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arxiv: 2412.03932 · v2 · pith:2LJUXZKNnew · submitted 2024-12-05 · 📡 eess.SY · cs.SY

A Physics-Informed Scenario Approach with Data Mitigation for Safety Verification of Nonlinear Systems

Ali Aminzadeh , MohammadHossein Ashoori , Amy Nejati , Abolfazl Lavaei This is my paper

Pith reviewed 2026-05-23 08:09 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords physics-informed scenario approachbarrier certificatessafety verificationnonlinear systemsdata mitigationscenario optimizationprobabilistic guarantees
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The pith

Filtering data samples by closeness to a physics model reduces the dataset size needed for barrier-certificate safety verification.

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

The paper develops a physics-informed scenario approach for safety verification of nonlinear systems. It selects data samples such that physics-based model outputs and observed data are sufficiently close, then uses those samples in scenario optimization to build barrier certificates. This step aims to remove redundant samples and cut the large datasets normally required while targeting the same probabilistic guarantees for unknown dynamics. A sympathetic reader would care because standard scenario methods become impractical when data collection is costly or limited for complex nonlinear systems.

Core claim

The central claim is that a physics-informed scenario approach selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close. This guides the scenario optimization process to eliminate redundant samples and potentially reduce the required dataset size for constructing guaranteed barrier certificates that ensure system trajectories remain within safe regions over an infinite time horizon.

What carries the argument

The physics-informed sample selection that filters observed data by closeness to physics-model outputs before feeding them into scenario optimization for barrier certificates.

If this is right

  • The method reduces the dataset size required to construct guaranteed barrier certificates.
  • It eliminates redundant samples during scenario optimization for nonlinear systems.
  • Probabilistic safety guarantees are intended to hold for the unknown true dynamics.
  • The approach applies to safety verification over an infinite time horizon.
  • It is validated through three case studies demonstrating practical data reduction.

Where Pith is reading between the lines

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

  • The same closeness filter could be tested on other certificate types or optimization-based verification problems beyond barrier certificates.
  • If the physics model is only a coarse approximation, adjusting the closeness threshold might trade data savings against guarantee tightness.
  • The reduced sample count could lower the computational cost of solving the underlying scenario optimization problem in real-time settings.

Load-bearing premise

That filtering samples by closeness to the physics model output preserves the probabilistic safety guarantees of the standard scenario approach for the unknown true dynamics.

What would settle it

An experiment showing that a barrier certificate obtained from the filtered samples is violated by true-system trajectories at a rate exceeding the scenario-approach probability bound.

Figures

Figures reproduced from arXiv: 2412.03932 by Abolfazl Lavaei, Ali Aminzadeh, Amy Nejati, MohammadHossein Ashoori.

Figure 1
Figure 1. Figure 1: Physics-informed BC for the supply-demand model with (a) deterministic guar￾antee and (b) probabilistic guarantee. The quadratic BC is plotted for a small segment in blue, with conditions (2.2a) and (2.2b) being satisfied. Green and red dashed lines represent the initial and unsafe level sets, respectively. We compute φ = 6.18×10−5 and µ(φ) = 0.45φ (cf. Remark 4.3), while estimating L = 11.51 using [NLJ+23… view at source ↗
Figure 2
Figure 2. Figure 2: Physics-informed sampling strategy according to (4.2) for (a) supply-demand and (b) Logistic growth examples, focusing on the region where the maximum jump in sampling occurs. analysis. The regions of interest are as follows: X ∈ [0.1, 1], X0 ∈ [0.1, 0.3], and Xu ∈ [0.7, 1]. We specify the BC structure as B(q, x) = q1x 2 + q2x + q3. Deterministic guarantee. We are given a sample size of S = 90, 000. We sel… view at source ↗
Figure 3
Figure 3. Figure 3: Physics-informed BC for the Logistic growth model with (a) deterministic guar￾antee and (b) probabilistic guarantee. The quadratic BC is plotted for a small segment in blue, with conditions (2.2a) and (2.2b) being satisfied. Green and red dashed lines represent the initial and unsafe level sets, respectively. starting from X0 remain within the safe domain throughout the infinite time horizon with 95% confi… view at source ↗
read the original abstract

This paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs) to ensure that system trajectories remain within safe regions over an infinite time horizon. Designing BCs often relies on an accurate dynamics model; however, such models are often imprecise due to the model complexity involved, particularly when dealing with highly nonlinear systems. In such cases, while scenario approaches effectively address the safety problem using collected data to construct a guaranteed BC for the unknown dynamical system, they often require solving an optimization problem with substantial amounts of data. To address this, we propose a physics-informed scenario approach that selects data samples such that the outputs of the physics-based model and the observed data are sufficiently close. This approach guides the scenario optimization process to eliminate redundant samples and potentially reduce the required dataset size. We validate our approach through three case studies, showcasing its practical application in reducing the required data.

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.

Referee Report

2 major / 2 minor

Summary. The paper develops a physics-informed scenario approach for safety verification of nonlinear systems using barrier certificates (BCs). It selects data samples such that the outputs of an imprecise physics-based model are sufficiently close to the observed data, with the goal of eliminating redundant samples and reducing the dataset size needed to construct a guaranteed BC for the unknown true dynamics. The method is validated on three case studies demonstrating practical data reduction.

Significance. If the filtering step preserves the original probabilistic safety guarantees without introducing bias relative to the unknown true dynamics, the approach could meaningfully lower the data requirements of scenario optimization for barrier-certificate synthesis, a practical bottleneck in data-driven safety verification. The case studies supply empirical evidence of reduced sample counts, but the theoretical contribution hinges on whether the sample-complexity relation is adjusted or shown to remain valid post-filtering.

major comments (2)
  1. [theoretical analysis / main theorem on sample complexity] The central claim that the physics-informed selection 'eliminates redundant samples' while retaining safety guarantees for the unknown dynamics requires an explicit derivation (or reference to a corrected bound) that accounts for the conditioning induced by the closeness filter ||physics_model_output - observed_data|| < threshold. Standard scenario bounds assume i.i.d. draws from the true distribution; the selection step produces a non-i.i.d. subsample whose distribution depends on the (inaccurate) model. Without this derivation the probabilistic guarantee does not automatically transfer.
  2. [problem formulation and algorithm description] The optimization problem formulation after data mitigation must be stated precisely (including any change to the number of decision variables or the violation probability) so that the reader can verify whether the original scenario bound still applies or a new one is derived. The abstract and validation sections alone do not supply this information.
minor comments (2)
  1. [case studies] Clarify the exact definition of the closeness threshold and whether it is chosen a priori or tuned; this affects reproducibility of the reported data reductions.
  2. [numerical results] Add a brief comparison table showing, for each case study, the original scenario sample size N versus the mitigated size together with the achieved violation probability and computation time.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our manuscript. The comments highlight important aspects of the theoretical guarantees and problem formulation that we will clarify in the revision.

read point-by-point responses

  1. Referee: [theoretical analysis / main theorem on sample complexity] The central claim that the physics-informed selection 'eliminates redundant samples' while retaining safety guarantees for the unknown dynamics requires an explicit derivation (or reference to a corrected bound) that accounts for the conditioning induced by the closeness filter ||physics_model_output - observed_data|| < threshold. Standard scenario bounds assume i.i.d. draws from the true distribution; the selection step produces a non-i.i.d. subsample whose distribution depends on the (inaccurate) model. Without this derivation the probabilistic guarantee does not automatically transfer.

    Authors: We agree that the data selection step conditions the samples on closeness to the (imprecise) physics model output and therefore departs from the standard i.i.d. assumption. In the revised manuscript we will add an explicit analysis of the filtered sample set. The derivation will bound the change in violation probability induced by the deterministic filter, showing either that the original scenario bound continues to apply or supplying a modestly adjusted sample-complexity expression that accounts for the worst-case effect of model inaccuracy on the acceptance probability. revision: yes

  2. Referee: [problem formulation and algorithm description] The optimization problem formulation after data mitigation must be stated precisely (including any change to the number of decision variables or the violation probability) so that the reader can verify whether the original scenario bound still applies or a new one is derived. The abstract and validation sections alone do not supply this information.

    Authors: We will insert a dedicated subsection that writes the post-mitigation scenario program in full mathematical detail. The decision variables remain exactly the coefficients of the barrier-certificate function; the only change is the cardinality of the constraint set (now the filtered sample set). We will state the violation probability parameter explicitly and indicate whether it is left unchanged or adjusted by the new sample-complexity result derived in response to the first comment. revision: yes

Circularity Check

0 steps flagged

No circularity: method extends scenario optimization without reducing guarantees to inputs by construction

full rationale

The paper proposes filtering data samples for scenario optimization of barrier certificates by closeness to a physics-based model output, aiming to reduce dataset size while preserving safety verification. No equations or steps in the provided abstract or description show a self-definitional loop, a fitted parameter renamed as a prediction, or a load-bearing self-citation chain that forces the central result. The derivation remains self-contained against the standard scenario approach assumptions, with the data mitigation presented as an empirical heuristic rather than a mathematical identity. External validation via case studies is claimed but does not indicate internal reduction to inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract supplies no explicit free parameters, axioms, or invented entities; the central claim rests on the unstated assumption that the physics model provides a useful reference for sample selection without invalidating guarantees.

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