Calligraphy practice method and system based on user calligraphy practice effect

Abstract

The invention discloses a calligraphy practice method and system based on a calligraphy practice effect of a user. The method comprises the following steps: collecting writing track data and writing statistical data in a calligraphy practice process of the user; based on the writing track data, extracting writing characteristics of the user in three dimensions of a font structure, pen wielding strength and writing rhythm, and fusing a quantitative index and a deep learning score to obtain a quality coefficient of each dimension; constructing a multi-dimensional capability vector and a capability time sequence of the user based on the quality coefficient; training a time sequence prediction model based on the ability time sequence and the writing statistical data; constructing a sample based on the writing statistical data, generating a prediction label by using the prediction model, and generating a symbolic rule for describing a relationship between the practice behavior and the ability change by using a symbolic regression method in a fitting manner; and for the candidate Chinese character set, predicting an expected capability improvement amount after practicing each Chinese character in combination with a symbol rule, calculating a comprehensive benefit value of each Chinese character by integrating the expected improvement amount and the current short plate weight of each dimension of the user, and selecting a target practicing character set to generate a personalized practicing task according to the comprehensive benefit value. According to the invention, accurate evaluation and personalized intelligent recommendation of calligraphy practice are realized.

Description

Technical Field

[0001] This invention relates to the field of intelligent calligraphy technology, specifically to a calligraphy practice method and system based on the user's calligraphy practice results. Background Technology

[0002] In today's digital age, calligraphy, as an important part of traditional Chinese culture, is increasingly being taught in a digital and intelligent manner. With the continuous advancements in computer technology, image processing technology, and artificial intelligence algorithms, it has become possible to utilize these technologies to assist calligraphy practice. Through smart devices and software, the calligraphy practice process can be recorded, analyzed, and the writing results evaluated, providing calligraphy learners with new learning pathways and methods.

[0003] However, existing calligraphy practice systems and methods on the market still have many problems. On the one hand, the accuracy and reliability of judging and scoring students' handwriting are insufficient. Most existing technologies only analyze simple dimensions such as the basic shape and number of strokes, failing to comprehensively and accurately consider the complex and crucial factors in Chinese character writing, such as the structure, stroke strength, and writing rhythm. This leads to biased assessments of students' writing levels and makes it difficult to provide targeted improvement suggestions. On the other hand, the recommendation of practice characters lacks scientific rigor and personalization. Existing systems often recommend characters based on a fixed character library order or simple difficulty levels, failing to fully consider individual differences such as students' writing levels, weaknesses, and learning progress. This results in recommended practice characters that do not meet students' actual improvement needs, affecting the effectiveness of calligraphy practice and learning efficiency. Summary of the Invention

[0004] In view of the problems existing in the prior art, the present invention provides a calligraphy practice method and system based on the user's calligraphy practice effect, realizes personalized training, and effectively improves the efficiency and effect of the user's calligraphy practice.

[0005] This invention is achieved through the following technical solution: A calligraphy practice method based on the user's calligraphy practice results includes the following steps: Step 1: Collect the user's writing trajectory data and related writing statistics during calligraphy practice; Step 2: Based on the writing trajectory data, extract the user's writing features in three skill dimensions: character structure, pen pressure, and writing rhythm; for each skill dimension, integrate the quantitative indicators calculated based on the writing features with the corresponding skill dimension scores generated based on the deep learning model to obtain the quality coefficients of each skill dimension, including structural deviation coefficient, pressure stability coefficient, and rhythm fluency coefficient. Step 3: Based on the quality coefficients of each skill dimension, construct a multi-dimensional ability vector representing the user's current writing level, and form an ability time series reflecting the evolution of the user's ability based on the historical multi-dimensional ability vector; Step 4: Based on the ability time series and the writing statistics, train a time series prediction model to obtain a writing ability prediction model that can predict the user's future writing ability. Step 5: Construct feature samples based on the writing statistics, generate corresponding prediction ability labels using the writing ability prediction model, and form a training dataset; use the symbolic regression method to fit the training dataset, and search for and generate symbolic rules that can describe the relationship between practice behavior and ability changes. Step 6: For the candidate Chinese character set, predict the expected improvement in ability in the three skill dimensions after practicing each Chinese character based on the symbol rules; calculate the comprehensive benefit value of each Chinese character by combining the expected improvement in ability with the training weights of each dimension determined by the user's current ability status; select a target practice character set from the candidate Chinese character set based on the comprehensive benefit value, and generate a personalized practice task based on the target practice character set.

[0006] Preferably, the writing trajectory data includes at least a pen tip coordinate sequence, stroke pressure data, and timestamp information for each stroke; The writing statistics include at least the number of practice sessions, the number of structured practice sessions, and the time interval between practice sessions.

[0007] Preferably, the method for determining the structural deviation coefficient is as follows: Based on the pen tip coordinate sequence, a user character topology map is constructed, and the graph editing distance between the user character topology map and the standard character topology map is calculated. Simultaneously, the user character topology map and related features are input into a deep temporal evaluation model to obtain a structure score. The graph editing distance and the structure score are weighted and fused to obtain a structure deviation coefficient.

[0008] Preferably, the method for determining the force stability coefficient is as follows: Based on the stroke pressure data, the stroke pressure variance is calculated; simultaneously, the similarity between the user's pressure pattern and the pre-stored excellent pressure template is calculated, and the stroke pressure data and related features are input into the depth time series evaluation model to obtain a pressure stability score; the stroke pressure variance, the similarity, and the pressure stability score are weighted and fused to obtain a pressure stability coefficient.

[0009] Preferably, the method for determining the rhythm fluency coefficient is as follows: Based on the timestamp information of each stroke, a user rhythm sequence is constructed; the dynamic time warping distance between the user rhythm sequence and the pre-stored excellent rhythm template sequence is calculated; simultaneously, the user rhythm sequence and related features are input into the deep temporal evaluation model to obtain a rhythm fluency score; the DTW distance and the rhythm fluency score are weighted and fused to obtain a rhythm fluency coefficient.

[0010] Preferably, the method for training the time series prediction model is as follows: The multidimensional ability vector is paired with the writing statistical feature vector associated with the same exercise in a temporal sequence to form a serialized training sample. The temporal prediction model is constructed using a temporal deep neural network; the serialized training samples are input into the model for training; the training objective of the model is: given the writing statistical feature sequence and ability vector sequence within the user's history window, predict the multidimensional ability vector for one or more future practice sessions; By minimizing the loss function between the predicted ability vector and the true ability vector, the parameters of the temporal deep neural network are optimized to obtain the trained writing ability prediction model.

[0011] Preferably, in step 5, feature samples are constructed based on the writing statistics, and corresponding prediction ability labels are generated using the writing ability prediction model to form a training dataset, including: A feature space is constructed based on historical writing statistics, and feature vectors are generated by sampling in the feature space. The feature vectors are input into the writing ability prediction model to obtain the corresponding prediction ability vectors. A training dataset for symbolic regression is constructed based on the feature vectors and the corresponding prediction ability vectors.

[0012] Preferably, the method for searching and generating symbolic rules that can describe the relationship between practice behavior and ability changes is as follows: For each of the aforementioned skill dimensions, a symbolic expression space consisting of basic operators and operands is constructed; For candidate symbolic expressions in the symbolic expression space, calculate their fitting error on the training dataset and evaluate the complexity of their expression structure; A genetic algorithm-based search strategy is adopted to search for the optimal symbolic expression in the symbolic expression space with the goal of minimizing the comprehensive objective function; wherein, the comprehensive objective function is the sum of the fitting error and the structural complexity of the expression weighted by the complexity penalty coefficient; The optimal symbolic expression and its determined parameters are used as the symbolic rule describing the relationship between practice behavior and ability change in this skill dimension.

[0013] Preferably, the method for determining the total efficiency of each Chinese character is as follows: Determine the weight of weaknesses in each skill dimension based on the current calligraphy practice ability vector; For each Chinese character in the candidate Chinese character set, obtain the preset multi-dimensional training feature vector of that Chinese character; For each Chinese character in the candidate character set and in conjunction with the optimal symbol rule, estimate the expected improvement in ability across each skill dimension after practicing that character; and calculate the comprehensive benefit value of each Chinese character based on the expected improvement in ability across each skill dimension and the user's weakness weights across each skill dimension.

[0014] A calligraphy practice system based on the user's calligraphy practice results includes: The calligraphy data acquisition module is used to collect the writing trajectory data and related writing statistics of users during calligraphy practice. The writing quality assessment module is used to extract the user's writing features in three skill dimensions: character structure, pen pressure, and writing rhythm based on the writing trajectory data. For each skill dimension, the quantitative index calculated based on the writing features is combined with the corresponding skill dimension score generated based on the deep learning model to obtain the quality coefficient of each skill dimension, including the structural deviation coefficient, the pressure stability coefficient, and the rhythm fluency coefficient. The ability profiling module is used to construct a multi-dimensional ability vector representing the user's current writing level based on the quality coefficients of each skill dimension, and to form an ability time series reflecting the evolution of the user's ability based on the historical multi-dimensional ability vectors. The calligraphy skill acquisition module is used to train a time-series prediction model based on the ability time series and the writing statistics data to obtain a writing ability prediction model that can predict the user's future writing ability. The rule extraction module is used to construct feature samples based on the writing statistics, generate corresponding prediction ability labels using the writing ability prediction model, and form a training dataset; the training dataset is fitted using the symbolic regression method, and symbolic rules that can describe the relationship between practice behavior and ability changes are searched and generated. The character practice recommendation module is used to predict the expected improvement in the three skill dimensions after practicing each character in a candidate character set, based on the symbol rules; calculate the comprehensive benefit value of each character by combining the expected improvement in the expected improvement with the training weights of each dimension determined by the user's current ability status; select a target practice character set from the candidate character set based on the comprehensive benefit value, and generate a personalized practice task based on the target practice character set.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects: This application provides a calligraphy practice method based on user calligraphy practice effects. By collecting writing trajectory data and statistical data during user calligraphy practice, it performs a refined and multi-dimensional quantitative assessment of writing quality from three core skill dimensions: character structure, pen stroke strength, and writing rhythm, forming quality coefficients for each dimension. Furthermore, based on these quality coefficients, it constructs a time series reflecting the user's ability evolution and uses a time-series prediction model to predict the user's future writing ability. Further, through symbolic regression, it mines interpretable mathematical rules describing the mapping relationship between specific practice behaviors and ability changes from a large amount of practice data. Finally, using these rules, combined with the user's current weaknesses (weights of weaknesses in each dimension), it predicts the targeted improvement effect of practicing different Chinese characters and quantifies the comprehensive benefit value of each candidate character, thereby intelligently selecting the target practice character set that maximizes the user's ability improvement and generating personalized practice tasks. This solution breaks through the limitations of traditional calligraphy systems with single evaluation dimensions and rigid recommendations, achieving a complete closed loop from accurate multi-dimensional diagnosis and data-driven ability evolution modeling to personalized recommendations based on interpretable rules. It can dynamically adapt to each user's ability level, scientifically quantify the benefits of practice, truly achieve individualized instruction, and effectively improve the efficiency and effectiveness of calligraphy practice.

[0016] This application also proposes a calligraphy practice system based on the user's calligraphy practice results, an electronic device, and a computer storage medium, which possess all the advantages of the aforementioned calligraphy practice methods based on the user's calligraphy practice results. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of this application and should not be regarded as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a flowchart of the calligraphy practice method based on the user's calligraphy practice effect according to the present invention.

[0019] Figure 2 This is a block diagram of the calligraphy practice system based on the user's calligraphy practice results according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of the embodiments of this application clearer, the technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. The components of the embodiments of this application described and shown in the accompanying drawings can generally be arranged and designed in various different configurations.

[0021] Therefore, the following detailed description of the embodiments of this application provided in the accompanying drawings is not intended to limit the scope of the claimed application, but merely to illustrate selected embodiments of the application. All other embodiments obtained by those skilled in the art based on the embodiments of this application without inventive effort are within the scope of protection of this application.

[0022] A calligraphy practice method based on the user's calligraphy practice results includes the following steps: Step 1: Collect calligraphy practice data from the user's calligraphy practice process; The calligraphy practice data includes writing trajectory data and writing statistics; the writing trajectory data includes at least pen tip coordinate sequence, stroke pressure data, and timestamp information for each stroke; the writing statistics include at least the number of practice sessions, the number of structural practice sessions, and the practice time interval. Step 2: Based on the writing trajectory data, calculate the user's quality coefficients in the three skill dimensions of structure, strength, and rhythm: structural deviation coefficient, strength stability coefficient, and rhythm fluency coefficient. The structural deviation coefficient is obtained by fusing the graph editing distance between the user's glyph topology graph and the standard glyph topology graph, as well as the structural score output by the deep temporal evaluation model. The force stability coefficient is obtained by fusing the stroke pressure variance, the similarity between the user's force pattern and the excellent force template, and the force stability score output by the deep temporal evaluation model. The rhythm fluency coefficient is obtained by fusing the dynamic time warping distance between the user's rhythm sequence and the excellent rhythm template sequence, as well as the rhythm fluency score output by the deep temporal evaluation model.

[0023] Step 3: Based on the structural deviation coefficient, strength stability coefficient, and rhythm fluency coefficient obtained in Step 2, construct a multi-dimensional ability vector representing the user's current calligraphy level, and construct a time series of the user's ability evolution over time based on the historical multi-dimensional ability vector.

[0024] Step 4: Train a time-series deep regression model based on the ability time series and writing statistics to obtain a writing ability prediction model, which is used to predict the multidimensional ability vector for the next time period.

[0025] Step 5: Sample feature vectors based on historical writing statistics, input feature vectors into writing ability prediction model to obtain corresponding predicted ability vectors, combine feature vectors and predicted ability vectors to form samples, construct training dataset for symbolic regression based on all samples, and use symbolic regression algorithm to automatically search and generate optimal symbol rules in predefined expression space based on the training dataset for symbolic regression. The optimal sign rule is determined by minimizing the comprehensive objective function, which is a weighted sum of the data fitting error and the expression structure complexity penalty term. Step 6: For each Chinese character in the candidate character set and in conjunction with the optimal symbol rule, estimate the expected improvement in ability in each skill dimension after practicing the Chinese character; calculate the comprehensive benefit value of each Chinese character based on the expected improvement in ability in each skill dimension and the user's weakness weight in each skill dimension; select a target practice character set from the candidate character set based on the comprehensive benefit value, and use the target practice character set for calligraphy practice.

[0026] This adaptive calligraphy practice method, based on improving user calligraphy practice results, extracts quantitative indicators of structure, strength, and rhythm from handwriting data and integrates them with deep learning model scoring to achieve accurate and multi-dimensional diagnosis of users' writing levels. It further transforms historical practice data into a user ability evolution model and uses symbolic regression to mine interpretable learning patterns from the data. Ultimately, based on these patterns and the user's current weaknesses, the system can quantitatively predict the targeted improvement effects of practicing different Chinese characters, intelligently recommending a set of characters that maximizes overall benefits within a limited practice time, achieving truly personalized instruction. This method uses a multi-dimensional fusion evaluation system to overcome the shortcomings of traditional methods with single evaluation dimensions, resulting in a more comprehensive and accurate assessment. Secondly, through data-driven modeling and symbolic regression, the system can not only predict trends but also provide interpretable reasons for recommending specific characters, enhancing credibility and educational value. Finally, the entire process forms a complete closed loop from accurate diagnosis to personalized planning and feedback optimization, dynamically adapting to changes in user abilities, thereby significantly improving the efficiency and effectiveness of calligraphy practice.

[0027] Example 1 An adaptive calligraphy practice method based on improving user calligraphy practice results includes the following steps: Step 1: Collect calligraphy practice data from the user's calligraphy practice process, including writing trajectory data and writing statistics. The specific process is as follows: S1.1 Collect writing trajectory data of the user during the writing of Chinese characters, which includes at least: pen tip coordinate sequence, used to determine the starting point, ending point, turning point and skeleton shape of the user's writing strokes; stroke pressure data, used to characterize the changes in force of the user during the writing process; and timestamp information of each stroke, used to record the writing time of each stroke and the pause time between strokes.

[0028] S1.2 Writing statistics include the number of practice sessions, the number of structural practice sessions, and the time intervals; 1) Number of practice sessions: Based on the user identifier and the encoding of the current practice Chinese character, the user's practice behavior is statistically analyzed and labeled to iteratively update various practice statistics, including but not limited to: the cumulative number of practice sessions for each Chinese character; the cumulative number of practice sessions for various structural elements and radicals; the time interval between each practice session; the daily / weekly / monthly practice frequency; and the number and proportion of specific practice sessions for different skill dimensions such as structure, strength, and rhythm.

[0029] 2) Number of structural practice sessions: Based on the pre-built mapping relationship between Chinese character components and structures, the current Chinese character is classified into the corresponding structure or component category (e.g., left-right structure, top-bottom structure, or a certain radical component), and the cumulative number of practice sessions under that structure category is updated. This is to characterize the intensity of a user's practice across different structural types.

[0030] For different preset training skill dimensions, it is also necessary to mark this exercise as having an emphasis based on the attributes of the current exercise task: structural training, strength training, rhythm training, or comprehensive training. This information is then used to update the number of specific exercises for the three dimensions of structure, strength, and rhythm, as well as the exercise frequency over a recent period (such as the last week or the last month), in order to reflect the user's exercise distribution across each sub-skill dimension.

[0031] 3) Time Interval: To represent the time interval information of the practice, while recording the start and end times of this practice, the time of the user's last practice for the same Chinese character, the same structural category, or the same training skill dimension is retrieved, and the time interval between two adjacent practice sessions is calculated: The time interval sequence of the most recent practice sessions and the daily / weekly / monthly practice frequency are written into the practice record for subsequent skill acquisition curve modeling and adaptive recommendation strategy optimization.

[0032] Step 2: Quantitatively evaluate the calligraphy practice data across multiple skill dimensions, determine the quality coefficients and corresponding confidence levels for each skill dimension, and determine diagnostic labels representing the current writing level based on the quality coefficients of the multiple skill dimensions.

[0033] Among them, the multi-skill dimensions include at least font structure, stroke strength, and writing rhythm; the quality coefficients corresponding to each skill dimension include structural deviation coefficient, strength stability coefficient, and rhythm fluency coefficient.

[0034] In this embodiment, the calligraphy practice data (pen tip coordinate sequence, stroke pressure data, timestamp information, practice times, structural practice statistics, and time intervals) collected in step 1 are preprocessed and feature extracted to construct explicit feature vectors for three skill dimensions: structure, strength, and rhythm. Based on this, a deep temporal evaluation model based on recurrent neural networks, long short-term memory networks (LSTM), or Transformer learning curves is introduced. A graph neural network (GNN) is used to encode the character skeleton topology. A multi-task learning framework is employed to simultaneously output structure scores, strength scores, rhythm scores, fine-grained diagnostic labels, and corresponding confidence scores. These are then fused with traditional measurement results through index generation to obtain the final structure deviation coefficient γ, strength stability coefficient δ, and rhythm fluency coefficient η. The specific method is as follows: I. Calculation method of structural deviation coefficient γ (deep temporal evaluation model + graph editing distance fusion); Based on the pen tip coordinate sequence and timestamp information collected in step 1, the writing trajectory is preprocessed (including outlier removal, smoothing, stroke segmentation, etc.), the stroke skeleton is extracted, and a user character topology map is constructed. With standard glyph topology diagram In the topological graph, nodes represent key stroke feature points, and edges represent the connections between strokes.

[0035] For the structural dimension, the graph edit distance between the user glyph topology graph and the standard glyph topology graph is first calculated. ;

[0036] in, To be The edge in Transform into Corresponding edge The cost function takes into account both the relative differences in length and the differences in direction and angle of the corresponding edges. Based on this, a normalization function is used to map the graph editing distance to the intermediate coefficient of structural deviation based on traditional metrics. Using logical function form:

[0037] in, This represents the median coefficient of structural deviation based on graph edit distance. This is the gain coefficient. This is a preset reference distance threshold used to adjust the sensitivity and reference point of the mapping.

[0038] At the same time, the user's glyph topology map The input is fed into a graph neural network encoder to obtain a structural feature representation vector. The data is then combined with temporal features extracted from writing trajectory data (such as stroke duration sequences and pause duration sequences) and statistical features extracted from writing statistics data (such as the cumulative number of practice sessions for the current Chinese character, the cumulative number of practice sessions for the corresponding structure category, and the time interval between adjacent practice sessions) and input into a deep temporal evaluation model to obtain the structure score for that practice session. Its form can be expressed as:

[0039] in, This represents the auxiliary feature vector related to this exercise, including the number of exercises, structure category exercise statistics, time intervals, etc. The parameters of the subnetwork for structure evaluation are provided. The model is trained offline based on expert-annotated structure scores through multi-task learning.

[0040] To obtain the final structural deviation coefficient The structural deviation coefficient is obtained by weighted linearly fusing the structural score of the deep temporal evaluation model and the intermediate coefficient based on graph edit distance. Defined as:

[0041] in, To integrate the weight parameters, cross-validation or learning them during model training can be used. Coefficients The value ranges from 0 to 1. The closer the value is to 1, the greater the deviation from the standard character structure. The closer the value is to 0, the closer the structure is to the standard.

[0042] The deep temporal evaluation model can also output a structure-related fine-grained diagnostic label probability vector. (e.g., center of gravity too high / too low, left-right imbalance, etc.) and structural assessment confidence level This is used for subsequent feedback display and abnormal sample handling.

[0043] II. Calculation method of force stability coefficient δ (stability score of force dimension + pressure variance + template similarity) Regarding the force dimension, the complete writing process is divided into several stroke segments based on stroke pressure data. Pressure data sequence within each stroke segment Calculate statistical characteristics such as mean and variance.

[0044] No. The pressure variance within a stroke is defined as:

[0045] in, For the first The average value of the stroke pressure sequence.

[0046] Calculate the average pressure variance of all strokes based on the pressure variance of each stroke segment. :

[0047] in, This represents the total number of strokes in a Chinese character.

[0048] The intermediate coefficient for force stability is determined based on the average pressure variance. The expression is as follows:

[0049] in, The preset attenuation factor, The closer to 1, the smaller the pressure variance and the more stable the intensity.

[0050] Simultaneously, several excellent intensity templates are pre-learned from expert samples, and the similarity between the user's current intensity pattern and these templates is calculated. Let the user's overall intensity pattern feature vector be... No. A good strength template is Then we can define the first The cosine similarity of the templates is:

[0051] The maximum similarity can be further taken as the overall similarity between the user strength pattern and the excellent template set:

[0052] The deep temporal evaluation model outputs a strength stability score based on the fusion of temporal features and stress statistics. It can be represented in the following form:

[0053] in, This is the implicit representation obtained by encoding the trajectory and pressure time series by a time-series neural network.

[0054] Final strength stability coefficient By depth rating Intermediate coefficients based on variance and template similarity The result obtained by fusing within the linear normalization framework is:

[0055] in, ; The value ranges from 0 to 1. The larger the value, the more stable the user's pen stroke pressure and the closer it is to the excellent pressure mode. Similarly, the deep time-series assessment model also outputs a probability vector of intensity-related diagnostic labels. (For example, excessive fluctuations in force, insufficient force at the end of a stroke, etc.) and the confidence level of force assessment It is used for generating subsequent teaching suggestions and handling abnormal data.

[0056] III. Calculation method of rhythm fluency coefficient η (multi-rhythm template + depth scoring + DTW) For the writing rhythm dimension, the writing time of each stroke is calculated based on the timestamp sequence. The duration of pauses between adjacent strokes This constitutes the user's stroke duration sequence and pause duration sequence:

[0057] The user rhythm sequence is obtained by alternating and combining stroke duration sequences and pause duration sequences. :

[0058] Multiple excellent rhythm style templates were pre-extracted from standard template libraries and samples from renowned artists, each style... Corresponding standard rhythm sequence For each template, the Dynamic Time Warping (DTW) algorithm is used to calculate the distance between the user's rhythm sequence and the template sequence. .

[0059] In the Dynamic Time Warping (DTW) algorithm, the distance matrix is ​​first constructed, and its elements are defined as follows:

[0060] Then, search the distance matrix for the optimal path from the top left corner to the bottom right corner. The sum of all elements along this path is the DTW distance. (Dynamic time-normalized distance):

[0061] Among various rhythm style templates, the one that best matches the user's rhythm is selected, and its distance is:

[0062] The intermediate coefficient of rhythmic fluency is determined based on the dynamic time warping distance; The intermediate coefficient of rhythmic fluency based on a single template is defined as follows:

[0063] In the case of multiple templates, the intermediate coefficient of rhythmic fluency is defined as:

[0064] in, The maximum acceptable time adjustment distance is preset, and different values ​​can be set according to the number of strokes.

[0065] The deep temporal evaluation model integrates rhythm sequences and rhythm-related statistical features to output a rhythm fluency score. It can be represented in the following form:

[0066] in, For rhythm-related statistical features (such as total duration, rhythm variability, average pauses, etc.).

[0067] Rating for smoothness of rhythm DTW-based intermediate coefficient of rhythmic fluency The final rhythmic smoothness coefficient is obtained by merging the components. In one implementation, it can be defined as:

[0068] in, ,and . The value range is 0–1. The larger the coefficient, the closer the user's writing rhythm is to a certain excellent rhythm style and the smoother the overall writing is.

[0069] The deep temporal evaluation model also outputs a probability vector of rhythm-related diagnostic labels. (e.g., too many / too few pauses, inconsistent tempo) and the confidence level of tempo assessment For results with low confidence, the indicator generation and post-processing subunit can reduce the weight of this result in the user's long-term capability profile, or mark this exercise as a suspicious sample.

[0070] In summary, step 2, through three sub-processes—preprocessing, feature extraction, and deep evaluation—maps the original writing trajectory data and practice statistics into structural deviation coefficients. Stability coefficient of force Rhythm fluency coefficient In the above structural deviation coefficient Stability coefficient of force Rhythm fluency coefficient Based on this, we obtain fine-grained diagnostic label probability vectors and confidence information corresponding to the three skill dimensions.

[0071] Let the shared latent representation vector of the deep temporal evaluation model be... For the three dimensions of structure, intensity, and rhythm, diagnostic label output headers are set respectively, and the corresponding diagnostic label sets are denoted as follows:

[0072] Among them, the labels for the structural dimension can include high center of gravity, low center of gravity, left-right imbalance, excessive horizontal tilt, etc.; the labels for the strength dimension can include excessive strength fluctuation, insufficient strength at the beginning of the stroke, insufficient strength at the end of the stroke, etc.; and the labels for the rhythm dimension can include too many pauses, too few pauses, and fluctuating rhythm.

[0073] Correspondingly, the diagnostic label probability vectors for the three skill dimensions are defined as follows:

[0074] in, This represents the element-wise Sigmoid function. To diagnose the label output layer weight matrix, This is the bias vector. Each component is located in the interval [0,1], representing the probability that the corresponding diagnostic label is "true".

[0075] For each skill dimension and each diagnostic label A binary diagnostic result can be obtained through threshold decision:

[0076] Similarly, it can be defined and ; in, For the structural dimension The decision thresholds for each diagnostic label can be optimized using a validation set. Finally, these diagnostic labels, along with the three-dimensional quality coefficients, are output as the basis for subsequent feedback presentations and the generation of teaching suggestions, helping users and teachers understand the specific reasons behind high and low scores.

[0077] For the confidence output, the deep evaluation subunit shares the implicit representation. Based on this, confidence output heads are set up for the three skill dimensions of structure, strength, and rhythm, and the confidence scores for structure assessment, strength assessment, and rhythm assessment are defined as follows:

[0078] in, The weight vector for the confidence output layer for each skill dimension. The corresponding bias is given. All three confidence values ​​are in the range [0,1]. The closer the value is to 1, the higher the confidence level of the model's evaluation results for the corresponding dimension.

[0079] Simultaneously construct a comprehensive confidence index For example, the average confidence level of the three skill dimensions can be used:

[0080] Based on the aforementioned confidence level, outlier samples are suppressed or labeled. If the confidence level of a particular evaluation falls below a preset threshold... In such cases, the following strategies can be implemented: On the one hand, the results of this exercise can be weighted and smoothed when constructing the user capability vector to reduce its impact on the long-term profile; on the other hand, this exercise can be marked as a suspicious sample, prompting the system or user to recollect data as needed. For example, suppose the original capability vector obtained from this evaluation is:

[0081] The smoothed capability vector at the previous time step is Then, weighted smoothing based on confidence level can be performed to obtain a new capability vector. :

[0082] You can also use them separately according to skill dimensions. The three components are weighted sequentially. Through this design, the impact of assessment results with low confidence on user capability profiles is significantly weakened, thereby improving the robustness of the entire abnormal and accidental touch data.

[0083] Step 3: Based on the quality coefficients (structural deviation coefficients) of each skill dimension Stability coefficient of force Rhythm fluency coefficient (and corresponding confidence information) to construct a multi-dimensional ability vector representing the user's current calligraphy level, and then construct a time series of the user's ability evolution over time.

[0084] User capability profiles are generated based on multi-dimensional capability vectors, providing a unified representation of user capabilities for subsequent skill acquisition modeling and personalized recommendations; this specifically includes the following three processes: S3.1, Indicator Normalization and Multidimensional Capability Vector Construction; 1) In a certain user's... In this exercise, a multidimensional capability vector is constructed based on its three-dimensional quality coefficient and its confidence level. Structural deviation coefficient: ,correspond ; Force stability coefficient: ,correspond ; Rhythm smoothness coefficient: ,correspond ; Corresponding confidence level: .

[0085] The expression for the multidimensional capability vector is as follows:

[0086] in,

[0087] Among them, the larger the structural deviation coefficient, the worse it is (the greater the deviation); the larger the strength stability coefficient and rhythm fluency coefficient, the better it is (the more stable / the smoother it is).

[0088] To ensure that all three skill dimensions reflect the intuitive meaning that higher numerical values ​​equate to greater ability, the structural dimension is unified in direction, and structural mastery, strength mastery, and rhythm mastery are defined as follows:

[0089] Thus, the three levels of mastery All values ​​are within the range of [0,1], and the larger the value, the stronger the ability of that skill dimension.

[0090] Based on this, the mastery of structure, strength, and rhythm is normalized to construct a standardized multidimensional capability vector:

[0091] in, That is, the user in the first During each practice session, the immediate ability scores for the three sub-skills of structure, strength, and rhythm are calculated; all three components are between 0 and 1, with the closer to 1 indicating a better performance in that skill dimension.

[0092] For samples with low confidence, the weighted smoothing strategy given in step 2 can be used (utilizing...). Alternatively, a weighted average of the current capability vector and several historical capability vectors can be used (or a comprehensive confidence level) to mitigate the impact of outliers.

[0093] S3.2, Constructing a capability time series; To characterize the changes in a user's learning process over time, a capability time series is constructed based on multidimensional capability vectors at historical moments, and the user's writing level is determined based on the capability time series.

[0094] For a given user, the time series of abilities generated from each practice session is recorded as follows:

[0095] in This indicates practice sessions ordered by time, with each... It also includes information such as practice timestamps, Chinese character codes or task IDs, and cumulative practice counts.

[0096] Based on the ability time series, calculate time statistical features, such as the moving average ability of the most recent K practice sessions, to represent the average level at the current stage:

[0097] This moving average can be used to determine: whether the user's recent grasp of the structure has increased significantly; whether the stability of the intensity fluctuates greatly (which can be viewed in conjunction with variance); and whether the smoothness of the rhythm is continuously improving or entering a plateau period.

[0098] S3.3, Multi-level capability aggregation and profile parameter generation; Based on the capability time series, further aggregation is performed at multiple granularities to form a hierarchical capability profile; among which, multi-granularity aggregation includes single-task aggregation, structural aggregation and skill dimension aggregation; 1) Single-task aggregation is converted into single-word aggregation; For a certain Chinese character (or a specific practice task), let the set of practice indices corresponding to it be . Then the aggregation capability vector of the character can be defined as:

[0099] Used to indicate the user's input of Chinese characters The overall grasp of a word can reveal whether a particular word has been mastered or remains weak.

[0100] 2) Structural aggregation is the structural aggregation of fonts; By using structural category mapping (such as left-right structure, top-bottom structure, enclosing structure, etc.), multiple Chinese characters can be classified into structural types. Let the structure type be... The corresponding set of practice indices is Then the average capability vector of this structure type is:

[0101] Through different structural types It depicts users' preferences and weaknesses regarding different character structures, such as left-right and top-bottom structures.

[0102] 3) Skill dimension aggregation aggregates the structural dimension, intensity dimension, and rhythm dimension to represent the user's current overall ability level.

[0103] At a global scale, by aggregating the three dimensions along the time axis, we obtain the overall average level and trend of users in terms of structure, intensity, and rhythm. For example, the overall average ability vector can be defined as:

[0104] Building upon this, three-dimensional capabilities can be integrated into a comprehensive capability index through weighted summation, principal component analysis, or simple neural networks. It is used for overall ranking and periodic evaluation.

[0105] S3.4, Image Parameter Generation and Storage The competency profile generation module will extract and maintain a set of parameterized profile information for each user based on the aforementioned time series and multi-level aggregation results, including but not limited to: the current average mastery level of each skill dimension (such as the average mastery level of the most recent data). etc.); historical best level (e.g.) (etc.); short-term improvement rate (which can be estimated by the time series slope); parameters such as initial level, learning speed, upper limit, and forgetting characteristics obtained from fitting the learning curve (which can be filled in by the output of the subsequent skill acquisition modeling module).

[0106] These parameters are written into the user capability profile parameter table as a long-term profile record for the user, and stored together with the user's basic information, the most recent update time, the profile version number, etc., for subsequent skill acquisition modeling and adaptive recommendation modules to call.

[0107] Step 4: Based on the capability time series and written statistical data, and combined with the time series deep regression model, predict the multidimensional capability vector for the next time period.

[0108] Based on the ability time series generated in step 3 and the writing statistics collected in step 1, a time-series deep regression model is introduced to model and predict the user's skill acquisition process in the three skill dimensions of structure, intensity, and rhythm. A learning curve that evolves with the number of practice sessions and practice time is constructed, providing a computable skill evolution basis for subsequent symbolic rule extraction and personalized recommendations. Specifically, the process includes the following: S4.1 Constructing a sample sequence based on capability time series and writing statistics; For each user u, obtain the capability time series generated in step 3:

[0109] in, These represent the mastery of the three skill dimensions of structure, intensity, and rhythm during the t-th practice session (the higher the better).

[0110] Simultaneously, writing statistics related to this exercise are obtained from step 1 to form a feature vector. This includes, but is not limited to: the cumulative number of practice sessions for the current character. The cumulative number of practice sessions for the current structure / component category. Number of practice sessions for each skill level and their recent frequency; time interval between sessions and the previous practice session. The encoding characteristics of the current practice object category (character structure type, difficulty level, etc.). This can be denoted as:

[0111] Then, on a user-by-user basis, the capability time series and feature vectors are paired by time, and the pairing results are arranged chronologically to obtain the sample sequence:

[0112] S4.2 Construct and train a time-series deep regression model to obtain a writing ability prediction model.

[0113] A temporal deep neural network model is employed, including but not limited to at least one of recurrent neural networks, long short-term memory networks, gated recurrent units, or Transformer architectures, to predict a user's calligraphy ability at the current or future moment based on a sample sequence of historical practice behaviors.

[0114] For the current target time t, select the feature vectors of a historical window of length L to construct the input feature vector sequence:

[0115] Use historical capability time series as auxiliary input:

[0116] Using time-series networks Encode the historical feature vector sequence to obtain the latent learning state representation at the current time step. :

[0117] in, These are parameters for the timing encoder. It can be viewed as the user's learning state vector at time t.

[0118] Representing the implicit learning state Input multilayer feedforward network The system outputs predictive ability values ​​for three skill dimensions: structure, intensity, and rhythm, forming a predictive ability vector. :

[0119] in, These are the decoder parameters. The network employs a multi-task learning framework and shares... It simultaneously fits the mastery level of three skill dimensions.

[0120] During the training phase, the true ability vector for the next practice session As a monitoring signal, a multi-task regression loss is constructed. Weighted mean square error is used:

[0121] Among them, d takes three skill dimensions: structure, intensity, and rhythm. Weights are assigned to each skill dimension. ,t represents the model's predictive ability value. This represents the true capability value. It is calculated using a gradient descent-like algorithm. Optimize.

[0122] After training, the deep regression model can predict the expected level of the current or future practice in terms of structure, intensity, and rhythm for any given historical practice sequence.

[0123] S4.3. Based on the predicted ability vector output by the deep regression model, a parametric function model is used to mathematically model and fit the user's learning trajectory across various calligraphy skill dimensions. A nonlinear optimization method is then used to estimate the parameter set representing individual learning characteristics, including initial ability level, learning rate, ability ceiling, and forgetting parameters. This process transforms the user's learning behavior into quantifiable mathematical expressions, providing a structured and interpretable skill evolution model for subsequent personalized recommendations and teaching strategy optimization.

[0124] Taking the number of practice sessions (n) as the independent variable, and using the structural dimension as an example, we can obtain the sequence of how ability changes with the number of practice sessions: Similarly, we can obtain... Here It can take the actual observed values ​​or the predicted values ​​of the deep regression model under different n values.

[0125] Several candidate function families are pre-defined for each skill dimension, including power-law, exponential convergence, and logarithmic growth. Example formats include: A power-law learning curve in the structural dimension (ability increases with the number of practice sessions, but the rate of increase decreases):

[0126] in, Represents the potential upper limit of the structural dimension (the level that n approaches when n is very large); Control the initial gap (the gap between n=1 and the upper limit); Control the rate at which progress decreases as the number of practice sessions increases.

[0127] The exponentially convergent learning curve of the strength dimension:

[0128] in, Indicates the upper limit of the strength dimension; Indicates the initial gap; To control the learning rate, the larger C is, the faster the convergence.

[0129] The rhythm dimension can be represented by a logarithmic growth model:

[0130] in, Approximates the starting level; Control the rate of logarithmic growth.

[0131] In summary, each skill dimension has a set of parameters to be estimated, such as:

[0132] These parameters correspond to individualized features such as upper limit, learning rate, and initial level; Given a skill dimension d (e.g., a structural dimension), select a model from the candidate function family. Through nonlinear least squares fitting :

[0133] Gradient descent or other numerical optimization methods can be used to solve the problem. For multiple candidate function families (power-law, exponential, logarithmic, etc.), their fitting errors and model complexities (e.g., AIC / BIC) can be compared, and the optimal model type can be selected as the learning curve for the user in that skill dimension.

[0134] To characterize the phenomenon of regression due to prolonged inactivity, a forgetting parameter is further introduced into the time dimension. Taking the structural dimension as an example, let's assume the user's most recent practice time... Structural capability is Then at the time interval If no practice is performed, its effective structural capability at time T can be approximated as:

[0135] in, This is the forgetting parameter for the structural dimension; a larger value indicates faster forgetting. This represents the baseline level when this dimension is not practiced for an extended period.

[0136] Similarly, forgetting parameters can be defined for the dimensions of intensity and rhythm. These parameters collectively constitute the user's forgetting characteristics. These parameters, along with the previously mentioned learning curve parameters, form a complete individualized skill model.

[0137] S4.4 Dynamically update and write the parameterized results (deep regression model parameters, learning curve parameters for each skill dimension, and forgetting parameters) into the user's competency profile to form a structured long-term learning archive.

[0138] Once a user generates a new practice record and completes a quality assessment, this module can be updated periodically or incrementally: deep regression model parameters; learning curve parameters for each sub-skill dimension. Forgetting parameters wait.

[0139] The updated parameters are written into the user's ability profile record, with corresponding fields such as: structural dimension: current average mastery, historical best level, learning rate, upper limit parameter, forgetting parameter; intensity dimension: current average stability, convergence speed, upper limit parameter, etc.; rhythm dimension: current rhythm fluency, rhythm acquisition rate, etc.; as well as comprehensive ability score and its changing trend.

[0140] These parameters provide foundational data for extracting symbolic rules in calligraphy skill acquisition, enabling the extraction of explicit mathematical rules from deep models. On the other hand, they provide a basis for judging the current learning stage (rapid improvement period / plateau period / forgetting risk period) for personalized practice character recommendations, enabling the construction of recommendation goals that maximize the expected improvement in ability.

[0141] Step 5: Construct a feature space based on historical writing statistics, and randomly sample a large number of representative feature vectors from the feature space. The feature vector is input into the writing ability prediction model to obtain the corresponding predicted ability vector. The feature vector and the predicted ability vector are combined to form a sample. A training dataset for symbolic regression is constructed based on all samples. For the symbolic regression dataset, the symbolic regression method based on genetic algorithm is used to search for the optimal symbol rule in the predefined expression space.

[0142] S5.1, for each skill dimension Several explanatory variables that influence the learning process of this skill dimension are selected to form the input feature vector of symbolic regression. .

[0143] For example, explanatory variables may include: cumulative practice counts n (number of practice counts for single words, single structures, or specific skill dimensions); average practice frequency f over a recent period (e.g., weekly / monthly practice frequency); and the time interval between the last practice and the current practice. Current level of basic capabilities (For example, the average ability of the last K iterations); a numerical representation of discrete features such as the difficulty and structure type of the current practice object. The feature vector can be denoted as:

[0144] For each skill dimension d, the input feature vector can be used to perform symbolic regression on two types of target quantities: Direct fitting ability level:

[0145] Or fit the ability increment per unit time / single practice session:

[0146] In this embodiment, based on the deep regression model in step S4, random sampling is first performed in the input feature space to generate a large number of representative input feature vectors. These feature vectors are input into a deep regression model to obtain the corresponding predictive power values. Construct samples with corresponding predictive power values This leads to the formation of a dataset for symbolic regression. ;

[0147] in, This represents the total number of samples generated for the skill dimension d.

[0148] S5.2, Training Dataset Based on Symbolic Regression The symbolic regression algorithm is used to automatically search and generate the optimal symbolic rule in a predefined expression space. The optimal symbolic rule is the symbolic rule that achieves the best balance between the fitting accuracy of the dataset and the simplicity of the expression.

[0149] 1) Automatically search and generate candidate symbol rules in a predefined symbolic expression space.

[0150] For each skill dimension d, define a set of candidate symbolic expressions. , where each candidate expression All of these can be represented as an expression tree consisting of the following basic operators: Unary operators: ; Binary operators: ; Leaf node: Input feature vector Each component and constant term (e.g.) wait).

[0151] The expression for this symbol rule is as follows:

[0152] in, Explicit functions This represents the set of constant parameters (such as coefficients, exponents, etc.) in an expression.

[0153] 2) In the process of symbolic regression, it is necessary to evaluate the performance of candidate expressions and constrain their structure in order to select symbolic rules that are both accurate and concise.

[0154] Fit accuracy assessment: Mean squared error (MSE) was used. In the dataset Above, given a candidate expression The fitting accuracy is evaluated by calculating the mean squared error over the skill dimension d, and the expression for the mean squared error is as follows:

[0155] The complexity function constrains the candidate expression; To prevent the symbolic regression process from generating excessively long, complex, and difficult-to-interpret expressions (e.g., overfitting or lack of generalization ability), the structural complexity of candidate expressions needs to be constrained. Therefore, a complexity function is introduced. This function takes into account two structural properties of the expression tree: depth. and number of nodes Complexity function The expression is as follows:

[0156] in, Hyperparameters used to control the impact of depth and number of nodes on weights.

[0157] 3) The overall goal of symbolic regression is to find the candidate expression space. Search for a function , Search for a function To minimize the weighted sum of fitting error and complexity function, a genetic algorithm-based search strategy is adopted to efficiently solve this optimization problem. Each candidate expression is represented as an individual expression tree. The population is iteratively optimized through evolutionary operators such as crossover, mutation, and selection. During the evolution process, the fitness function is used to evaluate the quality of individuals. At the same time, the maximum depth and number of nodes of the expression tree are limited to control the search space, thereby determining the optimal symbol rule.

[0158] Weighted sum of fitting error and complexity function:

[0159] in, This is a complexity penalty coefficient used to balance fitting accuracy and model simplicity.

[0160] The optimization objective of symbolic regression is formalized as a regularized search problem, which can be formalized as:

[0161] The optimal sign rule is determined using a genetic algorithm-based search strategy, as follows: Each candidate expression Represented as an expression tree; A population is constructed using expression trees as individuals, and iteratively updated through operators such as crossover (subtree swapping), mutation (node ​​replacement), and replication. In each generation, the weighted sum of the fitting error and the complexity function is used. As a fitness metric, individuals are selected and evolved; at the same time, by limiting the maximum depth and maximum number of nodes of the expression tree, the search space is kept controllable. After iterative optimization, a set of candidate rules is obtained, which is then filtered and selected to obtain the final symbolic rule.

[0162] 4) To ensure that the symbolic regression process is both statistically rigorous and pedagogically interpretable, the dataset for each skill dimension is first divided into a training set, a validation set, and a test set. The training set is used for expression fitting and optimization. On the validation set, a comprehensive scoring function that integrates fitting error and complexity penalties is used to sort and filter the candidate expressions in the candidate rule set. Several expressions with high scores, simple structures, and clear semantics are selected to form a candidate rule set. On this basis, calligraphy education experts are further introduced to review the rationality of the candidate rules based on their teaching experience (such as the marginal diminishing effect of practice and the law of spaced forgetting). Formulas that violate common sense or are difficult to explain are eliminated, resulting in the final symbolic rules that conform to the data patterns and teaching logic.

[0163] Specifically, for each skill dimension d, the dataset will be... Divided into training set Validation set and test set During the search process, the symbolic regression algorithm fits the training set... And optimize The validation error is calculated on the validation set and used for early stopping and model selection. Finally, the generalization ability of the selected rule is evaluated on the test set.

[0164] For each candidate expression Performance on the validation set can be measured by a comprehensive metric, such as:

[0165] in, This represents the mean squared error on the validation set. A higher score indicates higher accuracy and lower complexity.

[0166] Measured by comprehensive indicators Sort all candidate expressions and select several rules with high scores, concise forms, and reasonable physical meanings to form a rule set for skill dimension d. :

[0167] in The number of rules to retain for this skill dimension (e.g., 1–3). During the selection process, candidates with highly similar expression forms and highly correlated predicted behaviors can be merged or eliminated to avoid redundancy.

[0168] For the final candidate symbol rules, experts in the field of calligraphy education were brought in to review them to check whether they conformed to general calligraphy teaching experience (such as diminishing marginal returns to ability as the number of practice sessions increases, and the decline in ability due to excessively long time intervals). Formulas that obviously violated common sense and were difficult to explain were eliminated or adjusted.

[0169] 5) Structure and store the symbolic rules that conform to data patterns and teaching logic in the skill rule library.

[0170] Specifically, each symbol rule that has been selected will be stored in the form of an explicit mathematical formula.

[0171] For each rule The system records the following in the skill and rule library: Skill dimension d (structure / strength / rhythm); Rule ID, version number; Explicit expression structure (operator tree or intermediate expression format); Parameter vector The corresponding fitting error, complexity score, and validation / test set performance metrics.

[0172] Each rule can be abstractly represented as:

[0173] in, Metadata such as timestamps, training data size, and the set of operators used.

[0174] The overall goal of this symbolic regression is to find a symbolic function in a predefined candidate expression space that simultaneously achieves high fitting accuracy and strong interpretability. To strike a balance between the two, the optimization process not only focuses on the function's fitting error to the training data but also constrains the structural complexity of the expression by introducing a complexity penalty term, preventing overfitting or lengthy, poorly interpretable formulas. This problem can be formalized as a regularized search problem. To efficiently search within this combinatorial space, strategies based on genetic programs or algorithms are typically employed. This method encodes each candidate expression as a tree-structured individual and iteratively evolves a new population of expressions by simulating crossover, mutation, and replication operations in natural selection. In each generation, the quality of individuals is evaluated by a comprehensive objective function (i.e., a weighted sum of fitting error and complexity penalty), guiding the search direction. Simultaneously, by limiting the maximum depth and number of nodes in the expression tree, the search process is ensured to be controllable and ultimately converge to a set of symbolic rules that are both accurate and concise, with good interpretability.

[0175] Step 6: Based on the feature vector and optimal symbol rule of each Chinese character in the character library, determine the ability enhancement prediction value. Based on the ability enhancement prediction value of each Chinese character in each skill dimension and the user's weakness weight in each skill dimension, determine the single-character comprehensive benefit function of each Chinese character. Based on the single-character comprehensive benefit function of each Chinese character, determine the recommended target practice character set.

[0176] S6.1 Select the set of Chinese characters currently available for training from the character library. Each Chinese character The "Chinese Character Feature Database" pre-associates three-dimensional feature vectors:

[0177] in, :Chinese character The structural complexity or structural training intensity index; :Chinese character The intensity control requirements indicators; :Chinese character The rhythm changes and rhythm training intensity indicators.

[0178] For each Chinese character Record the estimated cost or time spent on the practice. For example, estimate the time required to complete a certain number of writing sessions (such as 1 or 3 sessions) for subsequent optimization under time budget constraints:

[0179] S6.2. Determine the weight of the weakness in each skill dimension based on the current ability vector of calligraphy practice. The calculation method for the weight of the weakness in each skill dimension is as follows: First, based on the quality coefficients of each skill dimension from the current amount of practice, determine the user's ability vector at the current moment: ; In this capability vector, each skill dimension component is within the range [0,1], with larger values ​​indicating stronger capabilities. To reflect the idea of ​​addressing weaknesses, the degree of weakness (capability gap) for each skill dimension is defined as follows:

[0180] Then, the degree of weakness in the three skill dimensions is normalized to obtain the weakness weight of each skill dimension (the weaker the weakness, the greater the weight):

[0181]

[0182] Obviously: .

[0183] S6.3. Determine the capability enhancement prediction value based on the feature vector and optimal symbol of each Chinese character in the character library.

[0184] Suppose that we recommend an exercise to the user, targeting a specific candidate Chinese character. Consider writing the character in one or more subsequent practice sessions, and estimate the improvement in ability after practicing the character based on the rules of symbolism.

[0185] Let the current skill dimension d be the ability. ,Character The expected improvement in ability on skill dimension d is denoted as . That is, utilizing the symbolic rules of the skill dimension d. By using information such as the number of practice sessions, frequency, time interval, and character features as feature vectors, the predicted ability increment value for the Chinese character is obtained. For example:

[0186] in: For user u targeting Chinese characters The current practice state feature vector may include: the cumulative number of practice sessions for the character or structure, the estimated number of practice sessions after the next practice session (n+1), the current skill level mastery, and the character's features. Time intervals, etc.; The optimal symbol rule is selected on the skill dimension d.

[0187] If symbol rules The fit is of the ability level rather than the increment (e.g.) Then, the expected increment can be obtained by subtracting the current capability from the predicted capability:

[0188] in, For the words The ability level of this skill dimension is predicted by the learning curve model or symbolic rule after a predetermined number of practice sessions.

[0189] S6.4 To ensure the stability of the capacity increase forecast, the capacity increase forecast will be set at... Truncate or normalize the interval, for example:

[0190] S6.5. Increase the predicted value based on the ability of each Chinese character in each skill dimension. and the weight of the three-dimensional shortcomings Determine the single-character comprehensive benefit function of this Chinese character. Comprehensive benefit function The expression is as follows: In the simple case where the time cost of practice is not considered:

[0191] When considering the cost of practice (e.g., estimated writing time) In the case of ), define unit cost-benefit:

[0192] Thus, the single-word comprehensive benefit function It reflects the importance of addressing weaknesses, the expected overall improvement in ability that practicing this character can bring, and takes into account the time cost. S6.6. Based on the single-character comprehensive benefit function of each Chinese character, determine the recommended target practice character set.

[0193] Let K be the target number of practice words to be recommended in this round (or the total time budget B). Then the recommendation problem can be formalized into a simple optimization problem.

[0194] For example, if the cost of each word is similar, a "top K" strategy can be used:

[0195] In this case, simply follow Sort the characters from largest to smallest and take the first K characters.

[0196] For example, if we consider the practice time budget B (e.g., the total practice time for this round does not exceed B minutes), then the problem can be written as a constrained optimization:

[0197] A greedy algorithm can also be used: based on unit cost-benefit analysis. Sort by size from largest to smallest, and select items in sequence until the budget constraint is met.

[0198] Target practice word set The recommendation rationale for each word is also output, such as the expected improvement in the structural dimension. ; Expected increase in intensity Expected improvement in the rhythm dimension Comprehensive benefit value Corresponding to the weight of the weakest link wait.

[0199] Based on the output results, the system will display an explainable recommendation to the user, such as: "There is a significant weakness in the rhythm dimension. This round of practice will focus on recommending Chinese characters with rich rhythm variations. It is estimated that this round of practice can improve the rhythm fluency by about 0.1."

[0200] The system can also update its recommendation strategy based on actual skill improvement after practice. For example, it can record the actual reward for each character or category of characters. (such as the actual observed increase in overall capability), and compared with the estimated value. By comparing the strategies, the recommendation policy can be gradually adjusted using multi-armed slot machines or reinforcement learning algorithms, so that the system can approach the optimal policy in the long run.

[0201] Based on the user capability profile in step S3, the skill acquisition model in step S4, and the symbolic rules extracted in step S5, the expected capability improvement of each Chinese character in the candidate character set across the three skill dimensions of structure, intensity, and rhythm is estimated. A comprehensive benefit function is constructed to rank and optimize the candidate characters, generating a personalized target practice character set that meets the constraints of practice time or number of characters. This includes: constructing the candidate character set and character features; estimating the weight of skill dimension weaknesses and the expected capability improvement; constructing the comprehensive benefit function and optimizing the recommendation; and outputting the recommendation results and updating the strategy.

[0202] Step 7: Construct a set of training tasks based on the comprehensive benefit value of Chinese characters, time cost, and number of practice sessions. Users then practice calligraphy based on the set of training tasks.

[0203] S7.1, Based on the comprehensive benefit value Determine the target number of practice sessions for Chinese characters The allocation method is as follows:

[0204] in, The number of basic practice sessions for each character (e.g., 1 or 2 times). To adjust the coefficient for additional practice sessions, This indicates rounding down. Characters with higher overall effectiveness will be allocated more practice sessions.

[0205] S7.2, Based on the comprehensive benefit value of Chinese characters The training task set for this round is constructed based on factors such as time cost and number of practice sessions (or minimum number of practice sessions). :

[0206] S7.3, Based on the training task set for this round For a certain skill dimension Given the known expected improvement in single-word ability Based on this, estimate the training plan for this round. Overall expected increase:

[0207] Furthermore, based on the overall expected improvement in each skill dimension, the comprehensive expected improvement for this round of the plan is determined (weighted by the weakness):

[0208] The aforementioned expected increase can be used as a basis for progress prediction when the task is issued, and can be used to generate interpretable feedback in the future.

[0209] S7.4. Based on the user's terminal, time preferences, and system policies, the training task is... Perform scheduling to generate a task schedule with time information:

[0210] in, These are the suggested start and end times or time windows for the practice session; you can simply provide the start and end timeframes for this training session, without needing to time each character individually. Based on the schedule, compile the task schedule. Pushed to the user's terminal in the form of a task list, including: List of Chinese characters to be practiced in this round and the target number of practice sessions for each; Training focus for each Chinese character (weighting of structure / strength / rhythm dimensions); The estimated total practice time and expected improvement range.

[0211] During the user's actual writing training, writing trajectory data is collected in real time, and the completion status and evaluation results of each writing session are sent back to the server, including the following information: Each task unit The number of practice sessions completed. ; Timestamps and completion times for each practice session; S7.5. Based on the three-dimensional quality coefficients and diagnostic labels output in step 2, determine whether there are any tasks that are not completed, timed out, or interrupted.

[0212] The task completion rate for a single Chinese character can be defined as:

[0213] The overall completion rate of this round of tasks can be defined as:

[0214] Task completion rate information will serve as a prerequisite for determining whether the expected improvement is achievable: if the overall completion rate is too low, the actual improvement is expected to be significantly lower than anticipated. .

[0215] S7.6 At the end of the training task, summarize the actual evaluation results of this round of tasks, compare them with the expected results, and generate feedback information and progress predictions for users and teachers.

[0216] Let the capability vector before training (before the start of this round) be . The capability vector after training (the latest evaluation after this round) is Then, the actual observed capability enhancement vector can be defined as:

[0217] Compare with the aforementioned expected capability enhancement vector:

[0218] This allows us to calculate the achievement rate across the three skill dimensions in this round of training:

[0219] in, To prevent extremely small constants with a denominator of zero.

[0220] The fitted learning curve can be used to further estimate the evolution trend of user ability under different practice intensities over a future period. For example, the scenario of "continuing to practice at the current pace for the next week" can be abstracted into a new practice plan. Similarly, calculate the expected capability vector for a future period of time:

[0221] in, The expected improvement vector resulting from continuing practice according to the recommended plan over the next period of time; This represents the amount of ability decay estimated based on the forgetting model (when there is little or no practice).

[0222] Based on the above prediction results, the system can generate future-oriented phased goals for users, such as: "It is expected that after completing two more rounds of similar training, the structural mastery can be improved from 0.65 to about 0.75."

[0223] The numerical results are then translated into user-friendly language descriptions and combined with diagnostic tags to generate feedback in the following ways: which skill dimensions have shown significant improvement (e.g., structure improved by 0.08, rhythm improved by 0.05); which diagnostic problems have been alleviated (e.g., confidence in the "left-right imbalance" tag has decreased, and the frequency of the "excessive force fluctuation" tag has decreased); the difference between expectations and reality (e.g., "The completion rate of this round of practice was 80%, and the actual structure improvement was about 90% of the expectation"); and suggestions for the next round of training (e.g., "It is recommended to continue to strengthen rhythm practice, while appropriately increasing the frequency of force stability training").

[0224] Based on the target practice character set and its comprehensive benefit evaluation results, the recommended results are encapsulated into specific training tasks and distributed to terminal devices. During training execution, the user's completion status is monitored and recorded. Combined with the evaluation and modeling results from steps S2–S4, interpretable feedback information and progress predictions are generated, achieving closed-loop management of the calligraphy training process. This includes: training task encapsulation and plan generation; task scheduling and distribution; training process monitoring and result feedback; feedback generation and progress prediction.

[0225] Example 2 Correspondingly, this application also provides a calligraphy practice system based on the user's calligraphy practice results, including: The writing data acquisition module is used to collect the writing trajectory data and related writing statistics of users during calligraphy practice. The user writing quality assessment module is used to extract the user's writing features in three skill dimensions—character structure, pen pressure, and writing rhythm—based on the writing trajectory data. For each skill dimension, the quantitative index calculated based on the writing features is combined with the corresponding skill dimension score generated based on the deep learning model to obtain the quality coefficient of each skill dimension, including the structural deviation coefficient, the pressure stability coefficient, and the rhythm fluency coefficient. The user ability profile module is used to construct a multi-dimensional ability vector representing the user's current writing level based on the quality coefficients of each skill dimension, and to form an ability time series reflecting the evolution of the user's ability based on the historical multi-dimensional ability vector. The calligraphy skill acquisition module is used to train a time-series prediction model based on the ability time series and the writing statistics data to obtain a writing ability prediction model that can predict the user's future writing ability. The calligraphy acquisition rule extraction module is used to construct feature samples based on the writing statistics, generate corresponding prediction ability labels using the writing ability prediction model, and form a training dataset; the training dataset is fitted using a symbolic regression method to search for and generate symbolic rules that can describe the relationship between practice behavior and ability changes. The personalized practice character recommendation module is used to predict the expected improvement in the three skill dimensions after practicing each Chinese character in a candidate Chinese character set, based on the symbol rules; calculate the comprehensive benefit value of each Chinese character by combining the expected improvement in ...

[0226] The training task distribution module is used to generate personalized practice tasks based on the target practice word set.

[0227] It should be noted that, in the several embodiments provided in this application, it should be understood that the disclosed apparatus and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of modules is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple modules may be combined or integrated into another device, or some features may be ignored or not executed. The modules described as separate components may or may not be physically separated. The components shown as modules may be one or more physical units, that is, they may be located in one place or distributed in multiple different places. Some or all of the modules can be selected to achieve the purpose of the solution in this embodiment according to actual needs.

[0228] Furthermore, in the various embodiments of the present invention, the modules can be integrated into one processing unit, or each module can exist physically separately, or two or more modules can be integrated into one unit. The integrated unit described above can be implemented in hardware or as a software functional unit.

[0229] An electronic device provided in this application includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it implements the steps of the calligraphy practice method based on the user's calligraphy practice effect as described in any of the above embodiments.

[0230] Another electronic device provided in this application embodiment may further include: an input port connected to a processor for transmitting multimodal data collected by an external acquisition device to the processor; a display unit connected to the processor for displaying the processor's processing results to the outside world; and a communication module connected to the processor for enabling communication between the electronic device and the outside world. The display unit may be a display panel, a laser scanning display, etc.; the communication method adopted by the communication module includes, but is not limited to, Mobile High Definition Link (HML), Universal Serial Bus (USB), High Definition Multimedia Interface (HDMI), and wireless connection (including Wi-Fi, Bluetooth, Bluetooth Low Energy, and IEEE 802.11s-based communication technology).

[0231] This application provides a computer-readable storage medium storing a computer program. When the computer program is executed by a processor, it implements the steps of the calligraphy practice method based on the user's calligraphy practice effect as described in any of the above embodiments.

[0232] For descriptions of relevant parts of the calligraphy practice system, electronic device, and computer-readable storage medium based on user calligraphy practice effects provided in this application's embodiments, please refer to the detailed descriptions of the corresponding parts in the calligraphy practice method based on user calligraphy practice effects provided in this application's embodiments; they will not be repeated here. Furthermore, parts of the technical solutions provided in this application that are consistent with the implementation principles of corresponding technical solutions in the prior art have not been described in detail to avoid excessive elaboration.

[0233] The above content is only for illustrating the technical concept of the present invention and should not be construed as limiting the scope of protection of the present invention. Any modifications made to the technical solution based on the technical concept proposed in this invention shall fall within the scope of protection of the claims of this invention.

Claims

1. A calligraphy practice method based on the user's calligraphy practice results, characterized in that, Includes the following steps: Step 1: Collect the user's writing trajectory data and related writing statistics during calligraphy practice; Step 2: Based on the writing trajectory data, extract the user's writing features in three skill dimensions: character structure, pen pressure, and writing rhythm; For each skill dimension, the quantitative indicators calculated based on the writing features and the corresponding skill dimension scores generated based on the deep learning model are integrated to obtain the quality coefficients of each skill dimension, including the structural deviation coefficient, the strength stability coefficient, and the rhythm fluency coefficient. Step 3: Based on the quality coefficients of each skill dimension, construct a multi-dimensional ability vector representing the user's current writing level, and form an ability time series reflecting the evolution of the user's ability based on the historical multi-dimensional ability vector; Step 4: Based on the ability time series and the writing statistics, train a time series prediction model to obtain a writing ability prediction model that can predict the user's future writing ability. Step 5: Construct feature samples based on the writing statistics, generate corresponding prediction ability labels using the writing ability prediction model, and form a training dataset; use the symbolic regression method to fit the training dataset, and search for and generate symbolic rules that can describe the relationship between practice behavior and ability changes. Step 6: For the candidate Chinese character set, predict the expected improvement in ability in the three skill dimensions after practicing each Chinese character, based on the symbol rules; calculate the comprehensive benefit value of each Chinese character by combining the expected improvement in ability with the training weights of each dimension determined by the user's current ability status. Based on the comprehensive benefit value, a target practice character set is selected from the candidate Chinese character set, and a personalized practice task is generated based on the target practice character set.

2. The calligraphy practice method based on the user's calligraphy practice effect according to claim 1, characterized in that, The writing trajectory data includes at least the pen tip coordinate sequence, stroke pressure data, and timestamp information for each stroke; The writing statistics include at least the number of practice sessions, the number of structured practice sessions, and the time interval between practice sessions.

3. The calligraphy practice method based on the user's calligraphy practice effect according to claim 1, characterized in that, The method for determining the structural deviation coefficient is as follows: Based on the pen tip coordinate sequence, a user character topology map is constructed, and the graph editing distance between the user character topology map and the standard character topology map is calculated. Simultaneously, the user character topology map and related features are input into a deep temporal evaluation model to obtain a structure score. The graph editing distance and the structure score are weighted and fused to obtain a structure deviation coefficient.

4. The calligraphy practice method based on the user's calligraphy practice effect according to claim 1, characterized in that, The method for determining the force stability coefficient is as follows: Based on the stroke pressure data, the stroke pressure variance is calculated; simultaneously, the similarity between the user's pressure pattern and the pre-stored excellent pressure template is calculated, and the stroke pressure data and related features are input into the depth time series evaluation model to obtain the pressure stability score. The force stability coefficient is obtained by weighting and fusing the variance of the stroke pressure, the similarity, and the force stability score.

5. A calligraphy practice method based on user calligraphy practice results according to claim 1, characterized in that, The method for determining the rhythm fluency coefficient is as follows: Based on the timestamp information of each stroke, a user rhythm sequence is constructed; the dynamic time warping distance between the user rhythm sequence and the pre-stored excellent rhythm template sequence is calculated; simultaneously, the user rhythm sequence and related features are input into the deep temporal evaluation model to obtain a rhythm fluency score; the DTW distance and the rhythm fluency score are weighted and fused to obtain a rhythm fluency coefficient.

6. The calligraphy practice method based on the user's calligraphy practice effect according to claim 1, characterized in that, The method for training the time series prediction model is as follows: The multidimensional ability vector is paired with the writing statistical feature vector associated with the same exercise in a temporal sequence to form a serialized training sample. The temporal prediction model is constructed using a temporal deep neural network; the serialized training samples are input into the model for training; the training objective of the model is: given the writing statistical feature sequence and ability vector sequence within the user's history window, predict the multidimensional ability vector for one or more future practice sessions; By minimizing the loss function between the predicted ability vector and the true ability vector, the parameters of the temporal deep neural network are optimized to obtain the trained writing ability prediction model.

7. A calligraphy practice method based on user calligraphy practice results according to claim 1, characterized in that, Step 5 involves constructing feature samples based on the writing statistics, generating corresponding prediction ability labels using the writing ability prediction model, and forming a training dataset, including: A feature space is constructed based on historical writing statistics, and feature vectors are generated by sampling in the feature space. The feature vectors are input into the writing ability prediction model to obtain the corresponding prediction ability vectors. A training dataset for symbolic regression is constructed based on the feature vectors and the corresponding prediction ability vectors.

8. A calligraphy practice method based on the user's calligraphy practice effect according to claim 1, characterized in that, The method for searching and generating symbolic rules that can describe the relationship between practice behavior and ability changes is as follows: For each of the aforementioned skill dimensions, a symbolic expression space consisting of basic operators and operands is constructed; For candidate symbolic expressions in the symbolic expression space, calculate their fitting error on the training dataset and evaluate the complexity of their expression structure; A genetic algorithm-based search strategy is adopted to search for the optimal symbolic expression in the symbolic expression space with the goal of minimizing the comprehensive objective function; wherein, the comprehensive objective function is the sum of the fitting error and the structural complexity of the expression weighted by the complexity penalty coefficient; The optimal symbolic expression and its determined parameters are used as the symbolic rule describing the relationship between practice behavior and ability change in this skill dimension.

9. A calligraphy practice method based on user calligraphy practice results according to claim 1, characterized in that, The method for determining the total efficiency of each Chinese character is as follows: Determine the weight of weaknesses in each skill dimension based on the current calligraphy practice ability vector; For each Chinese character in the candidate Chinese character set, obtain the preset multi-dimensional training feature vector of that Chinese character; For each Chinese character in the candidate character set and in conjunction with the optimal symbol rule, estimate the expected improvement in ability across each skill dimension after practicing that character; and calculate the comprehensive benefit value of each Chinese character based on the expected improvement in ability across each skill dimension and the user's weakness weights across each skill dimension.

10. A calligraphy practice system based on the user's calligraphy practice results, characterized in that, include: The calligraphy data acquisition module is used to collect the writing trajectory data and related writing statistics of users during calligraphy practice. The writing quality assessment module is used to extract the user's writing characteristics in three skill dimensions: character structure, pen pressure, and writing rhythm, based on the writing trajectory data. For each skill dimension, the quantitative indicators calculated based on the writing features and the corresponding skill dimension scores generated based on the deep learning model are integrated to obtain the quality coefficients of each skill dimension, including the structural deviation coefficient, the strength stability coefficient, and the rhythm fluency coefficient. The ability profiling module is used to construct a multi-dimensional ability vector representing the user's current writing level based on the quality coefficients of each skill dimension, and to form an ability time series reflecting the evolution of the user's ability based on the historical multi-dimensional ability vectors. The calligraphy skill acquisition module is used to train a time-series prediction model based on the ability time series and the writing statistics data to obtain a writing ability prediction model that can predict the user's future writing ability. The rule extraction module is used to construct feature samples based on the writing statistics, generate corresponding prediction ability labels using the writing ability prediction model, and form a training dataset; the training dataset is fitted using the symbolic regression method, and symbolic rules that can describe the relationship between practice behavior and ability changes are searched and generated. The character practice recommendation module is used to predict the expected improvement in the three skill dimensions after practicing each character, based on the symbol rules and a set of candidate characters. The module then calculates the comprehensive benefit value for each character by combining the expected improvement with the training weights of each dimension determined by the user's current ability status. Based on the comprehensive benefit value, a target practice character set is selected from the candidate Chinese character set, and a personalized practice task is generated based on the target practice character set.

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