Inverse Analysis Research Articles

A review on inverse analysis models in steel material design

AbstractThis paper reviews various inverse analysis models used in steel material design, with a focus on integrating process, microstructure, and properties through advanced machine learning techniques. The study underscores the importance of establishing comprehensive models that effectively link these elements for enhanced materials engineering. Key models discussed include the convolutional neural network–artificial neural network‐coupled model, which employs convolutional neural networks for feature extraction; the Bayesian‐optimized generative adversarial network–conditional generative adversarial network model, which generates diverse virtual microstructures; the multi‐objective optimization model, which concentrates on process–property relationships; and the microstructure–process parallelization model, which correlates microstructural features with process conditions. Each model is assessed for its strengths and limitations, influencing its practical applicability in material design. The paper concludes by advocating for continued improvements in model accuracy and versatility, with the ultimate goal of enhancing steel properties and expanding the scope of data‐driven material development.

Kinematic Analysis and Trajectory Planning Based on a Six-Axis Robotic Arm

Kinematic analysis and time-optimal trajectory planning are applied to the robot in order to enhance its operational efficiency and preserve its continuous, smooth running trajectory. In this paper, the robot kinematics model is established based on the D-H parametric method with the Daqi Elfin series E05 six-axis robot as the research object. After that, forward and inverse kinematic analysis is carried out. And the segmented polynomial interpolation trajectory planning model of robotic arm is optimized in time based on the improved particle swarm algorithm. And MATLAB robot toolbox is used to build the robotic arm simulation model. From there, the trajectory planning simulation experiments are performed. As well as the experimental results show that the improved particle swarm algorithm effectively reduces the trajectory planning time. In the simulation experiment the time is reduced by 40.78% compared to the initial setting. The effectiveness of the robotic arm is greatly increased by this research.

The relationship between cereal intake and 3 common inflammatory joint diseases: A 2-sample Mendelian randomization study.

The association between cereal intake and inflammatory joint disease remains controversial. This study aims to use Mendelian randomization to comprehensively evaluate the causal relationship between cereal grain intake and Inflammatory joint diseases, including rheumatoid arthritis, psoriatic arthritis, and ankylosing spondylitis. This investigation used publicly available data from genome-wide association studies to aggregate statistics on the association between cereal intake and inflammatory joint disease. Several methods were employed to estimate 2-sample causality. The results of the random-effects inverse variance-weighted method analysis indicated that higher cereal intake reduced the risk of developing rheumatoid arthritis (odds ratio [OR] = 0.554; 95% confidence interval [CI]: 0.324-0. 948; P = .031) and psoriatic arthritis (OR = 0.336; 95% CI: 0.123-0.918; P = .033), and the results of the Mendelian randomization-Egger regression analysis showed no horizontal pleiotropy (P > .05) for the included single nucleotide polymorphisms. Using the leave-one-out method, no single nucleotide polymorphism was found to affect the overall effect estimate significantly, and there was no heterogeneity. Cereal intake had no causal effect on the risk of developing ankylosing spondylitis (OR = 0.636; 95% CI: 0.236-1.711; P = .370). There is genetic evidence that cereal consumption reduces the risk of developing Inflammatory joint diseases such as rheumatoid arthritis and psoriatic arthritis.

Concomitant osteochondral lesion of the talus affects in vivo ankle kinetics in patients with chronic ankle instability.

This cross-sectional study aimed to investigate the in vivo ankle kinetic alterations in patients with concomitant chronic ankle instability (CAI) and osteochondral lesion of the talus (OLT), which may offer opportunities for clinician intervention in treatment and rehabilitation. A total of 16 subjects with CAI (eight without OLT and eight with OLT) and eight healthy subjects underwent gait analysis in a stair descent setting. Inverse dynamic analysis was applied to ground reaction forces and marker trajectories using the AnyBody Modeling System. One-dimensional statistical parametric mapping was performed to compare ankle joint reaction force and joint moment curve among groups. The patients with OLT showed significantly increased dorsiflexion moment in the ankle joint compared with healthy subjects during 38.2% to 40.9% of the gait cycle, and increased eversion moment in the ankle joint compared with patients without OLT during 25.5% to 27.6% of the gait cycle. Compared with healthy subjects, the patients with OLT showed increased anterior force during 42% to 43% of the gait cycle, and maximal medial force (p = 0.005, ηp2 = 0.399). The patients with concomitant CAI and OLT exhibit increased dorsiflexion and eversion moment, as well as increased anterior and medial ankle joint reaction force during stair descent, compared with patients with CAI but without OLT and healthy subjects, respectively. Thus, a rehabilitative regimen targeting excessive ankle dorsiflexion and eversion moment may help to reduce ankle joint loading.

Simulating atherosclerotic plaque mechanics using polyvinyl alcohol (PVA) cryogel artery phantoms, ultrasound imaging and inverse finite element analysis.

The aim of this study is to demonstrate the potential of polyvinyl alcohol phantoms to simulate atherosclerotic features. In addition, a testing and simulation framework is developed for full PVA vessel material characterization using ring tensile testing and inflation testing combined with non-invasive ultrasound imaging and computational modelling. Strain stiffening behavior was observed in PVA through ring tensile tests, particularly at high (n=6) freeze-thaw cycles. Inflation testing of bi-layered phantoms featuring lipid pool inclusions demonstrated high strains at shoulder regions. The application of an inverse finite element framework successfully recovered boundaries and determined the shear moduli for the PVA wall to lie within the range 27 kPa to 53 kPa. The imaging-modelling framework presented facilitates the use and characterization of arterial mimicking phantoms to further explore plaque rupture. It also shows translational potential for non-invasive mechanical characterization of atherosclerotic plaques to improve the identification of clinically relevant metrics of plaque vulnerability.

Inverse kinematics analysis of a wrist rehabilitation robot using artificial neural network and adaptive Neuro-Fuzzy inference system

This paper offers a comprehensive investigation into the forward and inverse kinematics of a wrist rehabilitation robot, utilizing the Denavit-Hartenberg method for forward kinematics (FK) and a geometric approach, as well as artificial neural networks (ANN) and adaptive Neuro-Fuzzy inference systems (ANFIS) for inverse kinematics (IK) analysis. While the geometric method entails precise parameter measurements and faces uncertainties, ANN and ANFIS are explored as potential remedies to enhance accuracy and robustness. Evaluating 11 different training functions sourced from existing literature, our study conducts a thorough assessment of their performance within an ANN network. We aim to pinpoint the most suitable training function for achieving optimal IK solutions in the context of a wrist rehabilitation robotic. Additionally, the ANFIS model, trained using Fuzzy C-Means (FCM), sets itself apart from Grid Partitioning (GP) and Subtractive Clustering (SC). Among the ANN training functions, Bayesian regularization with 5 hidden layers emerges as the most effective, yielding low root mean square error (RMSE) values of 0.003, 0.004, and 0.007 degrees for pronation/supination (P/S), abduction/adduction (AB/AD), and flexion/extension (F/E), respectively. Conversely, ANFIS, trained with FCM, demonstrates satisfactory yet less precise results, with RMSE values of 0.191, 0.082, and 0.165 degrees for P/S, AB/AD, and F/E, respectively. Despite its adequacy, ANFIS trails behind ANN, showcasing RMSE reductions of 98.4%, 95.1%, and 95.7% for P/S, AB/AD, and F/E angles, respectively. This study contributes to leveraging ANN and ANFIS for IK analysis in wrist rehabilitation robotics, highlighting the efficacy of ANN, particularly when employing Bayesian regularization, to enhance accuracy.

FFT-based surrogate modeling of auxetic metamaterials with real-time prediction of effective elastic properties and swift inverse design

Auxetic structures, known for their negative Poisson's ratio, exhibit effective elastic properties heavily influenced by their underlying geometry and base material properties. While periodic homogenization of auxetic unit cells can be used to investigate these properties, it is computationally expensive and limits design space exploration and inverse analysis. In this paper, the fast Fourier transform (FFT)-based homogenization approach is adopted to efficiently generate data for developing surrogate models, bypassing concerns about periodic mesh generation and boundary conditions typically associated with the finite element method (FEM). Surrogate models are developed for the real-time prediction of the effective elastic properties of auxetic unit cells with orthogonal voids of different shapes. The generated surrogate models accept geometric parameters and base material properties as inputs to predict the effective elastic constants in real-time. This rapid evaluation enables a practical inverse analysis framework for obtaining the optimal design parameters that yield the desired effective response. The performance of the generated surrogate models is rigorously examined through a train/test split methodology, a parametric study, and an inverse problem. Finally, a graphical user interface (GUI) is developed, offering real-time prediction of the effective tangent stiffness and performing inverse analysis to determine optimal geometric parameters.

Relationship of Dose and Signal Enhancement Properties of Gadoquatrane, a New Tetrameric, Macrocyclic Gadolinium-Based Contrast Agent, Compared With Gadobutrol: A Randomized Crossover Study in Healthy Adults.

To investigate the signal-enhancement properties of the tetrameric gadolinium-based contrast agent (GBCA) gadoquatrane in relation to the administered dose and compare its properties to those of a standard dose of gadobutrol, as a representative of the currently established macrocyclic GBCAs for magnetic resonance imaging. In this randomized, single-blind, 4 × 4 crossover study, 43 healthy adults (19-50 years of age) received 3 single IV injections of gadoquatrane (0.01, 0.03, and 0.06 mmol gadolinium/kg body weight) and 1 injection of gadobutrol (0.1 mmol gadolinium/kg body weight) in randomized sequence with 1-week washout periods between administrations. The relative signal enhancement (RSE) was determined in predefined areas of interest in magnetic resonance image sets of the head-neck region. RSE-vs-dose curves (dose-response curves) were established by linear regression, and comparator-equivalent doses were determined by Bayesian inverse regression analysis. Further, 3 blood samples were taken after each injection for pharmacokinetic analyses, and safety data were assessed. The RSE increased with gadoquatrane dose. A linear function adequately fitted this relationship. In line with the more than 2-fold higher r1 relaxivity of gadoquatrane per gadolinium ion, gadobutrol-equivalent RSE was achieved with gadoquatrane at less than half the gadolinium dose and less than one eighth of the molecule dose.Administration of gadoquatrane and gadobutrol resulted in very similar dose-normalized gadolinium concentrations in plasma, indicating that the pharmacokinetic profiles are essentially the same. Both contrast agents were well tolerated. Adverse events were rare and not dependent on the dose administered. Gadoquatrane has the potential to be an effective GBCA that can be used at substantially lower doses in clinical routine than the currently established macrocyclic GBCAs.

ESTIMATING OPERATIONAL COSTS FOR ENHANCED CONTINUITY IN WATER SUPPLY AND SANITATION SERVICES: AN INVERSE DATA ENVELOPMENT ANALYSIS APPROACH IN CHILEAN UTILITIES

Study regionThe largest 23 water utilities in Chile providing water and sanitation services to 97.9% of total urban customers. Study focusThis study introduces an innovative methodological framework based on inverse data envelopment analysis technique to quantify the additional operational costs required for water utilities to enhance their water supply and sanitation continuity while maintaining their techno-economic efficiency. This framework is pivotal for setting realistic continuity targets and assessing potential impacts on water and sanitation tariffs, thereby aiding in policy and operational planning within the water sector. New hydrological insights for the regionThe analysis was performed across four distinct continuity scenarios revealing substantial cost variability contingent on continuity targets, current service levels, and the efficiency of each utility. Results showed a median operational cost increase that varied from 28.41% in the most stringent scenario to just 0.27% in the most lenient. The financial implications of meeting these costs through water and sanitation tariffs would necessitate a median monthly increase in water bills, ranging from $17.24 per household in the most demanding scenarios to only $0.01 per household in the more lenient scenarios. This research provides a valuable tool for water sector regulators and managers, enabling informed decision-making by balancing service improvement objectives with economic considerations and customer willingness to pay for enhanced service continuity.

A human digital twin approach for fatigue-aware task planning in human-robot collaborative assembly

Human-robot collaboration (HRC) has emerged as a pivotal paradigm in manufacturing, integrating the strengths of both human and robot capabilities. Neglecting human physical fatigue may adversely affect worker health and, in extreme cases, may lead to musculoskeletal disorders. However, human fatigue has rarely been considered for decision-making in HRC manufacturing systems. Integrating adaptive decision-making to optimise human fatigue in HRC manufacturing systems is crucial. Nonetheless, real-time perception and estimation of human fatigue and decision-making informed by human fatigue face considerable challenges. To address these challenges, this paper introduces a human digital twin method, a bidirectional communication system for physical fatigue assessment and reduction in human-robot collaborative assembly tasks. The methodology encompasses an IK-BiLSTM-AM-based surrogate model, which consists of inverse kinematics analysis (IK), bidirectional long short-term memory (BiLSTM), and attention mechanism (AM), for real-time muscle force estimation integrated with a muscle force-fatigue model for muscle fatigue assessment. An And-Or graph and optimisation model-based HRC task planner is also developed to alleviate physical fatigue via task allocation. The efficacy of this approach has been validated through proof-of-concept assembly experiments involving multiple subjects. The results show that the IK-BiLSTM-AM model achieves a minimum of 8% greater accuracy in muscle force estimation than the baseline methods. The 12-subject assessment results indicate that the task planner effectively reduces the physical fatigue of workers while performing collaborative assembly tasks.

The associations between oxidative stress and epilepsy: a bidirectional two-sample Mendelian randomization study

BackgroundStudies on the association between oxidative stress and epilepsy have yielded varied results. In this study, we aimed to investigate the causal relationship between oxidative stress markers and epilepsy.MethodsA bidirectional two-sample Mendelian randomization (MR) study was performed based on publicly available statistics from genome-wide association studies. To explore the causal effects, single nucleotide polymorphisms were selected as instrumental variables. Inverse-variance weighted method was performed for primary analysis, supplemented by weighted median, MR-Egger, simple mode, and weighted mode. Furthermore, sensitivity analyses were performed to detect heterogeneity and pleiotropy.ResultsOur results showed that part of the oxidative stress biomarkers are associated with epilepsy and its subtypes. Zinc is associated with increased risk of epilepsy and generalized epilepsy (odds ratio [OR] = 1.064 and 1.125, respectively). Glutathione transferase is associated with increased risk of generalized epilepsy (OR = 1.055), while albumin is associated with decreased risk of generalized epilepsy (OR = 0.723). Inverse MR analysis revealed that epilepsy is associated with increased levels of uric acid and total bilirubin (beta = 1.266 and 0.081, respectively), as well as decreased zinc level (beta = − 0.278). Furthermore, generalized epilepsy is associated with decreased ascorbate and retinol levels (beta = − 0.029 and − 0.038, respectively).ConclusionsOur study presented novel evidence of potential causal relationships between oxidative stress and epilepsy, suggesting potential therapeutic targets for epilepsy.

A New Approach to Characterize Superplastic Materials from Free-Forming Test and Inverse Analysis

For about 60 years, the aerospace industry has been strongly interested in superplastic forming processes to produce extremely light and complex-shaped components. Superplastic characteristics are found in lightweight metallic materials such as titanium-based, aluminum-based, and, more recently, magnesium-based alloys. Since the high ductility exhibited by superplastic materials is two orders of magnitude higher than that of conventional materials, complex-shaped components can be obtained. If made with conventional materials, they require expensive assembly operations. The behaviour of superplastic materials is summarized by a constitutive equation commonly obtained via tensile testing that subjects the tested material to a one-dimensional stress state. On the contrary, free-forming tests allows us to test the material by subjecting it to a stress state similar to that determined during a real superplastic-forming process. The aim of this work is to define the characteristic parameters of superplastic materials by free-forming tests. The behaviour of superplastic materials is commonly modelled using a power law which puts the material into a stress-to-strain-rate relationship. This law needs to identify two parameters characterizing superplastic materials: the strain rate sensitivity index and the strength coefficient. In this work, a new procedure is presented that implies the two material parameters vary with strain. It allows for a reduction in the number of constants needed to determine the material constitutive equation, thus requiring low simulation time compared to models that adopt the multiple-objective optimization based on genetic algorithms (GAs). It is more suitable to be used in the industrial field. Furthermore, the proposed procedure is compared with a conventional procedure which is also based on the inverse analysis carried out through the use of a finite element analysis. The results of the conventional procedure, based on the inverse analysis, which is conducted through the use of a finite element analysis, are used to calculate the material constants, and are compared with those coming from the procedure proposed in this work. The proposed procedure appears equally simple and gives more accurate results compared to the conventional procedure. In fact, the maximum percentage error, regarding the prediction of the forming times of a free-forming process, was reduced from 20% to 8%. The development of the proposed procedure, as well as the comparison of the results with a conventional procedure, required the development of an experimental activity. This activity consists of free-forming tests conducted at a constant pressure (the pressures employed vary from 0.2 to 0.4 MPa), at a temperature of 753 K, and on circular sheets (thickness 1.0 mm and radius 40 mm) in superplastic magnesium alloy AZ31.

Causal relationship between major depressive disorder, anxiety disorder and constipation: a two-sample Mendelian randomization study

BackgroundEpidemiological and other studies have shown correlations among major depressive disorder (MDD), anxiety disorder (AXD) and constipation. However, no consensus has been reached regarding their interdependence and pathogenesis. Herein, we sought to further explore the causal associations between them.MethodsBidirectional two-sample Mendelian randomization (MR) analysis was performed to confirm the causal link between MDD, AXD and constipation. Genetic instrumental variables for MDD, AXD, and constipation were obtained from publicly available genome-wide association studies (GWASs). In this MR analysis, inverse variance weighting (IVW) was used as the primary analysis method to evaluate the causal effect. Additionally, we employed Cochran’s Q test, MR‒Egger intercept and MR-PRESSO analysis to examine heterogeneity and pleiotropy. Moreover, leave-one-out analysis was employed to investigate the stability of the associations. Finally, a reverse analysis of Mendelian randomization was conducted.ResultsThe results revealed a causal relationship between MDD and an increased risk of constipation (p = 0.0001), whereas AXD (p = 8.52 × 10–1) did not increase the risk of constipation. In the inverse MR analysis, no causal associations were found (constipation to MDD: p = 9.37 × 10–1; constipation to AXD: p = 8.51 × 10–1).ConclusionThis MR study revealed genetic evidence supporting a causal relationship between MDD and constipation.

The rise of intelligent adaptive metasurfaces

Abstract Modern-day data science, together with physical science, are reshaping the landscape of artificial electromagnetic media, metasurfaces, on a scale not seen. Such interaction excels in computationally intensive tasks and real-world applications, such as inverse design, spectral analysis, autonomous devices, and neuromorphic computing. Here we foreground the rise of data-driven metasurfaces that are renovating our understanding and utilization of metasurfaces, moving away from human-based control towards automatic control based on real-time detection and updates of application requirement. To make the most of these emerging opportunities, we also comment on the perspectives of intelligent adaptive metasurfaces.

Influence of quenching and tempering heat treatment on heat flux to the workpiece in dry milling of AISI 1045 steel

Dry machining offers cost and environmental benefits in metal cutting, but the absence of cutting fluid can elevate workpiece temperature, impacting surface quality and dimensional accuracy. This study explores and quantifies the impact of quenching and tempering heat treatment on the heat flux to the work material in dry milling AISI 1045 steel. Inverse heat transfer analysis determines the maximum magnitude of a moving Gaussian heat source corresponding to the heat load into the milled part. The inverse estimates are obtained from temperature measurements taken when machining samples subject to different heat treatment conditions. The estimated heat flux and the measured temperature are discussed in the context of the metallo-thermomechanical connection with microstructural aspects, hardness, and thermal properties. The results reveal a substantial increase in thermal energy transferred to the milled steel when quenched and tempered, with a 33 % higher heat input compared to normalized conditions. This condition is mainly attributed to the increased hardness and reduced thermal conductivity of the tempered martensitic structure obtained through hardening. The estimates show deviations of less than ±5 %, according to uncertainty calculations based on thermal sensitivity and sensor accuracy.

Main Heat Transfer Mechanisms in Hot Stamping Processes: a Review

Objectives: The article reviews heat transfer mechanisms in the hot stamping process, highlighting models to calculate the interfacial heat transfer coefficient (IHTC), crucial for optimizing the cooling and quality of formed products. Theoretical Framework: In hot stamping of high-strength steels, the IHTC is affected by variables such as contact pressure, roughness and temperature. Cooling efficiency directly impacts the temperature distribution and martensitic microstructure of the material, essential for structural strength. Method: The review compares IHTC calculation methods, such as inverse heat conduction analysis and Newton's law of cooling, detailing the convection, radiation and conduction mechanisms at each stage of the process: transfer, positioning and forming. Results and Discussion: The inverse heat conduction analysis proved to be the most accurate for determining the IHTC, compared to the finite element method (FEM). The study suggests that efficient cooling channels and high conductivity materials in the matrix reduce cooling time and improve the quality of the final product. Research Implications: Findings provide a basis for improving thermal management in hot stamping, reducing cycle time and increasing productivity. Originality/Value: This work contributes a comprehensive reference on IHTC, assisting researchers and engineers in optimizing heat transfer and production efficiency in the manufacture of automotive components.

Inverse data envelopment analysis for parallel production systems: an analysis in four types of Chinese banks

Inverse data envelopment analysis for parallel production systems: an analysis in four types of Chinese banks

Design and analysis of terrestrial laser scanner based on a 3-SPR parallel mechanism for improved anti-occlusion scanning

Abstract Laser scanner technology swiftly captures point cloud data of objects and their surrounding environments, proving extensive applications across various sectors. However, it often encounters challenges related to incomplete point clouds due to occlusion from stationary objects. This paper presents a terrestrial laser scanning system based on a 3-SPR (3-Spherical Joint-Active Prismatic Joint-Rotating Joint) parallel mechanism (TLS-PM), specifically designed to enhance scanning coverage during single-station measurements, reduce positioning and workload during multi-station measurements, and mitigate point cloud gaps caused by occlusions.
Initially, a simulation model of the TLS-PM was developed, and both forward and inverse kinematic analysis were performed. Subsequently, the workspace was computed for different spherical joints using this model. An introduction to the TLS-PM’s error and the registration algorithm employed was then provided. Finally, through comparative analysis of simulations and experimental results, the device's measurement accuracy and its capability to resist occlusions were validated. Additionally, the TLS-PM’s anti-occlusion performance was evaluated under various scenarios in a simulated setting. The experimental results demonstrate that, when employing the same conventional point cloud processing algorithms, the TLS-PM significantly improves the background scanning coverage.

Controlling parameters of co-current and counter-current imbibition in naturally fractured reservoirs

Naturally fractured formations are complex petroleum reservoirs that are poor candidates for waterflooding due to difficulties in controlling sweep. Injected water can readily propagate through the fracture system, bypassing the hydrocarbon stored in the matrix. Instead, such systems rely on spontaneous imbibition (SI) from the matrix into the extensive fracture gathering system. SI is a crucial recovery mechanism that relies on capillary pressure-dominated fluid movement. SI can occur through two modes, co-current (COSI) and counter-current (COUSI), depending on the relative direction of fluid movement in response to prevailing boundary conditions. Analytical solutions that incorporate the diffusivity coefficient, which combines relative permeability and capillary pressure curves, are used to describe co-current and counter-current imbibition mechanisms. The perturbation method is one approach in solving these analytical equations. In-situ water saturation profiles, ascertained through experimental CT scanning, serve as validation benchmarks for both co-current and counter-current models. The understanding of the SI process can give more details about the fracture-matrix interactions and the exchange function. Sensitivity studies with respect to the parameterization of the driving force for imbibition, capillary pressure, and the resistive forces, captured in relative permeability curves, can guide experimental study planning and aid in inverse problem analysis in the characterization of naturally fractured reservoirs. The results of a parametric study show that capillary pressure curve parameters, such as capillary entry pressure and capillary exponent, significantly affect the position of the waterfront which indicates the imbibition rate. In addition, the water relative permeability exponent has greater impact on both shape and position of water profile than other relative permeability parameters. The nonwetting phase parameters, like oil endpoint relative permeability and oil exponent, have the least influence on water saturation profile.

Fast forward modeling of magnetotelluric data in complex continuous media using an extended Fourier DeepONet architecture

The calculations of magnetotelluric (MT) responses play a fundamental role in the inversion and resolution analysis for MT problems. Conventional numerical methods for forward modeling involve solving a large system of linear equations. Although these methods provide accurate and stable solutions, they are computationally expensive as the model size increases. In this study, we develop an efficient forward modeling network utilizing Extended Fourier DeepONet (EFDO) architecture for fast MT forward modeling in complex continuous media. By efficiently learning the mapping of differential operators from conductivity models to MT responses, the EFDO framework can effectively approximate the MT forward operator. Once trained, it can instantaneously predict the MT responses for complex continuous resistivity models under identical model discretization conditions. We first compare the accuracy of the EFDO with conventional finite volume (FV) based forward modeling solver and existing deep learning (DL) based modeling schemes. Numerical experiments demonstrate that the MT responses predicted by the EFDO exhibit high conformity with the solutions computed by the FV method. Compared to other DL-based solvers, such as the extended Fourier Neural Operator (EFNO) and UNet-Fourier Neural Operator (UFNO), the EFDO shows superior prediction accuracy while significantly reducing training resource requirements. In addition, the EFDO exhibits excellent generalization, maintaining outstanding prediction performance for the untrained frequencies of the same class samples. The EFDO can predict the MT responses at approximately 200 times the speed of the FV solver. The huge improvement in the computational speed makes the EFDO a promising candidate in simulation-intensive tasks such as detailed resolution analysis and high-dimensional MT probabilistic inversions, which involve tremendous forward evaluations.