lensing phenomena across a wide spectrum of astrophysical and cosmological contexts. These range from weak/strong gravitational lensing in electromagnetic surveys to the search for lensing signatures in gravitational wave events. Central to LensingFlow approaches are automated, modular workflows that leverage theoretical lensing models, advanced parameter estimation pipelines, and scalable automation platforms for efficiently processing large astronomical datasets. The underlying principles merge classical gravitational lensing formalisms with state-of-the-art computational and data management tools to address the practical demands of modern multimessenger surveys.

1. Conceptual Foundation and Architecture

LensingFlow is conceived as an automated workflow tailored to conducting large-scale gravitational lensing analyses, particularly in the context of gravitational wave (GW) astronomy (Wright et al., 27 Jul 2025). It is architected atop established infrastructures: the Asimov automation framework for parameter estimation (PE) job management, and CBCFlow for standardized metadata handling. The core design enables:

• Orchestration of disparate lensing analysis tasks with unified job submission, monitoring, and metadata storage.
• Automated ingestion of GW event metadata and dynamic assignment to analysis subworkflows based on event characteristics (e.g., probability of binary black hole mergers, low false alarm rates).
• Modular and extensible integration of multiple lensing analysis pipelines, supporting both current and future methodologies.

By building upon Asimov and CBCFlow, LensingFlow provides end-to-end lifecycle management for lensing analyses, ensuring seamless transitions from event selection to final candidate identification.

2. Workflow, Automation, and Job Management

LensingFlow manages the full analysis pipeline via a multi-stage, automated workflow. Key operational steps include:

• Event Selection: Filtering of GW events through metadata (from CBCFlow) to identify candidates for lensing analysis based on pre-defined criteria.
• Ledger and Workflow Initiation: Management of event analyses through an Asimov ledger, triggering both singlet and multiplet (pairwise or extended) pipelines as appropriate.
• Low Latency Filtering: Initial screening with fast pipelines (LensID, Posterior_Overlap, Phazap, Golum) to flag promising candidate pairs or events using metrics such as Bayes factors for parameter consistency and time delay plausibility.
• Prioritization and Scheduling: Use of an HTCondor-based scheduler and priority management system to allocate computational resources, ensuring high-significance candidates receive expedited processing.
• High Latency Analysis: Escalation of filtered candidates to computationally intensive, full Bayesian PE pipelines (e.g., joint analyses via Golum and Hanabi), and execution of specialized analyses for singlet events (e.g., with Gravelamps).
• Automated Metadata Handling: All results, configurations, and intermediate outputs are recorded in the CBCFlow metadata structure, providing reproducibility and traceability.

This hierarchical workflow substantially reduces computational expense by focusing detailed analyses only on high-priority candidates, as evidenced by an 85% reduction in required Bayesian analyses in mock data challenges (Wright et al., 27 Jul 2025).

3. Theoretical Lensing Models and Pipeline Integration

LensingFlow accommodates a wide variety of lensing regimes and pipelines:

• Geometric Optics Regime: Models events where multiple GW images manifest as distinct, temporally separated (or in special cases, superposed) signals. The observed strain for each image incorporates magnification, time delay, and phase shift:

$$h_j^L (f; \theta, \mu_j, \Delta t_j, n_j) = \sqrt{|\mu_j|} \exp[-2\pi i f \Delta t_j + i\pi n_j] h(f; \theta)$$

where $\mu_j$ is magnification, $\Delta t_j$ is total delay, $n_j$ is the Morse index, and $h(f;\theta)$ is the unlensed strain.

• Wave Optics Regime: Handles cases where diffraction dominates, with the strain modulated by integrals over the time-delay surface $T(x,y)$:

$$F(w,y) = \frac{w}{2\pi i} \int \exp[-iwT(x,y)] d^2x$$

• Statistical Consistency: Pipelines perform joint Bayesian modeling and compute metrics such as Bayes factors:

$$B^{(L_U)} = \int \frac{P(\Theta|d_1)P(\Theta|d_2)}{P(\Theta)} d\Theta$$

with further extensions to incorporate timing, magnification ratios, and phase shifts.

The pipeline ecosystem includes Gravelamps (for both modelled and unmodelled single-image lensing), Golum (specialized for joint multiplet analysis and Type II events), Atlenstics (for galaxy lens checks), Posterior_Overlap, Phazap, and machine learning classifiers such as LensID. All pipelines adhere to configurable Python classes, allowing scalable, reproducible workflow execution.

4. Lensing Regimes and Analytical Scope

LensingFlow systematically addresses all generally considered lensing regimes within GW astronomy:

• Singlet (Point-mass) Lensing: Isolated events producing single lensed images, potentially exhibiting lensing-induced waveform features.
• Multiplet Lensing: Events yielding multiple GW images differentiated by arrival time, magnification, and potential waveform phase distortion.
• Wave-Optics Lensing: Scenarios where the lens mass is sufficiently small (relative to the GW wavelength) for diffraction and frequency-dependent amplification to occur.
• High-Order Candidate Handling: For each event or candidate pair, appropriate pipelines are triggered in accordance with the anticipated lensing regime, with the flexibility to add additional regimes as theoretical models and detection thresholds evolve.

5. Proof-of-Concept Demonstration and Results

The initial deployment of LensingFlow on a purpose-built mock data challenge (MDC) with ten GW signals—each representing a different lensing regime—demonstrates the operational effectiveness of the workflow (Wright et al., 27 Jul 2025):

• Candidate Filtering: From 45 possible event pairs, low latency filters reduced the candidate set to 6 for further in-depth Bayesian analysis (an 85% computational reduction).
• Detection of All Regimes: The workflow successfully identified both singlet and multiplet lensing signatures, with automated escalation of candidates to full joint PE as needed.
• Reproducibility: All job configurations, logs, and results were stored in the CBCFlow metadata structure.
• Scalability: The system demonstrated the capability to efficiently manage analyses as the number of candidate events grows with future survey volumes.

6. Scalability, Extensibility, and Future Prospects

LensingFlow has been engineered to meet the scalability requirements of current and future GW detection campaigns. Key properties include:

• Horizontal Scaling: Designed to support increases in GW event rates, allowing near-real-time lensing analyses as detector sensitivity improves.
• Pipeline Agnosticism: Additional or more complex pipelines can be integrated to address new scientific objectives or accommodate expanded physical models.
• Advanced Prioritization: Dynamic job prioritization adapts as candidate significance evolves over the course of analysis.
• Toward Multi-messenger Lensing: The modularity of LensingFlow lends itself to adaptation for multimodal/multimessenger scenarios where electromagnetic and GW lensing are analyzed jointly.

A plausible implication is that, as datasets and survey scales expand, such platforms will become standard tools for managing the computational and logistical complexity of lensing analyses across astrophysical and cosmological domains.

7. Scientific Impact and Significance

By providing a reproducible, automated, and extensible framework for lensing search and analysis, LensingFlow addresses the logistical and scientific bottlenecks in identifying lensed GW events. Its capacity to triage, manage, and prioritize analyses based on quantitative statistical evidence enables:

• Efficient Large-scale Searches: Avoids wasteful use of resources on false positives, concentrating detailed analysis on high-value events.
• Robust Candidate Discovery: Minimizes human intervention and subjectivity, ensuring uniformity and transparency in the detection process.
• Enabling Population Studies: By systematically processing all catalogued events, LensingFlow facilitates statistically robust studies of lensing rates, the properties of lenses (e.g., compactness, mass, redshift distribution), and may ultimately inform population-level models of lensing objects and GW sources.

These capabilities position LensingFlow as a foundational methodology for gravitational wave lensing analyses in the current and next generation of astronomical surveys (Wright et al., 27 Jul 2025).