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arxiv: 2607.00178 · v1 · pith:UQ4REIF4new · submitted 2026-06-30 · ⚛️ physics.comp-ph

A Scoping Review of Physics Informed Machine Learning for Wave Propagation Modeling in Seismology

\'Oscar Rinc\'on-Carde\~no , Gregorio P\'erez-Bernal , Silvana Montoya-Noguera , Nicol\'as Guar\'in-Zapata This is my paper

Pith reviewed 2026-07-02 00:46 UTC · model grok-4.3

classification ⚛️ physics.comp-ph
keywords physics-informed machine learningseismologywave propagationscoping reviewforward modelinginverse problemsPINN
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The pith

Physics-informed machine learning has been applied to seismic wave propagation in both forward modeling and inversion, often matching numerical method accuracy at lower computational cost.

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

This scoping review maps applications of physics-informed machine learning to seismic wave propagation governed by partial differential equations. Selected studies are sorted by problem type, forward or inverse, and by the machine learning strategy employed. The survey finds that these methods have achieved accuracy levels comparable to conventional numerical techniques while incurring lower computational expense. Three mechanisms for embedding physical knowledge are distinguished: observational bias, inductive bias, and learning bias. The review concludes that such approaches remain complementary to standard numerical methods, especially for inverse problems and surrogate modeling, while noting persistent gaps in benchmarking consistency and scaling to three-dimensional or experimentally validated settings.

Core claim

Physics-informed machine learning has been applied to both forward modeling and inversion in seismology, often reaching accuracy comparable to standard numerical methods at lower computational cost. Application of three mechanisms for incorporating physical knowledge were identified: observational bias, inductive bias, and learning bias. Replication of the original PINN framework produced results consistent with and in most cases more accurate than those originally reported.

What carries the argument

Classification of studies by problem type (forward or inverse) and machine learning strategy, together with the three mechanisms for incorporating physical knowledge into the training process.

Load-bearing premise

The chosen databases and classification scheme captured a representative sample of relevant studies without major omissions or selection bias.

What would settle it

A large set of studies on physics-informed machine learning for seismic waves that were not retrieved by the search, or direct comparisons showing that the replicated methods fail to match reported accuracy.

read the original abstract

\emph{Background:} Standard numerical methods accurately simulate seismic waves but are computationally expensive, particularly for inverse problems. Machine learning approaches have been proposed as alternatives that can reduce computational cost while maintaining acceptable physical accuracy. \emph{Objective:} To map how physics-informed machine learning methods have been applied to seismic wave propagation modeling based on partial differential equations. \emph{Methods:} A scoping review was conducted using the OpenAlex and Scopus databases. Selected studies were classified by problem type (forward or inverse) and machine learning strategy to identify research trends, methodological patterns, and gaps in the literature. \emph{Results:} Physics-informed machine learning has been applied to both forward modeling and inversion in seismology, often reaching accuracy comparable to standard numerical methods at lower computational cost. Application of three mechanisms for incorporating physical knowledge were identified: observational bias, inductive bias, and learning bias. To evaluate methodological reproducibility of a representative method, the original PINN framework was replicated in PyTorch, obtaining results consistent with and in most cases more accurate than those originally reported. From the reviewed literature, limitations remain in benchmarking consistency, training cost, and scalability to three-dimensional and experimentally validated problems. \emph{Conclusions:} Standard numerical methods remain the basis of seismological workflows, while physics-informed machine learning offers complementary approaches that are useful for inverse problems and surrogate modeling. Future work should focus on consistent benchmarking, hybrid formulations, and validation under realistic geophysical conditions.

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 manuscript is a scoping review that maps applications of physics-informed machine learning to seismic wave propagation modeling. It reports a literature search in OpenAlex and Scopus, classifies studies by problem type (forward/inverse) and ML strategy (observational, inductive, and learning bias), concludes that these methods often achieve accuracy comparable to numerical methods at lower cost, presents a PyTorch replication of the original PINN framework yielding consistent or improved results, and notes remaining limitations in benchmarking consistency, training cost, and scalability to 3D/experimental cases. The conclusion positions PIML approaches as complementary to standard numerical methods for inverse problems and surrogate modeling.

Significance. If the sampled literature is representative, the review would usefully synthesize trends and gaps in PIML for seismology. The explicit replication of the PINN framework constitutes a concrete strength by demonstrating reproducibility for at least one case. The aggregate performance claim ('often' comparable accuracy at lower cost) would be informative for the field if supported by transparent search and selection procedures.

major comments (2)
  1. [Methods] Methods section (and abstract): the scoping review description provides no search strings, inclusion/exclusion criteria, screening counts, or PRISMA flow diagram. Without these, the representativeness of the OpenAlex/Scopus sample cannot be evaluated, directly undermining the load-bearing claim that PIML methods 'often' reach accuracy comparable to numerical methods at lower computational cost.
  2. [Results] Results section: the classification of studies into observational bias, inductive bias, and learning bias is stated without explicit operational definitions, decision rules, or a table mapping individual papers to categories. This makes it impossible to assess whether the taxonomy is applied consistently or exhaustively across the reviewed set.
minor comments (2)
  1. [Results] The replication is described only at a high level; adding quantitative metrics (e.g., L2 error values, training epochs) comparing the PyTorch implementation to the original would strengthen the reproducibility claim.
  2. Ensure every cited study is accompanied by a stable identifier (DOI or arXiv ID) so readers can locate the primary sources used for the trends and performance statements.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback on our scoping review. We agree that the Methods and Results sections require additional detail to ensure transparency and reproducibility. We address each major comment below and will incorporate revisions in the next version of the manuscript.

read point-by-point responses

  1. Referee: [Methods] Methods section (and abstract): the scoping review description provides no search strings, inclusion/exclusion criteria, screening counts, or PRISMA flow diagram. Without these, the representativeness of the OpenAlex/Scopus sample cannot be evaluated, directly undermining the load-bearing claim that PIML methods 'often' reach accuracy comparable to numerical methods at lower computational cost.

    Authors: We acknowledge the omission of these procedural details. The literature search was performed using specific queries in OpenAlex and Scopus, followed by screening according to defined inclusion/exclusion criteria, but these elements were not reported in the submitted manuscript. We will expand the Methods section to include the exact search strings, inclusion/exclusion criteria, screening counts, and a PRISMA flow diagram. This addition will allow readers to evaluate sample representativeness and will provide transparent support for the aggregate performance observations. revision: yes

  2. Referee: [Results] Results section: the classification of studies into observational bias, inductive bias, and learning bias is stated without explicit operational definitions, decision rules, or a table mapping individual papers to categories. This makes it impossible to assess whether the taxonomy is applied consistently or exhaustively across the reviewed set.

    Authors: We agree that the classification requires explicit operational definitions and a mapping to ensure consistency. We will add clear definitions and decision rules for each bias category (observational, inductive, and learning bias) in the Results section, along with a table (or supplementary table) that maps each reviewed study to its assigned category with brief justification based on the paper's methodology. revision: yes

Circularity Check

0 steps flagged

No circularity: scoping review performs literature synthesis with no derivations or self-referential predictions

full rationale

This is a scoping review paper whose core activity is database search, classification of existing studies by problem type and ML strategy, and one external replication of a prior PINN implementation. No equations, fitted parameters, or predictions are defined within the paper that could reduce to its own inputs by construction. The 'often reaching accuracy comparable' statement is an aggregate observation drawn from the reviewed literature rather than a derived result internal to this manuscript. Self-citations, if present, are not load-bearing for any uniqueness theorem or ansatz. The work is self-contained as a descriptive synthesis against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The review's conclusions rest on the representativeness of the database search and the validity of the classification scheme; no free parameters or invented entities are introduced.

axioms (1)
  • domain assumption OpenAlex and Scopus databases provide sufficient coverage of relevant studies on physics-informed machine learning for wave propagation.
    Methods rely on these two databases for the literature search.

pith-pipeline@v0.9.1-grok · 5816 in / 1167 out tokens · 40088 ms · 2026-07-02T00:46:50.918157+00:00 · methodology

discussion (0)

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