Traditional Learning Methods Research Articles

A big data-driven deep learning method for seismic wavefield separation of VSP data

Traditional VSP wavefield separation methods, like transform domain methods and median filtering, struggle with spatial aliasing and complex wave events picking. Many deep learning models trained on datasets from these traditional methods or synthetic datasets often face limitations in applicability and accuracy. Therefore, high-quality datasets are crucial for deep learning. We introduce an efficient iterative strategy designed to incrementally increase the diversity of datasets and their consistency with field data. This strategy involves using a pre-trained network to iteratively predict the VSP data that did not participate in its training. The process continues until clean upgoing and downgoing wavesare extracted. Then, the obtained clean upgoing and downgoing waves are recombined to form new datasets. Subsequently, we continue training the pre-trained network on the new datasets. This enables the final network to effectively adapt to complex VSP data. With this approach, datasets have been gradually upgraded from a simple convolutional seismic data model to more comprehensive wave equation-based datasets, and ultimately including a massive amount of field data. To improve model generalization and address real production needs, we generated a large-scale dataset totaling over one terabyte, enabling a truly big data-driven approach. Utilizing these comprehensive datasets, we trained a universal network for wavefield separation. Through tests with synthetic and field data not included in the training datasets, we show that the separation effect of the universal network is significantly superior to traditional and other deep learning methods.

A COMPARATIVE ANALYSIS OF AI - DRIVEN TRAININGANDMONITORING VS. TRADITIONAL METHODS INEMPLOYEELEARNING AND PRODUCTIVITY MEASUREMENT

Aim: This study aims to evaluate the effectiveness of AI-driven training and monitoringsystemscompared to traditional employee training and productivity measurement methods in corporateand organizational settings. Specifically, it seeks to analyze how AI-driven approaches impact learning outcomes, skill retention, engagement levels, and overall workplace productivity. Additionally, the study will assess whether AI-based monitoring provides more accurate, realtime, and personalized insights into employee performance compared to conventional evaluationtechniques. The findings will contribute to understanding the potential advantages andlimitations of AI-driven solutions in optimizing workforce development and productivitymeasurement. Materials and Methods: This study conducts a comparative analysis of AI-driventraining and monitoring versus traditional employee learning and productivity measurement methods. Participants from various corporate sectors, including IT, finance, healthcare, andmanufacturing, will be divided into two groups: one using AI-powered training and monitoringtools, and the other following traditional instructor-led training and conventional evaluationtechniques. The AI-driven group will utilize advanced Learning Management Systems (LMS)such as Courseware for Business and Linked-in Learning, offering adaptive learning andrealtime feedback. AI-powered monitoring tools, including workplace analytic and biometricfeedback, will assess engagement and performance. The traditional group led sessions, printed materials, and standardized performance reviews. A quasi-experimental design will be employed, beginning with a ore-training assessment to establish baselineknowledge and productivity levels. During training, the AI-driven group will receive adaptiverecommendations, while the traditional group follows fixed schedules. Apost-trainingassessment will evaluate skill retention and productivity improvements, with a long-termfollow-up over three to six months to measure sustained impact. Data will be analyzed throughquantitative methods (t-tests, ANOVA) to compare performance indicators like task completiontime, accuracy, and engagement. Qualitative analysis will include employee surveys andinterviews to assess experiences and perceived effectiveness. This approach will determinewhether AI-driven methods provide a significant advantage over traditional trainingandproductivity evaluation techniques. Conclusion: This study aims to determine the effectivenessof AI-driven training and monitoring compared to traditional methods in employee learningandproductivity measurement. By analyzing both quantitative performance metrics and qualitativeemployee feedback, the research will provide insights into how AI-powered approachesinfluence knowledge retention, engagement, and workplace efficiency. If AI-driven trainingproves superior, it could support the adoption of more personalized and data-driven learningstrategies in corporate settings. Conversely, if traditional methods remain equally effective, organizations may consider hybrid approaches that balance AI’s adaptability with the structuredguidance of conventional training. Ultimately, this study will contribute to a better understandingof AI’s role in optimizing workforce development and performance evaluation

The Effect of Conceptual Change Texts on Pre-Service Science Teachers' Achievement Levels Towards Astronomy

This study aims to develop conceptual change texts to change the misconceptions in astronomy courses and to compare the effect of conceptual change texts on the achievement levels of pre-service science teachers towards astronomy with classical text and traditional learning methods. The study employed a quasi-experimental design with a pre-test post-test control group. The study sample consisted of 4th-grade pre-service teachers studying in the Department of Science Teaching at a state university in Türkiye and taking the astronomy course. The first experimental group, consisting of 27 pre-service teachers, used conceptual change texts, and the second experimental group, consisting of 24 pre-service teachers, used classical texts in the experimental process. The control group of 26 pre-service teachers continued the lessons using the traditional learning method. In this respect, the study's sampling method was determined to be purposive sampling. The astronomy achievement test, developed by the researchers and used to measure the success of pre-service teachers in astronomy subjects, consists of 34 multiple-choice questions. Based on the pilot studies and expert opinions, researchers conducted validity and reliability studies of the test and calculated item difficulty and discrimination indices. In the study, t-tests for dependent groups, t-tests for independent groups and one-factor variance (one-way ANOVA) for unrelated samples were performed, and the results were evaluated. At the end of the intervention, the achievement score of the group to which conceptual change texts were utilized was significantly higher than the group using traditional teaching method.

Leveraging AI-enabled mobile learning platforms to enhance the effectiveness of English teaching in universities

The AI era has ushered in a new wave of opportunities for enhancing classroom education, particularly in the realm of higher education. This study investigates the integration of AI and mobile learning technologies to promote innovation and reform in education. It explores how AI-driven platforms, using soft computing networks, can improve students’ critical thinking skills and foster deeper engagement with academic subjects. The research also examines the deployment techniques and procedures for incorporating mobile learning technologies into higher education settings. A comparison experiment is conducted to assess the effectiveness of the AI-driven system against traditional learning methods, revealing that AI-based learning enhances student motivation and practical skills. The study highlights the broader implications of AI in education, including its potential to facilitate global collaboration, enhance educational equity, and address the evolving needs of digitally connected learners. Finally, the paper suggests directions for future research, including the application of AI across various academic disciplines and the exploration of ethical considerations in AI-driven education.

The impact of virtual reality environments on English language acquisition: Innovative immersive learning technologies for communication skills development

In the rapidly evolving digital landscape, virtual reality (VR) has emerged as a transformative tool in education, particularly in language acquisition. Traditional language learning methods often struggle to provide immersive, interactive, and engaging experiences that foster real-world communication skills. VR environments are increasingly transforming English language acquisition by providing immersive and interactive learning experiences that enhance communication skills development. This paper explores the impact of immersive VR technologies on English language acquisition, focusing on communication skills development through dynamic and interactive learning experiences. A novel Dynamic Monarch Butterfly Optimized Bidirectional Gated Recurrent Unit (DMBO-BiGRU) model is presented to analyze learner interactions within VR environments, assessing communication patterns, language complexity, and learning progression. The dataset, collected from student interactions in VR settings, was preprocessed using noise filtering and normalization to ensure data quality. t-Distributed Stochastic Neighbor Embedding (t-SNE) is employed to extract key features, such as fluency, vocabulary usage, and contextual appropriateness. The DMBO-BiGRU model leverages adaptive learning strategies to provide tailored feedback and optimizes language acquisition based on learners’ communication skills. The effectiveness of the suggested method is demonstrated through experimental results, which indicate good accuracy and positive VR learning scores. The results underscore how immersive, customized, and interactive experiences provided by VR-integrated deep learning models hold the potential to transform language acquisition, showing accuracy of 97.2%, VR score of 97.52%, training gain of 98.49%, detection score of 92.6%, and a retention rate of 96% at iteration 13. This work contributes to the growing field of technology-enhanced education, emphasizing the role of VR and AI-driven methods in enhancing English communication skills.

Fault Recognition Method and Application Based on Generative Adversarial Network

ABSTRACTIn view of the limitation of generalization ability faced by deep learning in fault identification, especially in the case of complex underground geological conditions and variable seismic data characteristics, it is often ineffective to directly use the network based on synthetic data training for fault prediction of real data. To overcome this challenge, this study proposes an innovative solution, which uses generative adversarial network‐UNet (GAN‐UNet) to extract features from data in depth. The network employs a U‐net architecture as the backbone to simultaneously extract all features from forward‐modeled synthetic data and real seismic data. These features are utilized as inputs for both the fault classifier and discriminator. The fault classifier distinguishes between fault and non‐fault segments, while the discriminator employs adversarial mechanisms to differentiate whether input features originate from real seismic data or synthetic data. Once the discriminator, after training, cannot accurately discern the precise source of features, the network model has effectively uncovered the fundamental shared features between the two datasets. This approach demonstrates effective fault recognition in practical seismic data. To verify the effectiveness of the method, we applied it to the actual seismic data sets of the North Sea F3 block and the western deep basin. The experimental results show that compared with the traditional deep learning method, this method shows significant advantages in fault recognition. It not only improves the accuracy of fault identification, but also enhances the adaptability of the model to complex geological conditions.

An Essencist Assessment of the Impacts of Artificial Intelligence on Educational Development in Nigeria

Artificial Intelligence (AI) is transforming education worldwide, offering new opportunities for personalized learning, efficiency in administration, and enhanced teaching methodologies. However, in Nigeria, the integration of AI into the educational sector raises philosophical, infrastructural, ethical, and socio-cultural questions. This paper examines AI’s impact on educational development in Nigeria through the lens of Essencism, a philosophical perspective that emphasizes the intrinsic nature of learning as an intellectual and moral process. The research adopted the qualitative method and collected data from existing literature such as textbooks, journals and other relevant materials. The study explores AI’s potential to enhance accessibility, bridge learning gaps, and support personalized education while critically assessing its limitations, including algorithmic bias, teacher displacement concerns, and infrastructural challenges. Furthermore, the paper addresses the governance of AI in Nigeria’s educational sector, analyzing the absence of clear policies, the implications of data privacy regulations, and the role of international organizations such as UNESCO in shaping AI adoption. It also discusses ethical considerations, particularly how AI affects traditional learning methods, cultural values, and the role of teachers in an AI-driven educational environment. The socio-cultural impacts of AI on Nigeria’s education system are explored, highlighting concerns about the depersonalization of learning and the risk of eroding Indigenous knowledge. Through an Essencist assessment, this paper argues that while AI presents opportunities for educational advancement, its integration must align with the essence of learning—critical thinking, ethical reasoning, and intellectual development. The study concludes that strategic policies, sustainable AI investments, and culturally sensitive approaches are essential for maximizing AI’s benefits while preserving the core values of education in Nigeria.

MAML-EEG: A Meta-learning Strategy Based Domain Generalization Framework for Unseen Subject Motor Imagery Classification

Abstract Since the acquisition of electroencephalogram (EEG) is time-consuming and costly, the target subjects is usually unknown in the practical application of motor imagery (MI) based brain-computer interface (BCI) system. Due to the heterogeneity of individuals, the distribution of MI signals among subjects is quite different, which makes it difficult for traditional deep learning methods to achieve cross-unknown subjects in practical applications. We propose a meta-learning (ML) based method which alleviates this problem by designing models that generalize well to new test subjects. Specifically, our framwork simulates train/test subject shift during training stage by randomly sampling partial samples of partial subjects to synthesize a virtual meta-task set within each batch. The final meta-optimization improves the test performance of multiple subjects while reducing the meta-training loss of each subject. We evaluated our method on cross-unknown subjects MI classification, as well obtaining its advanced performances on two calssic available MI datasets.

JILDYA‐Net: An Efficient Lightweight Multi‐Class Classification Architecture for Skin Lesions

ABSTRACTSkin lesion classification has become increasingly important yet challenging due to the time physicians spend manually analyzing very similar lesions. While traditional deep learning methods have historically offered dependable automated support in lesion detection, thus improving patient care, newer lightweight architectures bring distinct advantages like decreased computational requirements and quicker training, making them better suited for mobile devices, microcontrollers, and embedded systems. The present paper proposes JILDYA‐Net: A lightweight method designed for mobile applications and embedded systems, enabling accurate, rapid, and consistent diagnosis of skin lesions from dermoscopic images. The proposed approach aims to improve the analysis of dermoscopic images containing diverse features through two main components. First, a novel convolutional attention component called attention‐based structural feature enhancement is introduced to enhance skin lesion features. Then, an encoder‐based FNet enables faster processing and lower memory usage, which is especially beneficial for longer input lengths via Fourier Transforms. Additionally, an external attention module refines learned representations and emphasizes relevant features, accelerating convergence and improving model performance and stability during training. Furthermore, augmentation techniques are employed to address class imbalance sensitivity, generating additional data and reducing overfitting. Overall, the goal is to achieve optimal performance with a simple model that trains quickly. Regarding the evaluation metrics, we employ accuracy, sensitivity, specificity, and AUC. Our approach displays a competitive performance, validated through experiments on augmented and balanced versions of the HAM10000 and ISIC‐2019 datasets, as compared with state‐of‐the‐art methods. It demonstrates superior performance in accuracy, sensitivity, and specificity relative to competing methods.

Efficient and interpretable monkeypox detection using vision transformers with explainable visualizations

Monkeypox is a zoonotic disease that poses diagnostic challenges due to its resemblance to other pox-type skin lesions like measles and chickenpox. Traditional deep learning (DL) methods, especially convolutional neural networks (CNNs), often struggle with generalization when trained on small, imbalanced datasets. These methods also tend to lack interpretability and computational efficiency, limiting their use in real-time, resource-constrained settings. This study introduces a lightweight, explainable DL framework based on EfficientFormerV2, which merges the advantages of convolutional inductive biases with efficient token-mixing strategies. We used the publicly available Monkeypox Skin Image Dataset (MSID), which contains 770 images across four categories: Monkeypox, Chickenpox, Measles, and Normal. Through advanced preprocessing and augmentation, we expanded the dataset to 4,000 images, improving class representation and reducing overfitting. Also, we evaluated five models—EfficientFormerV2, T2T-ViT, DeiT, Xception, and MobileNetV4—using metrics like F1-score, specificity, PR AUC, and Matthews Correlation Coefficient (MCC) with 10-fold stratified cross-validation. EfficientFormerV2 performed the best, achieving an F1-score of 98.73%, specificity of 99.63%, PR AUC of 99.86%, and MCC of 94.15%. We used Grad-CAM visualizations to create class-specific heatmaps for better interpretability. This framework combines an efficient architecture, data-centric augmentation, and explainable AI (XAI), offering high accuracy and low-latency predictions, making it suitable for real-time monkeypox screening, especially in low-resource settings.

ОЦІНКА МОЖЛИВОСТІ РЕАЛІЗАЦІЇ ПЕРЕВАГ ДИСТАНЦІЙНОГО НАВЧАННЯ КУРСАНТІВ СПЕЦІАЛІЗОВАНИХ ВИЩИХ НАВЧАЛЬНИХ ЗАКЛАДІВ

Introduction. The rapid advancement of digital technologies has significantly transformed the education sector, introducing new opportunities and challenges. In the military education sector, the integration of distance learning holds particular importance due to its potential to accommodate the unique demands of military personnel. This sector faces specific challenges, including the need for secure communication channels, adaptation of military curricula to digital platforms, and balancing traditional and innovative teaching methods. Purpose. The article explores the application of distance education within higher military educational institutions (HMIs), identifying unique challenges and opportunities in adapting this model to meet the specialized needs of military academies. The focus is on evaluating the feasibility of integrating advanced digital technologies, such as artificial intelligence and adaptive learning, while ensuring the effectiveness, security, and operational alignment of educational processes. The study aims to determine how distance learning can support the development of professional competencies in military personnel while addressing institutional constraints. Methods. The research employs a comprehensive analysis of scientific, methodological, and professional educational resources. Three prominent Ukrainian HMIs—the Military Academy (Odesa), Odesa National University, and Odesa Maritime Academy—were selected as case studies to investigate the practical implementation of distance education models. This analysis includes the evaluation of distance learning platforms, the adaptability of digital tools to military-specific curricula, and the institutional frameworks governing educational methodologies. Results. The distance learning offers significant advantages, including personalized learning schedules, resource efficiency, and improved accessibility, which align with the goals of military education. However, the analysis showed that in military educational institutions the advantages of distance learning can be partially realized due to: 1. Difficulty in adapting standard digital tools to military curricula that require hands-on training and field exercises. 2. Limited access to secure and confidential communication networks for digital platforms in military environments. 3. Impossibility to adopting fully digital methodologies due to necessity to use specific equipment for training. The analysis highlights the importance of composing digital and traditional learning methods to overcome these limitations. Furthermore, the study underscores the role of artificial intelligence in enhancing adaptive learning environments, providing real-time feedback, and personalizing educational trajectories for military personnel. Originality. Unlike previous studies that primarily focus on civilian education, this research evaluates the unique demands of military training and the potential of digital tools to meet these needs. It also emphasizes the importance of customizing distance education to ensure alignment with military-specific operational standards and security protocols. Conclusion. The study concludes that while distance learning presents numerous benefits, same can be partly released during implementation in HMIs. The combination of traditional and digital methodologies is essential to maintain the quality and security of military oriented educational processes. Recommendations include: Most of the advantages of distance learning can be realized and have a positive impact on the educational process in specialized (military) high schools. The use of distance learning for specialized high schools is constructive in terms of structuring the schedule of classes, i.e., the formation of separate blocks of online and offline classes within one week. 3. A full time distance learning may lead to decreasing of the professional skills of cadets.

Bayesian Deep Reinforcement Learning for Operational Optimization of a Fluid Catalytic Cracking Unit

The emerging machine learning techniques provide great opportunities for optimal operation of chemical systems. This paper presents a Bayesian deep reinforcement learning method for the optimization of a fluid catalytic cracking (FCC) unit, which is a key process in the petroleum refining industry. Unlike the traditional reinforcement learning (RL) methods that use deterministic network weights, Bayesian neural networks are incorporated to represent the RL agent. The Bayesian treatment is integrated with the primal-dual method to handle the process constraints. Simulated experiments for FCC determined that the proposed algorithm achieves more stable control performance and higher economic profits, especially under parameter fluctuations and external disturbances.

A Deep Learning Based Hybrid Model Using LSTM and CNN Techniques for Automated Internal Fraud Detection in Banking Systems

The present work investigates the application of deep learning for detecting fraud in banks, particularly insider fraud that poses high risks to the financial sector. conventional rule-based systems are inadequate in the detection of various complexities brought by fraudsters with internal access to the companies’ accounts. To this end, an anomaly detection system with LSTM and CNN for transactional pattern evaluation was designed. Raw financial data and strictly generated fraud cases were used; the data were preprocessed with Pandas and NumPy; models’ training and their evaluation were carried out with TensorFlow and PyTorch. The proposed model also has 98.4% accuracy of detecting fraudulent transactions with 1.7% false positive rate. It was further confirmed that using the new approach has an improvement of 12% in the fraud detection compared with other traditional methods of machine learning. The evidences reported that insider fraud can be detected through the use of deep learning techniques while with a little needed for human involvement. This study emphasizes the importance of applying artificial intelligence in the security of banking systems and future developments of the explainable artificial intelligence in combating fraud in the sector.

Research on remaining useful life prediction method for bucket elevator bearings based on multi-module adversarial domain generation

Abstract Predicting the remaining useful life (RUL) of construction site bucket elevators using deep learning faces significant challenges due to variations in working conditions, which lead to data distribution divergences and limit the applicability of traditional transfer learning methods. To overcome these challenges, this study presents the Multi-module Adversarial Regularization and Synthesis for Domain Generalization with Domain-Adversarial Neural
Network (MARS-DG-DANN) framework. The framework integrates a time series predictive auxiliary and regularization model for feature extraction, a deep adversarial generative model to enhance domain generalization, and a multi-source domain adaptation technique for handling augmented domains. It further incorporates innovative methods, including a lossless spiral matrix signal transformation and an alternating training strategy for the generative model. Validation experiments conducted across three distinct conditions demonstrated the robustness and accuracy of the proposed framework in RUL prediction. By effectively addressing domain shifts, the MARS-DG-DANN framework significantly enhances the generalization performance of predictive models, providing a reliable solution for applications under diverse working conditions.

Traditional or Active Learning Methods in Financial Education? A Randomized Controlled Trial

Traditional or Active Learning Methods in Financial Education? A Randomized Controlled Trial

Gamified Learning Through Knowledge Horizons: An Educational Game-Based Approach

Abstract—Gamification has emerged as a transformative tool in education, leveraging interactive mechanics to enhance engage- ment and retention. This paper introduces Knowledge Horizons, an educational game integrating gamified elements across mul- tiple disciplines, including mathematics, science, social studies, and cognitive skills. Unlike traditional learning methods, this ap- proach fosters active participation and problem-solving through mini-games tailored to different subjects. By incorporating adap- tive difficulty levels, immersive mechanics, and diverse gameplay styles, Knowledge Horizons aims to address the limitations of conventional educational tools. This paper explores the game’s design, implementation, and its potential impact on student engagement and learning ou

Revolutionizing Nursing Education: Problem-Based Learning vs. Traditional Methods for Higher-Order Thinking: A Systematic Review

Traditional lecture-based teaching in nursing education faces increasing criticism for inadequately preparing students for the complex demands of contemporary healthcare. Problem-based learning (PBL) has emerged as an alternative pedagogical approach emphasizing active learning, critical thinking, and problem-solving through real-world clinical scenarios.This systematic review examines the effectiveness of PBL compared to traditional teaching methods in enhancing higher-order thinking skills among nursing students. A comprehensive search of electronic databases (PubMed et al.) encompassed studies published between 2019 and 2024. Studies focusing on nursing students or trainees in higher education settings, comparing PBL to traditional learning methods and reporting outcomes related to higher-order thinking skills were included. The review identified twenty-seven (27) studies that met the inclusion criteria, including qualitative and quantitative designs, systematic reviews, meta-analyses, and randomized controlled trials. The findings consistently indicate that PBL significantly improves critical thinking, problem-solving abilities, and applying theoretical knowledge to practice compared to traditional teaching approaches. PBL’s success stems from its ability to create an active, engaging learning environment that mirrors the challenges nurses face in real-world settings. The evidence strongly supports the integration of PBL into nursing education curricula. While traditional teaching methods retain value in conveying foundational knowledge, incorporating PBL is essential for equipping students with critical thinking and problem-solving skills necessary to deliver high- quality care in today’s complex healthcare landscape.

A visual learning approach to enhance the vocabulary acquisition of seventh grade students

Enhancing language proficiency hinges significantly on the acquisition of a rich vocabulary. Mastery of vocabulary is pivotal for effective communication, making the process of learning words a crucial aspect of language development. In this study, we have integrated semantic triangle theory with dual coding theory, to elevate the vocabulary of middle school language learners. To facilitate the learning of new words, we employed visual aids, including evocative photographs and real-world items sourced from online platforms. Both theories posit that each word is intricately linked to a referent and a linguistic symbol, aiding recognition by storing conceptual information in our minds. Our study focused on 60 students from a suburban school in India, seeking to assess the efficacy of visual aids in expediting vocabulary acquisition. The results revealed a noteworthy trend: the experimental group, utilizing visual aids, demonstrated a more seamless enhancement in vocabulary comprehension compared to the control group, which relied on traditional learning methods. The control group, engaging in conventional language acquisition, exhibited less significant progress. These findings underscore the potential of incorporating visual aids, such as photographs and real-world items, in the classroom setting, highlighting a promising avenue for enhancing middle school learners’ vocabulary acquisition and retention.

Influence of Technology Use on Numeracy Skills in Early Childhood Learners

This study investigates the influence of technology use on numeracy skills in early childhood education, focusing on the perceptions of kindergarten teachers and the relationship between digital tool integration and mathematical development. Data were collected from 100 preschool teachers across diverse educational settings using a descriptive- correlational research design. The study reveals a statistically significant positive correlation between technology use and numeracy skills, with a coefficient of 0.596 (p = 0.001), indicating that increased technology use enhances numeracy skills among young learners. The findings suggest that interactive digital tools can maintain learner focus, facilitate engagement, and provide adequate educational resources, aligning with constructivist theories emphasizing active learning and social interaction. Additionally, the study highlights strong foundational numeracy skills among early learners, such as counting accuracy and number recognition, as critical predictors of future academic success. The research underscores the potential of technology to transform early education by providing personalized, engaging learning experiences that support mathematical development. However, it also emphasizes careful planning and strategic implementation to ensure digital tools complement traditional learning methods. Recommendations include integrating high-quality educational apps into curricula, balancing screen time with other activities, encouraging parental involvement, and ensuring equitable access to digital resources. Further research is suggested to explore the long-term impact of technology on numeracy skills and consider contextual factors such as the home learning environment. By harnessing digital tools, educators can create enriched learning environments that prepare young learners for future academic challenges.

Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching

The symbolic discovery of Ordinary Differential Equations (ODEs) from trajectory data plays a pivotal role in AI-driven scientific discovery. Existing symbolic methods predominantly rely on fixed, pre-collected training datasets, which often result in suboptimal performance, as demonstrated in our case study in Figure 1. Drawing inspiration from active learning, we investigate strategies to query informative trajectory data that can enhance the evaluation of predicted ODEs. However, the butterfly effect in dynamical systems reveals that small variations in initial conditions can lead to drastically different trajectories, necessitating the storage of vast quantities of trajectory data using conventional active learning. To address this, we introduce Active Symbolic Discovery of Ordinary Differential Equations via Phase Portrait Sketching (APPS). Instead of directly selecting individual initial conditions, our APPS first identifies an informative region within the phase space and then samples a batch of initial conditions from this region. Compared to traditional active learning methods, APPS mitigates the gap of maintaining a large amount of data. Extensive experiments demonstrate that APPS consistently discovers more accurate ODE expressions than baseline methods using passively collected datasets.