Simplified Version Research Articles

AUTOMATIC SOLVING OF PHYSICS WORD PROBLEMS

We present a system that solves simple physics word problems (PWPs) stated in the English language. The main feature of the system is that it is deterministic and yields a correct solution based on real physics formulas. The program generates the solution in a tabular form, showing givens, unknowns, and solution steps. We performed a thorough analysis on the previous work in this field. Most of the research was accumulated in math word problem (MWP) solvers. We have found that these programs are not capable of solving problems from Ukrainian physics textbooks. We identified several types of physics problems: theoretical, value conversion, value comparison, unknowns finding, value change. We developed separate problem-solving strategies for each type. The program uses named entity recognition (NER), a technique in natural language processing (NLP), to identify key elements in the problem text. We created a set of rules for marking these entities. Then, problem type recognition is performed. Depending on the type, the list of entities is converted into the internal problem representation. Value conversion and comparison problems are easy to handle. We developed a recursive algorithm for solving unknowns-finding problems which turned out to be a simplified version of Stanford Research Institute Problem Solver (STRIPS) algorithm. However, developing a universal algorithm for solving value-change problems presents a significant challenge. We believe this problem type belongs to the NP-hard class, indicating inherent difficulty in finding optimal solutions. The interface of the program is a web-application. The user can type the problem text and see the solution on a web page. Additionally, the result of NER is presented. Constructing a general problem solver is challenging. While our program can solve basic physics problems, complex problems involving forces, energy, etc., remain unsolved. However, our solver has great potential for future development. We have thoroughly analyzed its capabilities and limitations and proposed ideas for future research.

Reliability and validity of simple Chinese version of grit scale for elementary school students

BackgroundThe Grit scale (GS-12) is a widely used rating scale that assess passion and perseverance. The present study aimed to evaluate the reliability and validity of simple Chinese Version of Grit Scale (GS-SC) among Chinese adolescents.MethodsSeven hundred one primary school students were recruited as Sample 1. Item analysis and exploratory factor analysis (EFA) were conducted on Sample 1 to preliminarily examine the structure of the scale. Sample 2 consisted of 5,384 primary school students. Confirmatory factor analysis (CFA) and verification of reliability and validity were conducted on Sample 2 to establish a formal scale and further verify the psychometric properties by applying item response theory (IRT).ResultsEFA and CFA revealed a clear two-factor structure. The results demonstrated that the Simplified Chinese Version of Grit Scale had adequate internal consistency and re-test reliability. GS-CS also showed good criterion-validity with personality, self-control, effort regulation and academic achievement. Furthermore, all the items show a acceptable fit to the GRM and have good discrimination (ranging from 2.13 to 3.45) and moderate difficulty(ranging from-1.58 to 0.95).ConclusionsThe reliability and validity of the GS-SC are good, indicating that the scale can be used as an effective tool for measuring the grit of primary school students in China.

Unveiling multi-wave patterns: dynamic characterization and sensitivity analysis of the Yu-Toda-Sasa-Fukuyama model in lattice and liquid

In this study, an examination of the Yu-Toda-Sasa-Fukuyama equation is undertaken, a model that characterizes elastic waves in a lattice or interfacial waves in a two layer liquid. Our emphasis lies in conducting a comprehensive analysis of this equation through various viewpoints, including the examination of soliton dynamics, exploration of bifurcation patterns, investigation of chaotic phenomena, and a thorough evaluation of the model’s sensitivity. Utilizing a simplified version of Hirota’s approach, multi-soliton pattens, including 1-wave, 2-wave, and 3-wave solitons, are successfully derived. The identified solutions are depicted visually via 3D, 2D, and contour plots using Mathematica software. The dynamic behavior of the discussed equation is explored through the theory of bifurcation and chaos, with phase diagrams of bifurcation observed at the fixed points of a planar system. Introducing a perturbed force to the dynamical system, periodic, quasi-periodic and chaotic patterns are identified using the RK4 method. The chaotic nature of perturbed system is discussed through Lyapunov exponent analysis. Sensitivity and multistability analysis are conducted, considering various initial conditions. The results acquired emphasize the efficacy of the methodologies used in evaluating solitons and phase plots across a broader spectrum of nonlinear models.

On optical soliton solutions of the higher-order Lakshmanan-Porsezian-Daniel model having the cubic-quintic-septic law in the presence of spatio-temporal and chromatic dispersion

The higher-order Lakshmanan-Porsezian-Daniel equation (LPDE) with the cubic-quintic-septic (CQS) law having spatiotemporal and chromatic dispersion terms (STD-CD) is examined to derive new optical soliton solutions. To accomplish this aim, we operated on a simple version of the new extended auxiliary equation method (SAEM26). The optical soliton solutions of the LPDE with CQS as well as STD-CD are constructed in detail. Moreover, 3D-surface, contour, and 2D plots are presented for the bright and periodic singular soliton solutions. Additionally, the effects of diverse model parameters on the bright soliton structure are surveyed, and these effects are displayed with 2D graphics. The findings established in this work can positively contribute to research in nonlinear optics, while the SAEM26 can be effectively applied to similar nonlinear models.

Physical and unphysical regimes of self-consistent many-body perturbation theory

In the standard framework of self-consistent many-body perturbation theory, the skeleton series for the self-energy is truncated at a finite order N and plugged into the Dyson equation, which is then solved for the propagator G_NGN. We consider two examples of fermionic models, the Hubbard atom at half filling and its zero space-time dimensional simplified version. First, we show that G_NGN converges when N\to∞N→∞ to a limit G_∞\,G∞, which coincides with the exact physical propagator G_{exact}Gexact at small enough coupling, while G_∞ ≠ G_{exact}G∞≠Gexact at strong coupling. This follows from the findings of [Phys. Rev. Lett. 114, 156402 (2015)] and an additional subtle mathematical mechanism elucidated here. Second, we demonstrate that it is possible to discriminate between the G_∞=G_{exact}G∞=Gexact and G_∞≠G_{exact}G∞≠Gexact regimes thanks to a criterion which does not require the knowledge of G_{exact}Gexact, as proposed in [Phys. Rev. B 93, 161102 (2016)].

Passive confinement of reinforced concrete members revisited

AbstractPassive confinement provided by transverse reinforcement is taken into account in the design of reinforced concrete structures subjected to high compressive loading such as columns, piers, or tunnel lining segments. In current guidelines, several models exist to account for this beneficial effect. However, these approaches lack mechanical consistency regarding the three‐dimensional load dispersion of the confining forces. The article addresses this knowledge gap by introducing a new model based on a lower‐bound solution according to the theory of plasticity, along with a simplification regarding the governing confined concrete area. The proposed model and its simplified version are compared to the design approaches proposed by current guidelines, and both are successfully validated against experimental data. The simplified new model is a valuable alternative to existing models in current guidelines, as (i) it is mechanically more consistent, (ii) its application is more straightforward, and (iii) it allows the comprehensive treatment of rectangular and circular cross‐sections using the same equations.

Nonsmooth Pitchfork Bifurcations in a Quasi-Periodically Forced Piecewise-Linear Map

We study a family of one-dimensional quasi-periodically forced maps [Formula: see text], where [Formula: see text] is real, [Formula: see text] is an angle, and [Formula: see text] is an irrational frequency, such that [Formula: see text] is a real piecewise-linear map with respect to [Formula: see text] of certain kind. The family depends on two real parameters, [Formula: see text] and [Formula: see text]. For this family, we prove the existence of nonsmooth pitchfork bifurcations. For [Formula: see text] and any [Formula: see text] there is only one continuous invariant curve. For [Formula: see text] there exists a smooth map [Formula: see text] such that: (a) For [Formula: see text], [Formula: see text] has two continuous attracting invariant curves and one continuous repelling curve; (b) For [Formula: see text] it has one continuous repelling invariant curve and two semi-continuous (noncontinuous) attracting invariant curves that intersect the unstable one in a zero-Lebesgue measure set of angles; (c) For [Formula: see text] it has one continuous attracting invariant curve. The case [Formula: see text] is a degenerate case that is also discussed in the paper. It is interesting to note that this family is a simplified version of the smooth family [Formula: see text] for which there is numerical evidence of a nonsmooth pitchfork bifurcation. Finally, we also discuss the limit case when [Formula: see text].

An innovative approach to approximating solutions of fractional partial differential equations

The RPS-M (residual power series method) is a valuable technique for solving F-PDEs (fractional partial differential equations). However, the derivative of the residual function to obtain the coefficients of the series is required in RPS-M. This makes the application of the classical RPS-M limited to a certain extent due to the complexity of the derivation of the residual function for higher iterations. To overcome this obstacle, in this study, we present a simplified version of this approach with the help of Laplace transform that requires less computation and offers higher accuracy. This modified method does not require derivation as well as limit of the residual function to estimate the unknown coefficients of the series solution. To demonstrate its effectiveness, we apply the proposed method to nonlinear F-PDEs to obtain their semi-analytical solution. The obtained solutions exhibit excellent agreement when compared to results obtained using other established approaches. We have also provided the convergence analysis of the obtained solution. Furthermore, by comparing the outcomes for various values of the non-integer order σ, we observe that as the value approaches an integer order, the solution converges towards the exact solution.

Artificial intelligence-based prognostic model accurately predicts the survival of patients with diffuse large B-cell lymphomas: analysis of a large cohort in China

BackgroundDiffuse large B-cell lymphomas (DLBCLs) display high molecular heterogeneity, but the International Prognostic Index (IPI) considers only clinical indicators and has not been updated to include molecular data. Therefore, we developed a widely applicable novel scoring system with molecular indicators screened by artificial intelligence (AI) that achieves accurate prognostic stratification and promotes individualized treatments.MethodsWe retrospectively enrolled a cohort of 401 patients with DLBCL from our hospital, covering the period from January 2015 to January 2019. We included 22 variables in our analysis and assigned them weights using the random survival forest method to establish a new predictive model combining bidirectional long-short term memory (Bi-LSTM) and logistic hazard techniques. We compared the predictive performance of our “molecular-contained prognostic model” (McPM) and the IPI. In addition, we developed a simplified version of the McPM (sMcPM) to enhance its practical applicability in clinical settings. We also demonstrated the improved risk stratification capabilities of the sMcPM.ResultsOur McPM showed superior predictive accuracy, as indicated by its high C-index and low integrated Brier score (IBS), for both overall survival (OS) and progression-free survival (PFS). The overall performance of the McPM was also better than that of the IPI based on receiver operating characteristic (ROC) curve fitting. We selected five key indicators, including extranodal involvement sites, lactate dehydrogenase (LDH), MYC gene status, absolute monocyte count (AMC), and platelet count (PLT) to establish the sMcPM, which is more suitable for clinical applications. The sMcPM showed similar OS results (P < 0.0001 for both) to the IPI and significantly better PFS stratification results (P < 0.0001 for sMcPM vs. P = 0.44 for IPI).ConclusionsOur new McPM, including both clinical and molecular variables, showed superior overall stratification performance to the IPI, rendering it more suitable for the molecular era. Moreover, our sMcPM may become a widely used and effective stratification tool to guide individual precision treatments and drive new drug development.

A simplified pneumonia severity index (PSI) for clinical outcome prediction in COVID-19.

The Pneumonia Score Index (PSI) was developed to estimate the risk of dying within 30 days of presentation for community-acquired pneumonia patients and is a strong predictor of 30-day mortality after COVID-19. However, three of its required 20 variables (skilled nursing home, altered mental status and pleural effusion) are not discreetly available in the electronic medical record (EMR), resulting in manual chart review for these 3 factors. The goal of this study is to compare a simplified 17-factor version (PSI-17) to the original (denoted PSI-20) in terms of prediction of 30-day mortality in COVID-19. In this retrospective cohort study, the hospitalized patients with confirmed SARS-CoV-2 infection between 2/28/20-5/28/20 were identified to compare the predictive performance between PSI-17 and PSI-20. Correlation was assessed between PSI-17 and PSI-20, and logistic regressions were performed for 30-day mortality. The predictive abilities were compared by discrimination, calibration, and overall performance. Based on 1,138 COVID-19 patients, the correlation between PSI-17 and PSI-20 was 0.95. Univariate logistic regression showed that PSI-17 had performance similar to PSI-20, based on AUC, ICI and Brier Score. After adjusting for confounding variables by multivariable logistic regression, PSI-17 and PSI-20 had AUCs (95% CI) of 0.85 (0.83-0.88) and 0.86 (0.84-0.89), respectively, indicating no significant difference in AUC at significance level of 0.05. PSI-17 and PSI-20 are equally effective predictors of 30-day mortality in terms of several performance metrics. PSI-17 can be obtained without the manual chart review, which allows for automated risk calculations within an EMR. PSI-17 can be easily obtained and may be a comparable alternative to PSI-20.

An optimal advertising model with carryover effect and mean field terms

We consider a class of optimal advertising problems under uncertainty for the introduction of a new product into the market, on the line of the seminal papers of Vidale and Wolfe (Oper Res 5:370–381, 1957) and Nerlove and Arrow (Economica 29:129–142, 1962). The main features of our model are that, on one side, we assume a carryover effect (i.e. the advertisement spending affects the goodwill with some delay); on the other side we introduce, in the state equation and in the objective, some mean field terms that take into account the presence of other agents. We take the point of view of a planner who optimizes the average profit of all agents, hence we fall into the family of the so-called “Mean Field Control” problems. The simultaneous presence of the carryover effect makes the problem infinite dimensional hence belonging to a family of problems which are very difficult in general and whose study started only very recently, see Cosso et al. [Ann Appl Probab 33(4):2863–2918, 2023]. Here we consider, as a first step, a simple version of the problem providing the solutions in a simple case through a suitable auxiliary problem.

Evaluating the psychometric properties of the simplified Chinese version of PROMIS-29 version 2.1 in patients with hematologic malignancies

The Patient-Reported Outcomes Measurement Information System 29-item Profile version 2.1 (PROMIS-29 V2.1) is a widely utilized self-reported instrument for assessing health outcomes from the patients’ perspectives. This study aimed to evaluate the psychometric properties of the PROMIS-29 V2.1 Chinese version among patients with hematological malignancy. Conducted as a cross-sectional, this research was approved by the Medical Ethical Committee of the Institute of Hematology and Blood Diseases Hospital, Chinese Academy of Medical Sciences and Peking Union Medical College (registration number QTJC2022002-EC-1). We employed convenience sampling to enroll eligible patients with hematological malignancy from four tertiary hospitals in Tianjin, Shandong, Jiangsu, and Anhui province in China between June and August 2023. Participants were asked to complete a socio-demographic information questionnaire, the PROMIS-29 V2.1, and the Functional Assessment of Cancer Therapy-General (FACT-G). We assessed the reliability, ceiling and floor effects, structural, convergent discriminant and criterion validity of the PROMIS-29 V2.1. A total of 354 patients with a mean age of 46.93 years was included in the final analysis. The reliability of the PROMIS-29 V2.1 was affirmed, with Cronbach’s α for the domains ranging from 0.787 to 0.968. Except sleep disturbance, the other six domains had ceiling effects, which were seen on physical function (26.0%), anxiety (37.0%), depression (40.4%), fatigue (18.4%), social roles (18.9%) and pain interference (43.2%), respectively. Criterion validity was supported by significant correlations between the PROMIS-29 V2.1 and FACT-G scores, as determined by the Spearman correlation test (P < 0.001). Confirmatory factor analysis (CFA) indicated a good model fit, with indices of χ2/df (2.602), IFI (0.960), and RMSEA (0.067). The Average Variance Extracted (AVE) values for the seven dimensions of PROMIS-29 V2.1, ranging from 0.500 to 0.910, demonstrated satisfactory convergent validity. Discriminant validity was confirmed by ideal √AVE values. The Chinese version of the PROMIS-29 V2.1 profile has been validated as an effective instrument for assessing symptoms and functions in patients with hematological malignancy, underscoring its reliability and applicability in this specific patient group.

Partial Syndrome Measurement for Hypergraph Product Codes

Hypergraph product codes are a promising avenue to achieving fault-tolerant quantum computation with constant overhead. When embedding these and other constant-rate qLDPC codes into 2D, a significant number of nonlocal connections are required, posing difficulties for some quantum computing architectures. In this work, we introduce a fault-tolerance scheme that aims to alleviate the effects of implementing this nonlocality by measuring generators acting on spatially distant qubits less frequently than those which do not. We investigate the performance of a simplified version of this scheme, where the measured generators are randomly selected. When applied to hypergraph product codes and a modified small-set-flip decoding algorithm, we prove that for a sufficiently high percentage of generators being measured, a threshold still exists. We also find numerical evidence that the logical error rate is exponentially suppressed even when a large constant fraction of generators are not measured.

Realizability modulo theories

In this paper we study the problem of realizability of reactive specifications written in LTLT, which is the extension of LTL where atomic propositions can be literals from a first-order theory, including arithmetic theories. We present a solution based on transforming LTLT specifications into purely Boolean specifications by (1) substituting theory literals by Boolean variables, and (2) computing an additional Boolean formula that captures the dependencies between the new variables imposed by the literals. We prove that the resulting specification is realizable if and only if the original specification is realizable. Moreover, the resulting specification can be passed to existing Boolean off-the-shelf synthesis and realizability tools, which can handle only Boolean LTL specifications.A second contribution is to prove that LTLT realizability of theories with a decidable ∃⁎∀⁎ fragment is decidable for all combinations of LTL temporal modalities. We present a simple version of our method, which relies on SMT solving, and performs a brute-force search to construct the “extra requirement”. A third contribution is an algorithm that checks whether a candidate is a correct Booleanization in non-Boolean LTL realizability.

Leveraging regional mesh refinement to simulate future climate projections for California using the Simplified Convection-Permitting E3SM Atmosphere Model Version 0

Abstract. The spatial heterogeneity related to complex topography in California demands high-resolution (&lt; 5 km) modeling, but global convection-permitting climate models are computationally too expensive to run multi-decadal simulations. We developed a 3.25 km California climate modeling framework by leveraging regional mesh refinement (CARRM) using the U.S. Department of Energy (DOE)'s global Simple Cloud-Resolving E3SM Atmosphere Model (SCREAM) version 0. Four 5-year time periods (2015–2020, 2029–2034, 2044–2049, and 2094–2099) were simulated by nudging CARRM outside California to 1° coupled simulation of E3SMv1 under the Shared Socioeconomic Pathways (SSP)5-8.5 future scenario. The 3.25 km grid spacing adds considerable value to the prediction of the California climate changes, including more realistic high temperatures in the Central Valley and much improved spatial distributions of precipitation and snowpack in the Sierra Nevada and coastal stratocumulus. Under the SSP5-8.5 scenario, CARRM simulation predicts widespread warming of 6–10 °C over most of California, a 38 % increase in statewide average 30 d winter–spring precipitation, a near-complete loss of the alpine snowpack, and a sharp reduction in shortwave cloud radiative forcing associated with marine stratocumulus by the end of the 21st century. We note a climatological wet precipitation bias for the CARRM and discuss possible reasons. We conclude that SCREAM RRM is a technically feasible and scientifically valid tool for climate simulations in regions of interest, providing an excellent bridge to global convection-permitting simulations.

Exploring ZnO nanoparticles: UV–visible analysis and different size estimation methods

The study investigates several theoretical and empirical methods for determining the size of zinc oxide nanoparticles (ZnO NPs) and studies their characteristics by using solely UV–visible spectroscopy. The investigation begins with the green synthesis of three samples of ZnO NPs using three different reducing agents Aspergillus Niger fungal biomass (AN), Aloe barbadensis Mille (ABM) and Ocimum tenuiflorum (OT) leaves, respectively with Zinc Sulphate as a precursor involving precipitation method. The study analyses the UV–visible data of each sample to obtain optical bandgap, Urbach energy, refractive index, optical conductivity. and apply several methods or Models such as Effective Mass Approximation (EMA) or Brus Equation (BE), Hyperbolic Band Model (HBM), Meulenkamp's Expression (ME), Tight Binding Model (TBM) and a simplified version of EMA (SEMA) to estimate the size of ZnO NPs. The effectiveness of size-determining models was assessed using two sets of one-way analysis of variance (ANOVA) for each ZnO sample and models Followed by Tukey post-hoc analysis to identify the exact sample that is different from other samples.

Smooth least absolute deviation estimators for outlier-proof identification

The paper proposes to identify the parameters of linear dynamic models based on the original implementation of least absolute deviation estimators. It is known that the object estimation procedures synthesized in the sense of the least sum of absolute prediction errors are particularly resistant to occasional outliers and gaps in the analyzed system data series, while the classical least squares procedure unfortunately becomes of little use for reliably identifying systems in the presence of destructive measurement errors. Bearing in mind that the classic task of minimizing the quality functional of absolute deviations encounters fundamental analytical problems, it is proposed to use a dedicated iterative estimator for off-line evaluation of the parameters of the analyzed process. In addition, a simplified recursive version of the absolute deviation estimation procedure was developed, which allows for practical on-line tracking of the evolution of variable parameters of non-stationary systems. Importantly, a novel refinement of the discussed absolute deviation estimators was proposed to effectively overcome some inconvenient numerical effects. We also present an interesting comparison of the improved (by non-linear modification) iterative absolute-deviation estimator with the classical Gauss-Newton gradient algorithm, which leads to constructive conclusions. Finally, using computer simulations, the operation of the developed iterative and recursive estimators minimizing the absolute deviation is illustrated. The work ends with an indication of directions for further research.

The dynamics of the transpolar drift current

The governing equations for a viscous, incompressible fluid, in the thin-shell approximation, written in a coordinate frame which ensures validity at the North Pole, is simplified by invoking the f-plane approximation. Together with suitable stress conditions at the surface, describing the interaction of wind over ice and ice over water, a solution is developed for the Transpolar Drift current. This involves prescribing the near-surface geostrophic ocean flow and also, for ease of calculation, a simple version of the Ekman flow. Then, via the stress conditions at the surface, the near-surface wind consistent with these flows is obtained. An example, which exhibits the reduction in ice thickness as the flow moves over the North Pole towards the Fram Strait, and also describes the relative directions and speeds of the wind, ice and water, is presented in graphical form; this solution recovers what is observed. The considerable freedom available in this approach, allowing choices to be made for the geostrophic flow and the wind (both variable), and the ice profile at some initial position, is explained, opening the way to further, extensive investigations.

Comparison of standard goal attainment scaling (GAS) and the GAS-light method for evaluation of goal attainment during neurorehabilitation of the upper limb

Background: Goal attainment scaling (GAS) is now widely used as a person-centered measure of outcome from rehabilitation and has demonstrated validity in diverse populations with sensitivity to change. However, as originally described, it is time-consuming for use in busy clinical settings. The “GAS-light” is a simplified version designed for application in routine clinical practice. Although increasingly taken up by clinicians, published evidence of the validity of GAS-light method is currently lacking. Objective: To evaluate the validity and sensitivity of the GAS-light rating method as a measure of goal attainment in clinical neurorehabilitation practice. To examine its agreement with the standard GAS rating (as originally described by the developers) as the gold standard and to assess its clinical utility and acceptability. Methods design: A direct, head-to-head comparison of the 2 GAS rating methods in a cohort of adults undergoing upper limb motor rehabilitation programs across a range of rehabilitation settings, including hospital, community outpatient, and spasticity clinic services. Study population: 60 patients (n=54 poststroke) set a total of 136 goals (range 1–4 per patient). In this comparative study, patients acted as their own controls. Measures: The 2 rating methods were applied independently and in parallel from a single goal-setting discussion. Goal attainment was measured on the original 5-point GAS using a predetermined follow-up guide and the GAS-light with its 6-point verbal rating scale. The evaluation included concurrent validity (intraclass correlation coefficients and agreement between the 2 ratings) and sensitivity to change using the standardized response mean (SRM). Thirteen clinicians and 52 participants completed surveys of clinical utility and patient acceptance, respectively. Results: Individual absolute agreement of 2-way mixed-effects intraclass correlation between the tools indicated good agreement (ICC(A,1)=0.88, 95% CI: 0.80, 0.93), and small systematic bias (–1.72 (95% CI: −3.04, −0.41). Both tools measured similar levels of change over time (GAS SRM=1.79; GAS-light SRM=1.62). Clinicians perceived GAS-light had stronger clinical utility, being quicker and easier to administer, score, and understand. Patients perceived GAS-light as acceptable, comfortable, worthwhile, and helpful. Conclusions: GAS-light is reliable and sensitive to change, with better clinical utility than the standard GAS. Either tool may be used to assess goal attainment in clinical upper limb neurorehabilitation.

Deep residual network for interpolation and inverse problems

In this paper, we introduce the Power-Enhancing Residual Network, a simplified version of the highway network. This novel neural network architecture aims to enhance interpolation capabilities. By incorporating power terms in residual elements, this architecture enhances the network’s expressive capacity, leading to new possibilities in deep learning. We explore key design aspects such as network depth, width, and optimization techniques, showcasing its adaptability and performance advantages. Results highlight its precision and demonstrate superiority over conventional networks in accuracy, convergence speed, and computational efficiency. Additionally, we investigate deeper network configurations and apply the architecture to solve the inverse Burgers’ equation, illustrating its effectiveness in real-world problems. Overall, the Power-Enhancing Residual Network represents a versatile and transformative solution, pushing the boundaries of machine learning. The codes implemented are available at: https://github.com/CMMAi/ResNet_for_PINN.