Modeling Accuracy Research Articles

Trajectory compensation based adaptive control (TCAC) for high-precision piezoelectric actuators

Piezoelectric actuator (PEA) has been widely used in micro-systems, due to the advantages of nano-scale precision, rapid response speed, high stiffness, etc. Nevertheless, the intrinsic nonlinearities of PEA, particularly hysteresis, severely deteriorate its positioning and tracking control accuracy. In most existing control algorithms of PEA, the approximate inverse model of hysteresis is developed to compensate for motion error, which requires high modeling accuracy. To avoid the influence of complex modeling procedures and modeling errors on tracking precision, a trajectory compensation-based adaptive control method has been proposed in this paper. Firstly, a simple linear controller is used to establish the closed-loop feedback system and to guarantee the basic tracking performance of the PEA system. And then, the trajectory compensation is designed according to the frequency analysis of the closed-loop control system. Finally, nonlinear adaptive compensation is used to eliminate the residual errors of the above linear frequency domain model. Different from conventional controllers, the proposed method can achieve excellent tracking control performance without any hysteresis model of PEA. The stability and convergence of the proposed method have been theoretically proved. In addition to theoretical guarantees, the proposed method is validated experimentally and demonstrated to achieve the root-mean-square and maximum value of tracking errors to less than 8 nm and 25 nm, respectively, which has a clear accuracy advantage over other methods.

Dependencies for determining heat transfer coefficients and air resistance for heat exchangers with tubular-plate heat exchange surface

Problem. The article analyzes existing generalized dependencies for determining convective heat transfer coefficients and air resistance coefficients for tubular-plate surfaces widely used in the production of modern charge air coolers and radiators. It is established that practical application of such dependencies, in some cases, is associated with significant errors revealed during experimental checks. Consequently, there is a need to adjust such dependencies for corridor bundles of flat-oval tubes with transverse grouped finning by flat fins. Goal. The aim of this study is to correct experimental dependencies for heat exchange and resistance. Numerical coefficients are adjusted on this basis, while the structure of dimensional dependencies remains unchanged. Simultaneously, the study is conducted for further improvement of the methodology for obtaining similar dependencies. Methodology. Adjustment of generalized dependencies for determining convective heat transfer coefficients and air resistance coefficients for tubular-plate heat exchange surfaces is carried out experimentally. Results. New dependencies are proposed for determining heat transfer coefficients and air resistance coefficients for tubular-plate heat exchange surfaces. Their accuracy and efficiency are investigated over a wide range of regimes. Originality and practical value. Unlike known dependencies of a similar nature, the proposed dependencies are provided in a single complex that should be used in modern heat exchanger calculation methods. It is established that the maximum error in determining air temperature according to the proposed dependence does not exceed 0.3 °C for the entire investigated range, and the error in determining aerodynamic resistance does not exceed 8 %, indicating high accuracy of modeling. Such accuracy ensures the possibility of applying the proposed dependencies for engineering calculations.

Enhancing Financial Investment Decision-Making With Deep Learning Model

This paper introduces the ISSA-BiLSTM-TPA model to improve financial investment decision-making. Traditional deep learning models face limitations in handling the complexity and uncertainty of financial markets. Our approach incorporates attention mechanisms, Bidirectional Long Short-Term Memory (BiLSTM), and Temporal Pattern Attention (TPA) to enhance accuracy in modeling and forecasting financial time series. The attention mechanism focuses on crucial information, BiLSTM captures bidirectional dependencies, and TPA identifies optimal solutions. Experimental results show higher prediction accuracy compared to traditional models, offering more reliable decision support for financial practitioners. Continuous optimization aims to provide innovative decision-making tools for the finance industry, advancing deep learning technology in finance.

Turn‐to‐turn and phase‐to‐phase short circuit fault detection of wind turbine permanent magnet generator based on equivalent magnetic network modelling by wavelet transform approach

AbstractOne of the most common faults in electric machines is a turn‐to‐turn short circuit (TTSC), which may destroy coil insulation and demagnetise the magnet. In addition, the phase‐to‐phase short circuit (PPSC) fault, which can have even more destructive effects than the TTSC fault, is introduced and analysed. The equivalent magnetic network (EMN) method, with high modelling accuracy and a short computation time, is employed for healthy and faulty machines. The current signal under fault conditions is analysed in the dqo frame, showing the presence of the second harmonic component in its waveform. This fault detection index is processed using the signal processing technique of discrete(wavelet transform (DWT). Besides, energy analysis is used to distinguish TTSC and PPSC faults. Finally, finite element and EMN modelling results are compared with the experimental data of the prototyped permanent magnet generator. The results show that the combination of the proposed EMN method and DWT has very good accuracy and speed. Furthermore, the proposed fault detection method remains unaffected by various linear loads with different power factors.The cover image is based on the article Turn‐to‐turn and phase‐to‐phase short circuit fault detection of wind turbine permanent magnet generator based on equivalent magnetic network modelling by wavelet transform approach by Mehrage Ghods et al., https://doi.org/10.1049/elp2.12452

Advancing computational models for wave dynamics applications with quartic trigonometric tension b-spline techniques

This paper presents a computational model using Quartic Trigonometric Tension B-spline (QT-TB) function with collocation approach for nonlinear dispersive wave equation. Shallow water wave modeling plays a crucial role in various fields, including coastal engineering, oceanography, and natural hazard assessment. The QT-TB function is employed for spatial derivatives, integrating the nonlinear term through the linearization technique. While maintaining most characteristics of traditional polynomial B-splines, this method improves numerical solutions, enhancing accuracy in modeling. The performance of the method is rigorously assessed across three benchmark problems, with results compared to those of prior studies employing identical parameters. Detailed numerical illustrations are presented. Graphical representations are utilized to illustrate the single solitary wave motion, dynamics of coupled solitary waves and dynamics of triplet solitary waves in this study. Numerical experiments validate the method's accuracy and efficiency in capturing RLW-driven wave dynamics, establishing it as a reliable tool for various applications. The presented work includes an analysis of the stability of the proposed scheme, employing the Fourier method and shows that its unconditional stable.

Convergence and accuracy of FDTD modelling for periodic plasmonic systems

Despite the widespread use of the finite-difference time-domain (FDTD) method for modeling plasmonic systems, there is a lack of detailed convergence and accuracy studies for periodic nanoparticle systems in which both particle radius and interparticle distance are critical parameters. Using an in-house parallelized 3D-FDTD code for which we implemented interface field averaging, convergence and accuracy were evaluated for various spherical particle radii, inter-distances, and radius-to-mesh size ratios. We found that Interface Field Averaging (IFA) FDTD improved accuracy and convergence with respect to per-component (Per-C) meshing. In the worst case of this study, the convergence error decreased from 4.9% to 2.6% only by using IFA. Accuracy was verified by benchmarking our simulation results with COMSOL Multiphysics software. Furthermore, we notice that there exists no general rule for choosing the mesh size. Careful convergence testing should therefore be carried out systematically.

Analysis of the Accuracy of CAD Modeling in Engineering and Medical Industries Based on Measurement Data Using Reverse Engineering Methods

The reverse engineering (RE) process is often necessary in today’s engineering and medical industries. Expertise in measurement technology, data processing, and CAD modeling is required to ensure accurate reconstruction of an object’s geometry. However, errors are generated at every stage of geometric reconstruction, affecting the dimensional and geometric accuracy of the final 3D-CAD model. In this article, the geometry of reconstructed models was measured using contact and optical methods. The measurement data representing 2D profiles, 3D point clouds, and 2D images acquired in the reconstruction process were saved to a stereolithography (STL) model. The reconstructed models were then subjected to a CAD modeling process, and the accuracy of the parametric modeling was evaluated by comparing the 3D-CAD model to the 3D-STL model. Based on the results, the model used for clamping and positioning parts to perform the machining process and the connecting rod provided the most accurate mapping errors. These models represented deviations within ±0.02 mm and ±0.05 mm. The accuracy of CAD modeling for the turbine blade model and the pelvis part was comparable, presenting deviations within ±0.1 mm. However, the helical gear and the femur models showed the highest deviations of about ±0.2 mm. The procedures presented in the article specify the methods and resolution of the measurement systems and suggest CAD modeling strategies to minimize reconstruction errors. These results can be used as a starting point for further tests to optimize CAD modeling procedures based on the obtained measurement data.

DC3DPAFEM: An efficient and accurate 3-D direct current resistivity anisotropic forward modeling software for complex geological settings

Nowadays, there is a growing trend that direct current (DC) field surveys are shifting towards challenging areas characterized by mountainous topography and electrical anisotropy. Given these complex geological settings, there is an urgent need for 3-D DC forward modeling software capable of effectively addressing large-scale problems and delivering accurate modeling results to interpret field data. However, most open-source software packages face certain limitations, such as the high numerical cost to handle complex surface topography, the lack of consideration for anisotropic conductivity, the absence of mesh refinement techniques to guarantee accuracy in forward modeling, and the lack of parallel computing techniques to solve large-scale problems. In this study, we develop an efficient and highly accurate 3-D DC anisotropic forward modeling software, namely DC3DPAFEM, using the adaptive finite element algorithm based on the unstructured tetrahedral mesh. Firstly, we construct a strong compatible boundary value problem (BVP) for 3-D anisotropic DC problems by adopting a specialized secondary potential approach to handle the surface topography efficiently. Then, we develop a goal-oriented adaptive mesh refinement (AMR) technique to ensure accurate forward modeling results, even with a coarse initial mesh. To ensure time and memory efficiency, we employ a robust conjugate gradient (CG) algorithm preconditioned by the algebraic multigrid (AMG) solver to solve the large-scale linear system of equations resulting from complex geological structures. We aim to investigate the performance of the AMG scheme in anisotropic DC cases. Furthermore, we incorporate the domain decomposition technique into the iterative solution scheme for further efficiency gains. This technique significantly improves computing efficiency for large-scale problems in parallel clusters. Finally, we conduct comprehensive performance tests for DC3DPAFEM using a two-layer anisotropic model and a 3-D complex model with undulating terrain. The results of both examples validate the accuracy of DC3DPAFEM, as they closely align with the analytical solutions and the solutions obtained from the existing 3-D DC forward modeling code. Compared to traditional direct solver MUMPS and ILU-preconditioned iterative solvers, DC3DPAFEM exhibits highly scalable performance for large-scale problems, offering significant advantages in terms of memory and time consumption. Overall, DC3DPAFEM demonstrates substantial advances in efficiency, accuracy, and practicality through a series of numerical examples. This open-source code provides an efficient and available tool for developing a 3-D DC inversion method that can deal with large-scale problems involving intricate topography and anisotropic media.

Modeling of Heat and Mass Transfer in Cement-Based Materials during Cement Hydration—A Review

Cement-based materials encompass a broad spectrum of construction materials that utilize cement as the primary binding agent. Among these materials, concrete stands out as the most commonly employed. The cement, which is the principal constituent of these materials, undergoes a hydration reaction with water, playing a crucial role in the formation of the hardened composite. However, the exothermic nature of this reaction leads to significant temperature rise within the concrete elements, particularly during the early stages of hardening and in structures of substantial thickness. This temperature rise underscores the critical importance of predictive modeling in this domain. This paper presents a review of modeling approaches designed to predict temperature and accompanying moisture fields during concrete hardening, examining different levels of modeling accuracy and essential input parameters. While modern commercial finite element method (FEM) software programs are available for simulating thermal and moisture fields in concrete, they are accompanied by inherent limitations that engineers must know. The authors further evaluate effective commercial software tools tailored for predicting these effects, intending to provide construction engineers and stakeholders with guidance on managing temperature and moisture impacts in early-age concrete.

PρT measurements of 3-aminopropan-1-ol and N-(2-hydroxyethyl)morpholine from (293.15 to 473.15) K and up to 40 MPa and modeling with modified Tait and PC-SAFT equations

New density data has been reported for 3-aminopropan-1-ol (AP) and N-(2-hydroxyethyl)morpholine (NHEM) at temperatures ranging from (293.15–473.15) K at 19 pressures ranging from (0.1–40) MPa. The experimental measurements were carried out using an Anton Paar high-pressure vibrating tube densimeter with a combined expanded uncertainty of 1 kg m−3 at a 95 % confidence level. Contributions considered in the uncertainty analysis included the impurities in the materials used and apparatus specification. In addition, the density and speed of sound at ambient pressure (81.5 kPa) and temperatures (293.15–343.15) K were measured. The experimental density data were correlated with the modified Tait equation. Values of thermal expansion coefficient (αP ) and isothermal compressibility (κT) were calculated. The work is completed with the modeling of the experimental data using the perturbed-chain statistical associating fluid theory equation of state (PC-SAFT EOS). The parameters of the PC-SAFT equation of state, for the pure compounds, were determined by fitting the equation to the liquid PρT experimental data. Thermodynamic properties such as thermal expansion coefficient (αP), isothermal compressibility (κT), isobaric heat capacity (CP), and speed of sound (u) were calculated with the obtain parameters. Good agreement between experimental data and derived properties represented the modeling accuracy with the obtained parameters.

Optimising High-Pressure Processing (HPP) for Optimal Total Phenolic and Flavonoid Content in Kelulut (Stingless Bee) Honey

High-pressure processing (HPP) has the potential to enhance the total phenolic and flavonoid content (TPC and TFC) in Kelulut honey (KH). However, KH’s inherent variability possesses challenges in optimising these phytochemicals. This study hence explores the optimisation of KH through HPP, focusing on TPC and TFC. The Face-centered Central Composite Design (FC-CCD), involving two factors with three levels each (pressure of 200, 400, and 600 MPa, and time of 5, 10, and 15 min), was applied to investigate two response variables (total phenolic and flavonoid content). The optimisation identified the optimal parameters as 200 MPa for 15 min, with a desirability of 0.986, indicating precise modeling. Compared to other pressures (400 and 600 MPa) at common processing time (15 minutes), 200 MPa recorded higher TPC and TFC with differences of 25.71% to 30.92% and 13.78% to 14.19%, respectively. A verification step revealed that HPP-KH at 200 MPa for 15 minutes yielded a TPC of 15.278 ± 0.525 mg GAE/100 g and a TFC of 38.274 ± 1.980 mg RE/100 g, indicating the precise accuracy of the quadratic modeling. However, this discovery contradicts the consensus that pressures above 500 MPa increase TPC and TFC. Consequently, it underscores the need for tailored high-pressure strategies in KH processing, offering essential insights for industry applications and further research endeavors.

Predicting daily heating energy consumption in residential buildings through integration of random forest model and meta-heuristic algorithms

This research utilizes a sophisticated hybrid model integrating the Random Forest algorithm with meta-heuristic optimization techniques to estimate heating energy consumption in residential buildings. The study addresses key variables including architectural characteristics, occupancy, and ambient temperature. The primary objective is to enhance the prediction accuracy of heating energy consumption using a novel approach combining Random Forest with various meta-heuristic algorithms. The study employs six combinations of the Random Forest algorithm and meta-heuristic optimizers. To mitigate overfitting, K-Fold cross-validation is implemented during model training. The model's performance is evaluated using five statistical indices: coefficient of determination (R2), Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Relative Absolute Error (RAE), and Theil Inequality Coefficient (TIC). Results demonstrate the hybrid model's high predictive accuracy, with the Arithmetic Optimization Algorithm enhancing Random Forest's performance significantly. Notable statistical achievements include R2 = 0.977201, RMSE = 0.1179, MAE = 0.0573, RAE = 0.0930, and TIC = 0.0187. Additionally, the Ant Lion Optimizer shows excellent convergence, achieving a TIC value of 0.014986 after 101 iterations. The proposed hybrid model significantly outperforms traditional methods in predicting residential heating energy consumption. The integration of Random Forest with advanced meta-heuristic algorithms offers a robust framework for enhancing prediction accuracy in energy consumption modeling.

A multisource data‐driven monitoring model for assessing concrete dam behavior

AbstractThe pivotal role of dam infrastructure necessitates continuous health monitoring, which results in extensive sets of data. Most monitoring data‐based models in dam engineering concentrate on predicting dam behavior. However, little attention has been systematically paid to the processing of extensive monitoring data, modeling of comprehensive dam behavior, and assessment of overall dam operation status. Here, we propose a novel monitoring model comprising three main aspects: a multidimensional data mining method, a multipoint response prediction method, and a multilayer data fusion‐based assessment method. Utilizing monitoring data from a mega concrete arch dam, we evaluate and discuss the effects of data mining, modeling accuracy for dam behavior, robustness against data pollution, and sensitivity to anomalies. Comparisons with classical benchmarks demonstrate the performance of the proposed model for the dam.

A Fast Feedforward Small-World Neural Network for Nonlinear System Modeling.

It is well-documented that cross-layer connections in feedforward small-world neural networks (FSWNNs) enhance the efficient transmission for gradients, thus improving its generalization ability with a fast learning. However, the merits of long-distance cross-layer connections are not fully utilized due to the random rewiring. In this study, aiming to further improve the learning efficiency, a fast FSWNN (FFSWNN) is proposed by taking into account the positive effects of long-distance cross-layer connections, and applied to nonlinear system modeling. First, a novel rewiring rule by giving priority to long-distance cross-layer connections is proposed to increase the gradient transmission efficiency when constructing FFSWNN. Second, an improved ridge regression method is put forward to determine the initial weights with high activation for the sigmoidal neurons in FFSWNN. Finally, to further improve the learning efficiency, an asynchronous learning algorithm is designed to train FFSWNN, with the weights connected to the output layer updated by the ridge regression method and other weights by the gradient descent method. Several experiments are conducted on four benchmark datasets from the University of California Irvine (UCI) machine learning repository and two datasets from real-life problems to evaluate the performance of FFSWNN on nonlinear system modeling. The results show that FFSWNN has significantly faster convergence speed and higher modeling accuracy than the comparative models, and the positive effects of the novel rewiring rule, the improved weight initialization, and the asynchronous learning algorithm on learning efficiency are demonstrated.

Wheat Yield Estimation Study Using Hyperspectral Vegetation Indices

Wheat is the main grain crop in our country, and the traditional wheat yield estimation method is time-consuming and laborious. By estimating wheat yield efficiently, quickly and non-destructively, agricultural producers can quickly obtain information about wheat yield, manage wheat fields more scientifically and accurately, and ensure national food security. Taking the Xinxiang Experimental Base of the Crop Science Research Institute, Chinese Academy of Agricultural Sciences as an example, hyperspectral data for the critical growth stages of wheat were pre-processed. A total of 27 vegetation indices were calculated from the experimental plots. These indices were then subjected to correlation analysis with measured wheat yield. Vegetation indices with Pearson correlation coefficients greater than 0.5 were selected. Five methods, including multiple linear regression, stepwise regression, principal component regression, neural networks and random forests, were used to construct wheat yield estimation models. Among the methods used, multiple linear regression, stepwise regression and the models developed using principal component analysis showed a lower modelling accuracy and validation precision. However, the neural network and random forest methods both achieved a modelling accuracy R2 greater than 0.6, with validation accuracy R2 values of 0.729 and 0.946, respectively. In addition, the random forest method had a lower cross-validation RMSE value, with values of 869.8 kg/hm−2, indicating a higher model accuracy. In summary, the random forest method provided the optimal estimation for wheat yield, enabling the timely and accurate pre-harvest wheat yield prediction, which has significant value for precision agriculture management and decision making.

Numerical Simulation Study on the Impact of Excavation on Existing Subway Stations Based on BIM-FEM Framework

Building information modeling (BIM) and finite element method (FEM) models have a wide range of applications in underground engineering design, construction, and operation and maintenance. This study employs a BIM-FEM framework to numerically simulate the impact of excavation on existing subway stations, using the Yanjiang New City Station TOD project as a case study. This framework simplifies the smooth integration of BIM and FEM models, automating functions such as assigning material properties, conducting construction simulations, and generating high-quality meshes. Simulation results reveal significant horizontal and vertical displacements in diaphragm walls, support structures, and subway station structures, with the greatest impacts occurring closest to the excavation site. The BIM-FEM framework is validated as an effective tool for designing foundation pit support structures, enhancing numerical modeling accuracy and efficiency in underground engineering. The findings contribute to a better understanding of the dynamic interactions between excavation and underground structures, informing the development of construction strategies and protective measures to ensure structural safety.

Machine learning-based model for the intelligent estimation of critical heat flux in nanofluids

The rising demand for advanced energy systems requires enhanced thermal management strategies to maximize resource utilization and productivity. This is quite an important industrial and academic trend as the efficiency of energy systems depends on the cooling systems. This study intends to address the critical need for efficient heat transfer mechanisms in industrial energy systems, particularly those relying on pool boiling conditions, by mainly focusing on Critical Heat Flux (CHF). In fact, CHF keeps a limit in thermal system design, beyond which the efficiency of the system drops. Recent research materials have highlighted nanofluids’ superior heat transfer properties over conventional pure fluids, like water, which makes them a considerable substitution for improving CHF in cooling systems. However, the broad variability in experimental outcomes challenges the development of a unified predictive model. Besides, Machine Learning (ML) based prediction has shown great accuracy for modeling of the designing parameters, including CHF. Utilizing ML algorithms—Cascade Forward Neural Network (CFNN), Extreme Gradient Boosting (XGBoost), Extra Tree, and Light Gradient Boosting Method (LightGBM)— four predictive models have been developed and the benchmark shows CFNN’s superior accuracy with an average goodness of fit of 89.32%, significantly higher than any available model in the literature. Also, the iterative stability analysis demonstrated that this model with a 0.0348 standard deviation and 0.0268 mean absolute deviation is the most stable and robust method that its performance minorly changes with input data. The novelty of the work mainly lies in the prediction of CHF with these advanced algorithm models to enhance the reliability and accuracy of CHF prediction for designing purposes, which are capable of considering many effective parameters into account with much higher accuracy than mathematical fittings. This study not only explains the complex interplay of nanofluid parameters affecting CHF but also offers practical implications for the design of more efficient thermal management systems, thereby contributing to the broader field of energy system enhancement through innovative cooling solutions.

From field soil sampling to watershed model: Upscaling by integrating information entropy and interpolation method

Soil property data plays a crucial role in watershed hydrology and non-point source (H/NPS) modeling, but how to improve modeling accuracy with affordable soil samplings and the effects of sampling information on H/NPS modeling remains to be further explored. In this study, the number of sampling points and soil properties were optimized by the information entropy and the spatial interpolation method. Then the sampled properties were parameterized and the effects of different parameterization schemes on H/NPS modeling were tested using the Soil and Water Assessment Tool (SWAT). The results indicated that the required sampling points increased successively for soil bulk density (SOL_BD), soil saturated hydraulic conductivity (SOL_K) and soil available water capacity (SOL_AWC). Compared to the traditional database (Harmonized world soil database), the NSE and R2 performance by new scheme increased by 22.8% and 10.5%, respectively. The entropy-based optimization reduced the sampling points by 13.2%, indicating a more cost-effective scheme. Compared to hydrological simulation, sampled properties showed greater effects on NPS modeling, especially for nitrogen. This proposed method/framework can be generalized to other watersheds by upscaling field soil sampling information to the watershed scale, thus improving H/NPS simulation.

A hybrid deep learning approach to predict hourly riverine nitrate concentrations using routine monitored data

With high-frequency data of nitrate (NO3–N) concentrations in waters becoming increasingly important for understanding of watershed system behaviors and ecosystem managements, the accurate and economic acquisition of high-frequency NO3–N concentration data has become a key point. This study attempted to use coupled deep learning neural networks and routine monitored data to predict hourly NO3–N concentrations in a river. The hourly NO3–N concentration at the outlet of the Oyster River watershed in New Hampshire, USA, was predicted through neural networks with a hybrid model architecture coupling the Convolutional Neural Networks and the Long Short-Term Memory model (CNN-LSTM). The routine monitored data (the river depth, water temperature, air temperature, precipitation, specific conductivity, pH and dissolved oxygen concentrations) for model training were collected from a nested high-frequency monitoring network, while the high-frequency NO3–N concentration data obtained at the outlet were not included as inputs. The whole dataset was separated into training, validation, and testing processes according to the ratio of 5:3:2, respectively. The hybrid CNN-LSTM model with different input lengths (1d, 3d, 7d, 15d, 30d) displayed comparable even better performance than other studies with lower frequencies, showing mean values of the Nash-Sutcliffe Efficiency 0.60–0.83. Models with shorter input lengths demonstrated both the higher modeling accuracy and stability. The water level, water temperature and pH values at monitoring sites were main controlling factors for forecasting performances. This study provided a new insight of using deep learning networks with a coupled architecture and routine monitored data for high-frequency riverine NO3–N concentration forecasting and suggestions about strategies about variable and input length selection during preprocessing of input data.

Weak-formulated physics-informed modeling and optimization for heterogeneous digital materials.

Numerical solutions to partial differential equations (PDEs) are instrumental for material structural design where extensive data screening is needed. However, traditional numerical methods demand significant computational resources, highlighting the need for innovative optimization algorithms to streamline design exploration. Direct gradient-based optimization algorithms, while effective, rely on design initialization and require complex, problem-specific sensitivity derivations. The advent of machine learning offers a promising alternative to handling large parameter spaces. To further mitigate data dependency, researchers have developed physics-informed neural networks (PINNs) to learn directly from PDEs. However, the intrinsic continuity requirement of PINNs restricts their application in structural mechanics problems, especially for composite materials. Our work addresses this discontinuity issue by substituting the PDE residual with a weak formulation in the physics-informed training process. The proposed approach is exemplified in modeling digital materials, which are mathematical representations of complex composites that possess extreme structural discontinuity. This article also introduces an interactive process that integrates physics-informed loss with design objectives, eliminating the need for pretrained surrogate models or analytical sensitivity derivations. The results demonstrate that our approach can preserve the physical accuracy in data-free material surrogate modeling but also accelerates the direct optimization process without model pretraining.