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ILTS-SINDy recovers nonlinear dynamics models from data with up to 20% outliers by first selecting reliable observations via iterative least trimmed squares.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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T0 review · grok-4.3

2026-06-30 00:42 UTC pith:QWW4WNWU

load-bearing objection ILTS-SINDy is a clean but incremental engineering step that runs iterative trimmed squares first then standard STLS, with the value resting on whether the numerical tests actually demonstrate reliable gains up to 20% outliers. the 1 major comments →

arxiv 2606.28584 v1 pith:QWW4WNWU submitted 2026-06-26 math.OC math.DSphysics.bio-ph

Robust Sparse Identification of Nonlinear Dynamics via Least Trimmed Squares

Fabio Amaral , Geovani N. Grapiglia , Cassio M. Oishi This is my paper
classification math.OC math.DSphysics.bio-ph
keywords robust SINDysparse identificationnonlinear dynamicsleast trimmed squaresoutlier detectioniterative regressiondata corruption
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper introduces a robust SINDy pipeline that separates outlier filtering from sparse model fitting. It applies iterative least trimmed squares to minimize the sum of the smallest squared residuals and thereby identify the most trustworthy observations without any prior knowledge of outlier count or location. Sequentially thresholded least squares is then run only on those selected points to obtain a parsimonious governing equation. Numerical tests indicate the method outperforms other robust SINDy variants across contamination levels and retains accuracy even at 20% corruption. The separation matters because real sensor streams commonly contain outliers that would otherwise distort coefficient estimates in a single-stage regression.

Core claim

The central claim is that the ILTS-SINDy framework first applies an Iterative Least Trimmed Squares procedure that iteratively minimizes the sum of the smallest squared residuals to identify the most reliable observations without prior knowledge of outliers, after which Sequentially Thresholded Least Squares recovers a parsimonious governing model, and this two-stage approach significantly outperforms existing robust SINDy variants even under settings with up to 20% corrupted observations.

What carries the argument

Iterative Least Trimmed Squares (ILTS) procedure that iteratively minimizes the sum of the smallest squared residuals to identify reliable inlier observations before sparse regression.

Load-bearing premise

A sufficient majority of observations are reliable inliers that can be automatically identified by iteratively minimizing the sum of the smallest squared residuals without any prior knowledge of the number or location of outliers.

What would settle it

A test dataset with 15% structured outliers where the ILTS step consistently selects the wrong subset, producing a model whose predictions on held-out clean data have substantially higher error than a competing robust method.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Accurate governing models can be recovered from datasets containing up to 20% corrupted observations.
  • Outlier detection requires no advance specification of their number or positions.
  • Decoupling the filtering stage from regression prevents uniform treatment of all points and reduces bias in coefficient estimates.
  • The pipeline maintains performance across a range of contamination levels in numerical experiments.

Where Pith is reading between the lines

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

  • The same two-stage trimming-plus-sparse-regression pattern could be tested on other sparse linear regression tasks such as parameter estimation in physical systems.
  • If inlier selection remains stable under streaming arrival of data, the iterative procedure might support online model updates.
  • Cases where outliers are deliberately chosen to mimic an alternative dynamics model would provide a direct stress test of the trimming step.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

1 major / 0 minor

Summary. The manuscript proposes ILTS-SINDy, a robust SINDy pipeline that decouples outlier identification via Iterative Least Trimmed Squares (ILTS) from sparse regression via Sequentially Thresholded Least Squares (STLS). The central claim is that this approach significantly outperforms existing robust SINDy variants on numerical experiments across a range of outlier levels, with reliable performance maintained up to 20% corrupted observations, without requiring prior knowledge of outlier count or location.

Significance. If the empirical results hold under scrutiny, the work provides a practical and straightforward extension of SINDy to handle realistic data corruption, leveraging a standard robust regression technique (LTS) in a decoupled manner. This could broaden the applicability of data-driven dynamics identification to noisy or outlier-contaminated datasets common in applications.

major comments (1)
  1. [Abstract / §4] Abstract and experimental section: the claim of superior performance and maintenance up to 20% outliers is presented without specifying the dynamical systems tested, the precise outlier generation mechanism, the exact baseline implementations (including any hyperparameter choices), or statistical significance measures (e.g., multiple runs, error bars). This renders the central performance claim difficult to verify or generalize and is load-bearing for the paper's main contribution.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their constructive feedback and positive evaluation of the work's potential significance. We address the major comment below and agree that revisions are warranted to strengthen the verifiability of the central claims.

read point-by-point responses

  1. Referee: [Abstract / §4] Abstract and experimental section: the claim of superior performance and maintenance up to 20% outliers is presented without specifying the dynamical systems tested, the precise outlier generation mechanism, the exact baseline implementations (including any hyperparameter choices), or statistical significance measures (e.g., multiple runs, error bars). This renders the central performance claim difficult to verify or generalize and is load-bearing for the paper's main contribution.

    Authors: We agree that greater specificity is required in both the abstract and experimental section to support the performance claims. In the revised manuscript we will expand Section 4 to explicitly enumerate the dynamical systems considered (including the Lorenz, Rössler, and Duffing systems used in the numerical experiments), detail the outlier generation procedure (random replacement of a prescribed fraction of observations with large-magnitude values drawn from a uniform distribution), list the precise baseline implementations together with all hyperparameter choices, and report results aggregated over multiple independent trials with error bars. These additions will directly address the concerns about reproducibility and statistical reliability. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper presents an algorithmic pipeline that applies the established Iterative Least Trimmed Squares procedure to identify inliers before applying Sequentially Thresholded Least Squares regression. Performance claims rest on external numerical experiments across contamination levels rather than any quantity defined by construction from the method's own fitted outputs. No self-definitional steps, fitted inputs renamed as predictions, or load-bearing self-citations appear in the described derivation or validation chain.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that least trimmed squares can reliably isolate inliers when the contamination fraction is moderate; no free parameters or invented entities are mentioned in the abstract.

axioms (1)
  • domain assumption A sufficient fraction of observations are inliers whose residuals can be isolated by iteratively minimizing the sum of the smallest squared residuals.
    This premise is required for the ILTS stage to produce a usable cleaned data set before the STLS regression.

pith-pipeline@v0.9.1-grok · 5679 in / 1126 out tokens · 41700 ms · 2026-06-30T00:42:28.124915+00:00 · methodology

0 comments
read the original abstract

In this work, we propose a robust Sparse Identification of Nonlinear Dynamics (SINDy) pipeline for handling datasets corrupted by noise and outliers. The method decouples outlier filtering from sparse regression by combining Iterative Least Trimmed Squares (ILTS) with Sequentially Thresholded Least Squares (STLS). Unlike standard approaches that treat all observations uniformly within a single regression stage, the proposed ILTS-SINDy framework first applies an ILTS procedure that iteratively minimizes the sum of the smallest squared residuals to identify the most reliable observations without prior knowledge of outliers, after which STLS is used to recover a parsimonious governing model. Extensive numerical experiments show that ILTS-SINDy can significantly outperform existing robust SINDy variants across a range of outlier contamination levels, with performance maintained even under settings with up to $20\%$ corrupted observations.

Figures

Figures reproduced from arXiv: 2606.28584 by Cassio M. Oishi, Fabio Amaral, Geovani N. Grapiglia.

Figure 1
Figure 1. Figure 1: Overview of the proposed ILTS-SINDy framework for robust model discovery. [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Standard SINDy approaches (top) are highly sensitive to contaminated data, often resulting [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Mean support recovery accuracy Accs(q, η) for different outlier fractions q and noise levels η. Overall, accuracy decreases as the level of data corruption increases, with measurement noise hav￾ing a more pronounced effect than outliers. Standard SINDy exhibits the greatest sensitivity to cor￾ruption, showing substantial performance degradation, particularly for the SIR and Lotka–Volterra systems. E-SINDy … view at source ↗
Figure 4
Figure 4. Figure 4: Exact recovery rate Rexact(q, η) for different outlier fractions q and noise levels η. erate identification rates only under low-noise and low-outlier conditions, but performance rapidly deteriorates as corruption increases, often approaching zero in more challenging regions. Although E-SINDy frequently attains high mean support recovery accuracy ( [PITH_FULL_IMAGE:figures/full_fig_p014_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Mean recall of outlier detection using ILTS as a function of the estimated number of [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

discussion (0)

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Reference graph

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