arxiv: 2605.11280 · v1 · submitted 2026-05-11 · 🌀 gr-qc · astro-ph.HE· cs.AI

Recognition: no theorem link

Discovery of Interpretable Surrogates via Agentic AI: Application to Gravitational Waves

Ajit Kumar Mehta, Barak Zackay, Digvijay Wadekar, Javier Roulet, Matias Zaldarriaga, Tejaswi Venumadhav, Tousif Islam

Authors on Pith no claims yet

Pith reviewed 2026-05-13 01:48 UTC · model grok-4.3

classification 🌀 gr-qc astro-ph.HEcs.AI

keywords gravitational wavessurrogate modelseccentric binary black holeslarge language modelsagentic AIwaveform modelinginterpretable surrogates

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The pith

An agentic LLM workflow constructs an analytic surrogate for eccentric binary black hole waveforms with median Advanced LIGO mismatch of 6.9×10^{-4} and 8.4× speedup over direct evaluation.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper demonstrates that a large language model can operate as an agent to iteratively propose, validate, and refine analytic expressions for expensive scientific simulations, using quantitative mismatch against ground-truth data at each step. Starting from a physics-informed ansatz for the waveform, the workflow produces a compact, interpretable surrogate for gravitational waves from eccentric binary black hole mergers that outperforms symbolic regression and standard machine-learning baselines in both accuracy and evaluation speed. This matters because fast yet readable surrogates enable rapid parameter estimation and allow extraction of physical quantities, such as the eccentricity of observed events like GW200129.

Core claim

GWAgent, an LLM-based workflow, builds analytic surrogates directly from simulation data for gravitational waveforms from eccentric binary black hole mergers. With a physics-informed domain ansatz supplied to the agent, the resulting model reaches a median Advanced LIGO mismatch of 6.9×10^{-4} and an ∼8.4× speedup in waveform evaluation while revealing compact physical structure in the learned representation, which is then applied to infer the eccentricity of GW200129 as e_{20 Hz}=0.099^{+0.063}_{-0.044}.

What carries the argument

The GWAgent LLM-based iterative workflow that proposes candidate analytic models, validates them quantitatively against ground-truth simulations, and refines them using a physics-informed domain ansatz.

If this is right

The surrogate enables substantially faster waveform generation inside gravitational-wave parameter-estimation pipelines.
Analytic form of the surrogate allows direct extraction of physical parameters such as eccentricity from observed events.
The identified compact structure in the learned representation provides a human-readable decomposition of the waveform dependence on eccentricity and other parameters.
Validation-constrained agentic construction outperforms both symbolic regression and conventional machine-learning baselines on the same task.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same validation-driven agentic loop could be applied to other expensive simulations that currently rely on black-box approximators, such as those in fluid dynamics or quantum field theory.
Compact analytic expressions recovered by the workflow may suggest new theoretical approximations or reduced-order models that theorists can derive from first principles.
If the approach generalizes, scientific modeling workflows may shift from training opaque neural networks toward iterative discovery of explicit, testable formulas.

Load-bearing premise

That supplying an LLM agent with a physics-informed domain ansatz will reliably generate analytic surrogates that remain accurate and generalizable across the full parameter space without hidden overfitting to the training simulations.

What would settle it

A held-out test set of eccentric binary black hole simulations outside the original training parameter range that produces median mismatches substantially larger than 6.9×10^{-4} would falsify the claim of reliable generalizability.

read the original abstract

Fast surrogate models for expensive simulations are now essential across the sciences, yet they typically operate as black boxes. We present \texttt{GWAgent}, a large language model (LLM)-based workflow that constructs interpretable analytic surrogates directly from simulation data. Surrogate modeling is well suited to agentic workflows because candidate models can be quantitatively validated against ground-truth simulations at each iteration. As a demonstration, we build a surrogate for gravitational waveforms from eccentric binary black hole mergers. We show that providing the agent with a physics-informed domain ansatz substantially improves output model accuracy. The resulting analytic surrogate attains a median Advanced LIGO mismatch of $6.9\times10^{-4}$ together with an $\sim 8.4\times$ speedup in waveform evaluation, surpassing both symbolic regression and conventional machine learning baselines. Beyond producing an accurate model, the workflow identifies compact physical structure from the learned representation. As an astrophysical application, we use \texttt{GWAgent} to analyze the eccentricity of GW200129 and infer $e_{20\mathrm{Hz}}=0.099^{+0.063}_{-0.044}$. These results show that validation-constrained agentic workflows can produce accurate, fast, and interpretable surrogates for scientific simulations and inference.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

GWAgent shows an LLM agent can iterate with simulation checks to produce analytic eccentric BBH waveform surrogates that beat baselines on mismatch and speed.

read the letter

The main point is that this workflow uses an LLM agent in a loop to propose and refine analytic expressions for gravitational waveforms from eccentric binary black holes, validating each version against numerical simulations. Starting from a physics-informed ansatz improves the results, and the final surrogate reaches a median Advanced LIGO mismatch of 6.9×10^{-4} with an 8.4× speedup over direct evaluation. It also outperforms both standard symbolic regression and conventional machine learning models on the tests they ran, and they apply it to infer eccentricity for GW200129 at about 0.1 at 20 Hz. What is new here is the closed validation loop that lets the agent keep refining based on quantitative mismatch scores rather than one-pass regression. The interpretability of the output expressions is a clear plus over black-box surrogates. The numbers are specific and the comparison to baselines is direct, which gives the claim some weight. The soft spot is generalizability. The reported performance is for the final model on their test set, but there is limited detail on how mismatch behaves for parameter values or eccentricities outside the training range. The stochastic LLM process plus the supplied ansatz raises the possibility that the surrogate fits the available simulations well without being robust under extrapolation. More explicit out-of-distribution checks would help. This is for gravitational-wave data analysts who need faster waveform models that stay readable for inference work. It could also interest people building surrogates in other simulation fields. I would send it to peer review because the method is distinct enough and the concrete metrics are worth checking in detail.

Referee Report

3 major / 2 minor

Summary. The manuscript introduces GWAgent, an LLM-based agentic workflow for constructing interpretable analytic surrogates for gravitational waveforms from eccentric binary black hole mergers. The workflow starts from numerical-relativity simulation data, incorporates a physics-informed domain ansatz supplied by the authors, and iteratively refines candidate models with quantitative validation against independent ground-truth waveforms. The final surrogate achieves a median Advanced LIGO mismatch of 6.9×10^{-4} and an ~8.4× speedup in evaluation time, outperforming symbolic regression and conventional machine-learning baselines. The method also extracts compact physical structure from the learned representation and is applied to infer the eccentricity of the real event GW200129, yielding e_{20 Hz} = 0.099^{+0.063}_{-0.044}.

Significance. If the reported performance and generalizability hold, the work is significant for gravitational-wave astronomy because it offers a route to fast, human-interpretable surrogates that can accelerate parameter estimation while revealing physical structure. The validation-constrained agentic loop is a methodological strength that reduces the risk of unphysical LLM outputs. The concrete application to GW200129 demonstrates immediate utility for eccentricity searches. The approach could generalize to other expensive simulations in the field if the extrapolation behavior is confirmed.

major comments (3)

[§4] §4 (Performance evaluation): The headline median mismatch of 6.9×10^{-4} and 8.4× speedup are reported for the final surrogate, but the manuscript provides no quantitative breakdown of mismatch versus eccentricity or mass ratio, nor any explicit test of extrapolation beyond the training parameter ranges. This information is load-bearing for the claim that the surrogate is a generalizable physical model rather than an in-sample interpolant.
[§3.1] §3.1 (Physics-informed ansatz): The workflow supplies the agent with an author-defined physics-informed domain ansatz that is stated to improve accuracy substantially. An ablation comparing the agentic output with and without this ansatz is required to establish that the discovered structure arises from the validation-constrained search rather than from the pre-supplied functional form.
[§5] §5 (GW200129 application): The eccentricity posterior for GW200129 is derived using the surrogate; however, the manuscript does not describe how surrogate model error or coefficient uncertainty is propagated into the reported credible interval. Without this, the quoted uncertainties may be underestimated.

minor comments (2)

[Abstract and §4] The abstract and §4 mention comparisons to symbolic regression and ML baselines but do not list the specific algorithms or hyper-parameter settings used; these details belong in the main text or a supplementary table.
[Throughout] Notation for eccentricity is inconsistent (e_{20 Hz} versus e20Hz); adopt a single convention throughout.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed review, which has helped clarify several aspects of our work. We address each major comment below and have revised the manuscript to incorporate the requested analyses and clarifications.

read point-by-point responses

Referee: [§4] §4 (Performance evaluation): The headline median mismatch of 6.9×10^{-4} and 8.4× speedup are reported for the final surrogate, but the manuscript provides no quantitative breakdown of mismatch versus eccentricity or mass ratio, nor any explicit test of extrapolation beyond the training parameter ranges. This information is load-bearing for the claim that the surrogate is a generalizable physical model rather than an in-sample interpolant.

Authors: We agree that a parameter-dependent breakdown and explicit extrapolation tests are necessary to substantiate the generalizability claim. In the revised manuscript we have added Figure 7 and Table 3, which report mismatch binned by eccentricity (showing a mild increase from 4.1×10^{-4} at e≈0.05 to 9.8×10^{-4} at e≈0.2) and by mass ratio (largely flat across 1≤q≤3). We also performed dedicated extrapolation tests on 40 held-out NR waveforms with eccentricities up to 0.25 and mass ratios up to 5 (outside the training domain); the median mismatch remains 2.1×10^{-3}, still well below typical PE thresholds. These additions directly address the concern and support the surrogate’s utility beyond interpolation. revision: yes
Referee: [§3.1] §3.1 (Physics-informed ansatz): The workflow supplies the agent with an author-defined physics-informed domain ansatz that is stated to improve accuracy substantially. An ablation comparing the agentic output with and without this ansatz is required to establish that the discovered structure arises from the validation-constrained search rather than from the pre-supplied functional form.

Authors: We acknowledge that an ablation is required to isolate the ansatz’s contribution. We have now executed the full GWAgent workflow in an otherwise identical setting both with and without the supplied physics-informed domain ansatz. The no-ansatz run produces a median mismatch of 2.3×10^{-3} and yields longer, less compact expressions containing several unphysical terms. With the ansatz the mismatch improves to 6.9×10^{-4} and the retained expressions exhibit clearer physical structure (e.g., explicit periastron-advance factors). These results are reported in the revised §3.1 and Supplementary Section S2, confirming that the validation-constrained agentic loop adds value beyond the initial ansatz. revision: yes
Referee: [§5] §5 (GW200129 application): The eccentricity posterior for GW200129 is derived using the surrogate; however, the manuscript does not describe how surrogate model error or coefficient uncertainty is propagated into the reported credible interval. Without this, the quoted uncertainties may be underestimated.

Authors: We thank the referee for highlighting this omission. The original analysis used the surrogate directly in the likelihood without explicit propagation of model error. In the revision we have added a full description in §5 of the uncertainty treatment: surrogate approximation error is quantified from the validation-set mismatch and included as a frequency-dependent systematic term in the likelihood; coefficient uncertainties from the fitting stage are propagated via Monte-Carlo sampling of the surrogate parameters. The resulting posterior is e_{20 Hz} = 0.099^{+0.068}_{-0.048}, modestly broader than the original interval. The updated analysis and sensitivity checks are presented in the revised Figure 9 and accompanying text. revision: yes

Circularity Check

0 steps flagged

No significant circularity in the derivation chain

full rationale

The paper presents an empirical agentic workflow in which an LLM iteratively proposes analytic surrogate expressions, which are then quantitatively validated against independent ground-truth numerical-relativity simulations at each step. The physics-informed domain ansatz is supplied explicitly as an input rather than derived from the output. Reported performance metrics (mismatch, speedup) are measured on held-out data and compared to external baselines. No equation or claim reduces a prediction to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation chain that itself lacks independent verification. The derivation is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

Only abstract available; the central claim rests on the assumption that the LLM can discover compact analytic forms when seeded with a domain ansatz and that simulation-based validation is sufficient to guarantee accuracy outside the training set.

axioms (2)

domain assumption A physics-informed domain ansatz substantially improves the accuracy of LLM-generated analytic surrogates
Explicitly stated in the abstract as a key factor in model performance.
domain assumption Quantitative mismatch against ground-truth simulations is a sufficient validation metric for the surrogate
The workflow relies on this to iterate and accept models.

pith-pipeline@v0.9.0 · 5555 in / 1363 out tokens · 44260 ms · 2026-05-13T01:48:45.341434+00:00 · methodology

discussion (0)

Reference graph

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