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REVIEW 4 major objections 5 minor 1 cited by

A comprehensive analysis of PINNs: Variants, Applications, and Challenges

T0 review · 4 major / 5 minor · reviewed 2026-08-07 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read This survey maps the full PINN landscape: core architecture, equation classes, variants, applications, and open challenges in one reference.

desk verdict A serviceable but unreliable PINN survey: the structure works, yet the core summaries of cited papers contain concrete errors that break the comprehensiveness claim until fixed. read the letter →

arxiv 2505.22761 v1 pith:L7GWHVK2 submitted 2025-05-28 cs.CE cs.AI

Afila Ajithkumar Sophiya , Akarsh K Nair , Sepehr Maleki , Senthil K. Krishnababu This is my paper
classification cs.CEcs.AI
keywords physics-informedneuralnetworksPINNsdifferentialequationsscientificmachinelearningdeepfractionalPDEssurvey
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper attempts to establish that physics-informed neural networks (PINNs) can be understood as a single coherent technology with a common architectural template, a small family of named variants, a set of equation classes they target, and a spread of real-world applications. It argues that existing surveys are either too shallow or too narrowly focused, and that a combined analysis is needed to guide both newcomers and practitioners. If the survey is accurate, it gives readers a reliable map for choosing a PINN variant for a problem class and for locating unresolved research gaps.

What carries the argument

The organizing object is the PINN architecture itself: a neural network that converts a differential equation into an unconstrained optimization problem through a loss function of the form $L(\Theta)=w_f L_f + w_{ic}L_{ic}+w_{bc}L_{bc}$, where $L_f$ is the squared residual of the governing equation at collocation points, $L_{ic}$ and $L_{bc}$ penalize mismatches with initial and boundary conditions, and derivatives are computed by automatic differentiation. The survey uses this template as the common baseline against which every variant, equation class, and application is compared.

What would settle it

A systematic literature search that finds a major PINN variant or application area absent from the survey, or an audit showing that a substantial share of the survey's one-line summaries mischaracterize the cited papers, would falsify the paper's claim to be comprehensive.

Watch

Extended reading notes

Core claim

The paper's central claim is that the PINN literature organizes cleanly along several axes: the underlying architecture (a neural network combined with automatic differentiation and a physics-constrained loss function), the class of equations being solved (ordinary, partial, and fractional differential equations), the family of variants (cPINNs, XPINNs, APINNs, fPINNs, DPINNs, fuzzy and interval PINNs, and others), and the application domains (medical imaging, power systems, fluid mechanics, and beyond). It further claims that the major challenges—optimization strategy, loss-function design, generalization, convergence analysis, and error estimation—cut across all of these axes, and that these shared problems define the most promising research directions.

Load-bearing premise

The survey is only as accurate and complete as the manually chosen set of papers it summarizes, and at least one of its summaries is already contradicted by the cited paper's own title.

Editorial extensions

If this is right

  • A practitioner can use the survey to match a PINN variant to a problem type, for example XPINNs for domain decomposition or fPINNs for fractional equations.
  • The taxonomy shows that most variants are modifications of the loss function, the differentiation scheme, or the domain-decomposition strategy, not fundamentally new architectures.
  • The challenges list acts as a research agenda, identifying optimization, generalization, convergence analysis, and error estimation as the open problems most worth attacking.
  • The application cases demonstrate where PINNs already work well, such as fluid mechanics and medical imaging, and where they remain immature.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The survey's comprehensiveness claim could be tested by running a systematic literature search to see whether any major PINN variant or application area is missing from its tables.
  • The paper's own observation that theoretical proofs are largely absent points toward a concrete research program: proving convergence and error bounds for specific PINN variants on specific equation classes.
  • The challenges the paper lists suggest that standardizing benchmark problems, error metrics, and convergence tests across PINN variants would be the natural next step for the field.
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Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This manuscript is a survey of physics-informed neural networks. It presents the general PINN architecture and its components, discusses PINNs for ODEs, PDEs, and fractional PDEs, catalogs PINN variants, surveys applications in medicine, power systems, and fluid mechanics, and lists open challenges and future directions. The paper claims to provide a comprehensive, integrated analysis that existing surveys lack, and its contributions are framed as a broad overview of architecture, variants, applications, and challenges.

Significance. If its characterizations were reliable, the survey would offer a useful point of entry to the PINN literature, and its consolidated tables and challenge list would help practitioners locate methods by equation type and application domain. The paper's scope is genuinely broad and it does make an effort to compare approaches across ODE, PDE, fractional, and application settings. However, the survey's usefulness rests on the faithfulness of its per-paper summaries, and several of those summaries are demonstrably incorrect in ways that affect the classification tables. The paper also lacks a defined selection methodology, which weakens the 'comprehensive' claim. These problems are correctable, but they are central to the survey's value, so the manuscript needs substantial revision before it can serve as a reliable reference.

major comments (4)
  1. [Section 5 and Table 3] The prose states that Fang et al. [31] proposed a PINN framework for 'time-dependent constrained surface PDEs', and Table 3 labels the row as 'Time dependant eliptical PDEs on 3D surfaces'. The cited paper's title is 'A physics-informed neural network framework for PDEs on 3D surfaces: Time independent problems'. The time-dependence classification is a substantive property, not a wording preference, and directly contradicts the source title; this is a load-bearing error in the survey's core classification.
  2. [Section 5 and Table 3] The text describes Sun et al. [27] as solving 'second-order parametric light wave equations' and calls the model a 'gPINN architecture' built with a 'second-order neural network structure'. The cited paper is titled 'A second-order network structure based on gradient-enhanced physics-informed neural networks for solving parabolic partial differential equations'. The equation class is misattributed ('light wave' versus 'parabolic'), so the table entry and the accompanying discussion do not faithfully represent the source.
  3. [References] References [4] and [65] are the same paper: Raissi, Perdikaris, and Karniadakis, 'Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations', Journal of Computational Physics, 378:686-707, 2019. Listing the same work twice inflates the bibliography and is a bibliographic error that should be fixed.
  4. [Sections 6 and 7] The acronym 'fPINNs' is used for fractional PINNs in Section 6 and in variant 4 of Section 7, but in variant 6 of Section 7 the same acronym is used for fuzzy PINNs proposed by Fuhg et al. [56]. Reusing the same acronym for two different methods within one survey creates genuine ambiguity and should be resolved, for example by a distinct label for the fuzzy variant.
minor comments (5)
  1. [Abstract and Section 2] The abstract says the contributions 'can be summarised into three sections', while Section 2 lists seven numbered contributions; the relationship between the three-part summary and the seven-item list should be reconciled.
  2. [Table 2 heading] The table heading reads 'PINNs used for solving solving ordinary differential equations'; the duplicated word 'solving' should be removed.
  3. [Sections 5 and 8] The name 'Beavers–Joseph–Saffman' is consistently misspelled as 'Bever–Joseph–Saffman', and 'Eulers' should be 'Euler's'; these typos should be corrected throughout.
  4. [Table 3] The row for [31] contains the spelling 'Time dependant eliptical PDEs'; 'dependant' should be 'dependent' and 'eliptical' should be 'elliptical'.
  5. [Section 5] The text refers to 'gPINN' for [27] but the source title uses 'gradient-enhanced physics-informed neural networks'; the notation should be introduced consistently and not conflated with other uses of 'gPINN'.

Circularity Check

0 steps flagged · score 1.0 of 10

No material circularity: the survey is an expository synthesis of external papers, with no derived result, fitted parameter, or load-bearing self-citation.

full rationale

This paper is a literature survey rather than a derivation chain. It does not fit parameters, make predictions from an ansatz, or invoke a uniqueness theorem; its claims are summaries and classifications of other papers. The only place where an inference could be circular would be if its own taxonomy were used to certify its completeness, but the paper is explicit that selection is discretionary ('only articles with commendable research contributions have been included in this study', Section 2) and that the coverage is limited ('we are forced to limit our discussion to a selected few due to the limited scope', Section 6). Section 9 itself notes that 'the majority of the existing literature lacks theoretical or mathematical proofs', which further shows the authors are not relying on their own prior theorems. The observed problems, such as the description of reference [31] as 'time-dependent' despite its title 'Time independent problems' (Section 5 and Table 3) and the overloaded acronym 'fPINNs' for both fractional and fuzzy PINNs (Sections 6 and 7), are accuracy or consistency flaws in the survey's reporting; they do not make any claim reduce to its own input. Because the paper is not self-referential in its argument, any weakness is a correctness/coverage concern, not circularity.

Assumptions & free parameters 0 free parameters · 2 assumptions · 0 invented entities

No original derivations, parameters, or entities are introduced; the paper is a narration of existing work. The main load-bearing input is the accuracy of the literature review.

assumptions (2)
  • domain assumption The 73 cited papers are accurately and representatively summarized.
    The survey's reliability rests entirely on the fidelity of its literature summaries; no independent verification or systematic selection criteria are provided.
  • domain assumption The categorization of PINN work into ODE, PDE, fractional, and application domains is a meaningful and complete partition.
    The survey imposes a structure on the literature that is not justified by a formal taxonomy or comparison with prior taxonomies.

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Cite this review

Pith. "Pith review of A comprehensive analysis of PINNs: Variants, Applications, and Challenges." pith.science (2026). https://pith.science/paper/L7GWHVK2

@misc{pith2026250522761,
  author       = {Pith},
  title        = {Pith review of: A comprehensive analysis of PINNs: Variants, Applications, and Challenges},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/L7GWHVK2}},
  note         = {Machine review of arXiv:2505.22761}
}
read the original abstract

Physics Informed Neural Networks (PINNs) have been emerging as a powerful computational tool for solving differential equations. However, the applicability of these models is still in its initial stages and requires more standardization to gain wider popularity. Through this survey, we present a comprehensive overview of PINNs approaches exploring various aspects related to their architecture, variants, areas of application, real-world use cases, challenges, and so on. Even though existing surveys can be identified, they fail to provide a comprehensive view as they primarily focus on either different application scenarios or limit their study to a superficial level. This survey attempts to bridge the gap in the existing literature by presenting a detailed analysis of all these factors combined with recent advancements and state-of-the-art research in PINNs. Additionally, we discuss prevalent challenges in PINNs implementation and present some of the future research directions as well. The overall contributions of the survey can be summarised into three sections: A detailed overview of PINNs architecture and variants, a performance analysis of PINNs on different equations and application domains highlighting their features. Finally, we present a detailed discussion of current issues and future research directions.

Figures

Figures reproduced from arXiv: 2505.22761 by the authors.

Figure 1
Figure 1. Generalised architecture of PINNs model be expressed as exact expressions with no approximation error. In AD, a function is decomposed into differentiable sub-functions, and intermediate variables hold the data in the function at different points. Rather than calculating a closed-form expression or estimating the derivative considering the neighboring points, AD takes advantage of this feature, and the chain rule is… view at source ↗

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Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A physics-informed neural network approach to the point defect model for electrochemical oxide film growth

    cond-mat.mtrl-sci 2025-10 conditional novelty 5.0 of 10

    A hybrid PINN anchored by one FEM data point reproduces point-defect-model film thicknesses to about 1% error, while the pure PINN overpredicts by 2,400-5,700%.

Reference graph

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Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.