Adaptive optimization mathematical mechanization symbol calculation system

Abstract

The invention relates to the field of symbolic calculation, discloses a self-adaptive optimization mathematical mechanization symbolic calculation system, and solves the problems of high calculation complexity, large calculation resource consumption, static calculation path and the like of high-dimensional symbolic calculation in the prior art by combining a multi-dimensional calculation model, an incremental optimization algorithm and a distributed calculation architecture. According to the system, a mathematical transformation technology (such as Fourier transformation and Laplace transformation) is adopted to convert a high-dimensional problem into a low-dimensional problem, so that the calculation difficulty is remarkably reduced. And meanwhile, the distributed computing architecture performs parallel processing on computing tasks, so that the computing speed is increased. The incremental optimization algorithm module dynamically adjusts the path according to the real-time calculation feedback, optimizes the time and memory consumption in the calculation process, and improves the utilization efficiency of resources.

Description

Technical Field

[0001] The present invention relates to the technical field of symbolic computation, and specifically to an adaptively optimized mathematical mechanization symbolic computation system. Background Art

[0002] With the wide application of symbolic computation in fields such as scientific computing and engineering computing, the demand for handling high-dimensional and complex computing problems is increasing continuously. Traditional symbolic computation methods mainly rely on directly solving expressions, and these methods usually encounter problems such as high computational complexity, long computational time, and large resource consumption.

[0003] Computational complexity problem in handling high-dimensional problems

[0004] In traditional symbolic computation methods, the handling of high-dimensional integration, differentiation and other problems relies on step-by-step calculation and analysis. As the dimension increases, the amount of computation grows exponentially, which leads to a sharp increase in time and memory consumption during the computation process. In the prior art, multi-dimensional computation is usually directly carried out in a high-dimensional space, and it is often difficult to efficiently reduce the complexity when dealing with high-dimensional symbolic computation problems, resulting in the inability to complete the computation task within a reasonable time. Especially when dealing with computations involving high-dimensional integration or multi-variable differentiation, directly handling these problems will lead to extremely low computational efficiency, which is a huge bottleneck for many application scenarios that require real-time computation.

[0005] Static computation path and lack of dynamic optimization

[0006] Traditional symbolic computation methods usually use a fixed computation path for calculation, and this path selection method lacks flexibility. Even if the computation time or memory consumption in certain steps exceeds the expectation, traditional methods cannot make timely adjustments. The selection of this static path cannot cope with the changes and bottleneck points that occur during the computation process, resulting in inefficient execution of some computation steps. For example, some computation steps may have too long computation time or too high memory consumption due to excessive data volume, complex operations, etc., and cannot automatically switch to a more efficient computation path. This not only wastes a large amount of computing resources, but also may slow down the progress of the entire computation process.

[0007] Inefficient utilization of computing resources and bottleneck problems

[0008] Traditional symbolic calculation methods usually rely on a single computing node for serial calculation, resulting in serious resource bottlenecks during the calculation process. When faced with complex high-dimensional problems, the processing power of a single computing node is far from sufficient to meet the requirements. Especially when dealing with calculation tasks such as multivariate and high-order differentials, the consumption of calculation time and memory is extremely large. Although distributed computing can solve certain problems, there are certain limitations in the task allocation of existing technologies. For example, the efficiency of task decomposition and scheduling is insufficient, and it is unable to optimize task allocation in real time according to the resource status of each computing node, resulting in some computing nodes being overloaded while other nodes are idle, causing the inefficient utilization of computing resources and the inability to improve the overall calculation speed.

[0009] The processing method of high-dimensional calculation tasks lacks precise control

[0010] High-dimensional calculation problems usually involve a large number of intermediate calculation results and temporary storage, which pose extremely high requirements for memory and computing power. When dealing with these problems, existing technologies often cannot flexibly adjust the memory usage during the calculation process. For example, some intermediate results during the calculation process may require a large amount of memory storage, and existing methods usually lack effective memory management strategies, resulting in excessive memory consumption or memory overflow. This deficiency in memory management not only affects the stability of the calculation process but also reduces the utilization rate of computing resources, resulting in poor processing effects for high-dimensional calculation tasks.

[0011] Therefore, the present invention proposes an adaptively optimized mathematical mechanization symbolic calculation system to solve the deficiencies of existing technologies Summary of the Invention

[0012] In view of the deficiencies of existing technologies, the present invention provides an adaptively optimized mathematical mechanization symbolic calculation system, which solves the problems of excessive calculation complexity, waste of computing resources, and insufficient path optimization in high-dimensional symbolic calculation problems. The system converts complex high-dimensional problems into low-dimensional problems by introducing a multi-dimensional calculation model and a distributed calculation architecture, and performs parallel processing among multiple computing nodes, thereby greatly improving the calculation efficiency. The system also includes an incremental optimization algorithm module, which can analyze the time and memory incremental data during the calculation process in real time and dynamically adjust the calculation path according to the feedback to optimize the utilization rate of computing resources. This technical solution effectively solves the problems of excessive resource consumption, long calculation time, and inflexible path selection in traditional symbolic calculation, and improves the processing ability and calculation efficiency of symbolic calculation.

[0013] To achieve the above objectives, the present invention is realized through the following technical solutions: An adaptively optimized mathematical mechanization symbolic calculation system, comprising:

[0014] A symbolic calculation complexity analysis module, which is used to receive an input mathematical symbolic expression, evaluate the calculation complexity of the symbolic expression, and generate complexity data for symbolic calculation;

[0015] An optimal path selection module, which selects the most suitable calculation path according to the complexity data generated by the symbolic calculation complexity analysis module, and dynamically adjusts the calculation path according to the real-time feedback calculation results;

[0016] An incremental optimization algorithm module, which is used to gradually optimize the calculation path according to the intermediate calculation results at each step of symbolic calculation, avoid redundant calculations, and reduce calculation time and resource consumption;

[0017] A multi-dimensional calculation model and distributed calculation module, which is used to handle high-dimensional problems during symbolic calculation, transform high-dimensional symbolic problems into low-dimensional problems through multi-dimensional integration, Laplace transform or Fourier transform, and use a distributed calculation architecture to allocate calculation tasks to multiple calculation nodes for parallel calculation, thereby accelerating the calculation process.

[0018] Preferably, the symbolic calculation complexity analysis module determines the calculation complexity of symbolic calculation by evaluating the number of variables, order, operation type, and number of operations of the symbolic expression in the input problem. The calculation complexity includes calculation time, memory consumption, and the critical path in the calculation task, and generates corresponding calculation optimization strategies through a preset complexity model. The complexity model includes a time complexity model and a memory consumption model based on the big O notation.

[0019] Preferably, the optimal path selection module includes:

[0020] A path selection unit, which is used to calculate and compare the time consumption and memory consumption of multiple possible calculation paths. The time consumption and memory consumption are obtained by real-time monitoring the performance data of each calculation step during the calculation process;

[0021] A path adjustment unit, which adjusts the symbolic calculation path according to the feedback data and the intermediate results during the calculation process to minimize the calculation time and memory consumption. The adjustment process is based on an incremental analysis algorithm, and new time and memory consumption data are fed back for optimization after each calculation is completed.

[0022] Preferably, the incremental optimization algorithm module dynamically adjusts the calculation path by real-time analyzing the time and memory increments of each step task during the calculation process. The incremental optimization algorithm module is optimized according to the following incremental data:

[0023] Time increment: Calculate the time difference when each subtask is executed. If the calculation time of the current task exceeds the preset time threshold, the path is automatically adjusted;

[0024] Memory increment: Analyze the memory consumption of each subtask during the calculation process, and switch to the memory optimization strategy when the memory threshold is reached. The strategy includes adjusting the calculation module with large memory occupancy or using the memory management algorithm for optimization.

[0025] Preferably, the multi-dimensional calculation model and the distributed calculation module adopt a variety of mathematical transformation technologies to reduce the dimension of the symbolic calculation task through Laplace transform and Fourier transform, simplify the calculation complexity of high-dimensional problems, and achieve distributed calculation in the following ways:

[0026] Task decomposition unit, which divides the input problem into multiple subtasks and allocates them to multiple computing nodes for execution according to the scale, computing resource requirements and complexity analysis results of the subtasks;

[0027] Distributed scheduling unit, which coordinates the allocation of calculation tasks among multiple computing nodes, optimizes the utilization of computing resources, reduces calculation bottlenecks, and the scheduling unit adjusts the task allocation scheme in real time through computing resource monitoring.

[0028] Preferably, a method for implementing an adaptively optimized mathematical mechanization symbolic calculation system includes the following steps:

[0029] S1. Receive the input mathematical symbol expression, perform symbolic calculation complexity analysis on it, evaluate the calculation time, memory consumption and possible bottleneck points during the calculation process of the symbol expression, and generate calculation complexity data;

[0030] S2. According to the generated complexity data, select the most suitable calculation path through the optimal path selection module, and dynamically adjust the calculation path according to the intermediate results during the symbolic calculation process to optimize the calculation process;

[0031] S3. Based on the incremental optimization algorithm, analyze the incremental data of each subtask during the calculation process in real time, adjust the calculation path to avoid redundant calculations, and maximize the calculation efficiency;

[0032] S4. Perform dimensionality reduction processing on the input problem, transform the high-dimensional problem into a low-dimensional problem by using Laplace transform or Fourier transform, and allocate the tasks to multiple computing nodes for parallel processing through the distributed calculation architecture. The distributed calculation architecture coordinates the allocation of tasks through the task decomposition unit and the scheduling unit.

[0033] Preferably, in step S1, the calculation complexity is evaluated through the number of variables, order, operation type and number of operations in the symbol expression, and an optimization strategy based on complexity is generated to select a suitable calculation algorithm.

[0034] Preferably, in step S2, the optimal path is selected according to the complexity data of symbol calculation. If the memory or time consumption of the calculation path exceeds a predetermined threshold, the system automatically adjusts the path, and the adjustment is performed based on an incremental optimization algorithm.

[0035] Preferably, in step S3, the incremental optimization algorithm adjusts the path in real time and optimizes the calculation process by calculating incremental data, where the incremental data includes time increment, memory increment, and the calculated results fed back.

[0036] Preferably, a device for implementing the system includes:

[0037] A symbol calculation complexity analysis unit, configured to receive an input mathematical problem, analyze the number of variables, order, and arithmetic operations of a symbol expression, and generate calculation complexity data;

[0038] An optimal path selection unit, which selects a calculation path according to the data provided by the symbol calculation complexity analysis unit and makes dynamic adjustments during the calculation process;

[0039] An incremental optimization unit, configured to analyze the time increment and memory increment of each calculation task in real time, and dynamically adjust the calculation path to optimize the calculation process;

[0040] A multi-dimensional calculation unit and a distributed calculation unit, configured to perform dimensionality reduction processing on high-dimensional symbol calculation problems, and distribute tasks to multiple calculation nodes for parallel processing through a distributed calculation architecture.

[0041] The present invention provides an adaptive optimization mathematical mechanization symbol calculation system, which has the following beneficial effects:

[0042] 1. The present invention adopts a technical solution combining a multi-dimensional calculation model and a distributed calculation architecture, achieving a remarkable technical effect of reducing calculation complexity. By introducing mathematical transformation techniques (such as Fourier transform, Laplace transform, etc.), the present invention transforms high-dimensional problems into low-dimensional problems, thereby reducing the dimensions involved in the calculation process. This innovation solves the calculation pressure and complexity problems brought by high-dimensional calculations in the prior art, and avoids the deficiencies of the traditional method in which the calculation amount explodes and the time consumption is too large. Especially for tasks involving high-order differentials, integrals, and signal processing, after adopting these transformations, the calculation amount is greatly reduced, and high-dimensional problems that cannot be quickly processed by traditional methods can be efficiently solved.

[0043] 2. Through the dynamic path adjustment technology of the incremental optimization algorithm module, the present invention realizes real-time optimization in the process of symbolic calculation. In each calculation step, the incremental optimization algorithm analyzes the actual time increment and memory increment, and then adjusts the calculation path. Compared with the existing technology that cannot flexibly adjust the path according to the calculation progress, the present invention performs real-time feedback and optimization after each calculation step, avoiding the continuation of inefficient calculation paths and ensuring the efficient use of calculation resources. This not only improves the calculation speed but also effectively reduces unnecessary resource waste in the calculation, greatly optimizing the overall symbolic calculation process.

[0044] 3. Through the task decomposition and load balancing technology of the distributed computing architecture, the present invention greatly improves the efficiency of symbolic calculation. Compared with the existing technology that uses a single computing node for serial processing, the present invention decomposes the calculation task into multiple subtasks and distributes them to multiple computing nodes for parallel execution. Each computing node independently processes a part of the task, which greatly shortens the total calculation time, especially suitable for large-scale symbolic calculation problems. The distributed computing architecture optimizes the use of computing resources, improves the throughput of the symbolic calculation system, and enables the system to efficiently process in parallel and quickly complete the calculation task when facing complex multi-dimensional calculations.

[0045] 4. The present invention combines the symbolic calculation complexity analysis module with the optimal path selection module to realize the dynamic selection and optimization of the path in the process of symbolic calculation. Compared with the existing technology with fixed and inflexible path selection, the present invention selects the optimal path by real-time analyzing the complexity data in the calculation process and dynamically adjusts the calculation path according to the real-time feedback. This flexible path optimization technology avoids the performance bottleneck problem caused by improper path selection in the traditional method, ensures that each step in the calculation process is as efficient as possible, and reduces the calculation time and memory consumption. By dynamically adjusting the calculation path, the present invention greatly improves the calculation efficiency and resource utilization rate of the system, ensuring the real-time optimization of the calculation process. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flowchart of the implementation method of the mathematical mechanization symbolic calculation system for adaptive optimization. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0047] Next, the technical solutions of the present invention will be clearly and completely described in conjunction with the drawings of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0048] Please refer to the attached Figure 1, an embodiment of the present invention provides an adaptively optimized mathematical mechanization symbolic calculation system, and the following will elaborate on each module of the system of the present invention.

[0049] Symbolic Calculation Complexity Analysis Module

[0050] The symbolic calculation complexity analysis module of the present invention is a core component of the adaptively optimized mathematical mechanization symbolic calculation system. Its main function is to receive the input mathematical symbol expression, analyze and evaluate the calculation complexity of the symbol expression, and generate the complexity data of the symbolic calculation. These data are used to guide the subsequent optimal path selection module and incremental optimization algorithm module, so as to achieve the goal of optimizing the calculation path, reducing the calculation time and memory consumption.

[0051] The key role of the symbolic calculation complexity analysis module is to anticipate the time and memory requirements during the calculation process and identify possible bottleneck points by evaluating the complexity of the symbolic calculation process. Based on this information, the system can achieve a more efficient symbolic calculation process.

[0052] In this embodiment, the working process of the symbolic calculation complexity analysis module includes the following main steps:

[0053] Receive and parse the input mathematical symbol expression

[0054] The symbolic calculation complexity analysis module first receives the input mathematical symbol expression, and then parses the symbols, variables, operator types, etc. in the expression. The complexity of the symbol expression is usually closely related to the number of variables, operation types, orders, and the number of operations included in the expression.

[0055] Number of variables: The number of variables in the symbol expression will directly affect the complexity of the calculation process. For example, each variable included in the expression may require complex operations, increasing the calculation steps.

[0056] Order: The order of the expression (such as the order of differentiation or integration) is also an important factor in the calculation complexity. Higher-order operations (such as higher-order derivatives or higher-order integrals) often lead to higher calculation complexity.

[0057] Operation type: Different operation types have different complexities. For example, the complexity of multiplication and division is usually higher than that of addition and subtraction, and complex operations such as differentiation, integration, and transformation consume more computing resources.

[0058] In this process, the symbolic calculation complexity analysis module will also analyze the structure of the expression to determine which parts may become bottlenecks and affect the calculation efficiency.

[0059] Generate calculation complexity data

[0060] After parsing the symbolic expression, the symbolic calculation complexity analysis module generates calculation complexity data based on the characteristics of each item in the expression. These data include the following items:

[0061] Calculation time: The calculation time of symbolic calculation depends on each operation in the symbolic expression. The calculation time is mainly affected by factors such as the type of operation, order, and number of variables. For example, the time complexity of differential and integral operations is usually higher than that of basic algebraic operations (such as addition, subtraction, multiplication, and division).

[0062] Memory consumption: The memory consumption of symbolic calculation mainly comes from the variables in the symbolic expression and their related intermediate calculation results. For complex expressions, especially operations involving a large number of temporary variables and intermediate calculation results, the memory consumption is large.

[0063] Bottleneck point identification: The symbolic calculation complexity analysis module identifies bottleneck points in the calculation process. Especially in multi-step operations, certain operations may cause a sharp increase in time or memory. The analysis of bottleneck points can provide important references for subsequent path selection and optimization.

[0064] These data are crucial for subsequent modules (such as the optimal path selection and incremental optimization modules). They provide a complexity-based optimization strategy for the entire calculation system, thus ensuring the efficiency of the calculation process.

[0065] Evaluation models for time complexity and memory complexity

[0066] In this embodiment, the symbolic calculation complexity analysis module adopts the following two complexity evaluation models:

[0067] Time complexity evaluation: The time complexity of symbolic calculation is usually represented by the big O notation. Specifically, the system analyzes the time requirements of each operation in the symbolic expression and generates a time complexity formula based on the complexity of the operation.

[0068] For each operation in the symbolic expression, the time complexity can be expressed as:

[0069]

[0070] Among them, T represents the total calculation time, f i represents the time complexity of the i-th operation, and n represents the total number of operation steps in the symbolic expression. The complexity of each operation is determined according to its operation type (such as addition, multiplication, differentiation, integration, etc.) and the number of variables it involves.

[0071] Memory complexity evaluation: Memory complexity mainly analyzes the amount of memory required for each step of calculation, especially operations involving a large number of temporary variables and intermediate results. The evaluation formula for memory complexity is:

[0072]

[0073] where M represents the total memory consumption, f i represents the memory consumption of the i-th operation, and n is the total number of calculation steps. The memory consumption includes not only the memory required to store intermediate results but also the memory management requirements that may occur during the operation process.

[0074] Bottleneck Analysis and Optimization Strategies

[0075] The symbolic computational complexity analysis module can also analyze the bottleneck points in the calculation process. Generally, bottleneck points usually occur in certain parts of the calculation steps, especially when the complexity of the operation is too high or the storage requirements for intermediate results are too large. To solve these problems, the symbolic computational complexity analysis module can predict and locate bottleneck points in advance through a detailed analysis of the operation process. For example, when the time complexity of a calculation step significantly exceeds that of other steps, the system can foresee that this step may become a bottleneck and optimize it.

[0076] Specifically, if a certain step of the calculation cannot be effectively completed within a certain time, the symbolic computational complexity analysis module will mark this step as a bottleneck and reduce the execution time of this step by dynamically adjusting the calculation path, thereby improving the overall calculation efficiency.

[0077] Application and Optimization of the Complexity Model

[0078] The symbolic computational complexity analysis module can also use the complexity model to provide a basis for selecting subsequent calculation paths. In some embodiments, the symbolic computational complexity analysis module will select appropriate optimization strategies according to factors such as the structure of the input expression, the type of operation, and the variable relationship. These optimization strategies can include:

[0079] Select a calculation path with low complexity: When the system detects that the computational complexity of a certain calculation path is low, the system will preferentially select this path for calculation.

[0080] Avoid redundant calculations: The symbolic computational complexity analysis module can avoid unnecessary calculations by identifying redundant calculation steps, thereby saving calculation time and memory resources.

[0081] Combination of Preset Complexity Model and Optimization Strategy

[0082] To ensure the efficiency of symbolic calculation, the symbolic computational complexity analysis module will also combine preset complexity models during the analysis process to generate optimization strategies for different calculation tasks. Specifically, these preset models include:

[0083] The time complexity model based on the big O notation is used to evaluate the time requirements of symbolic calculation;

[0084] An optimization model based on memory consumption, which is used to predict the memory consumption situation.

[0085] These preset models help the system make choices about the calculation path in the early stage, thus avoiding unnecessary consumption during the calculation process.

[0086] Through the implementation of the symbolic calculation complexity analysis module, the present invention can accurately evaluate the calculation time, memory requirements and bottleneck points during the symbolic calculation process. The design of this module can not only efficiently analyze the input mathematical symbolic expressions, but also provide reliable data support for the subsequent optimization module by generating complexity data. This method greatly improves the efficiency of the calculation process and ensures that the path can be adjusted in real time during the symbolic calculation process, reducing the waste of time and memory.

[0087] Optimal path selection module

[0088] In the present invention, the optimal path selection module is an important part of the adaptive optimization mathematical mechanization symbolic calculation system. Its main function is to select the most suitable calculation path according to the complexity data provided by the symbolic calculation complexity analysis module, and dynamically adjust the calculation path according to the real-time feedback calculation results. The purpose of the optimal path selection module is to minimize the calculation time and memory consumption through accurate path selection and real-time optimization, thereby improving the efficiency of the entire calculation process.

[0089] The operation of the optimal path selection module depends on the data provided by the symbolic calculation complexity analysis module. The symbolic calculation complexity analysis module analyzes and generates data on the calculation time, memory consumption and possible bottleneck points of the symbolic calculation. These data are passed as input to the optimal path selection module. The optimal path selection module selects the most suitable calculation path according to these data and dynamically adjusts the path during the calculation process according to the real-time feedback.

[0090] In this embodiment, the specific implementation of the optimal path selection module includes the following main parts:

[0091] Path selection unit

[0092] The path selection unit receives the calculation complexity data from the symbolic calculation complexity analysis module, first calculates the time consumption and memory consumption of multiple possible calculation paths, and makes a comparison to select the most suitable calculation path. Each calculation path corresponds to a series of calculation steps, and these steps may involve different operation types, operation orders and variable usage situations.

[0093] Generally, the path selection unit will consider in the following several dimensions:

[0094] Computation time: Prioritize the path with the shortest computation time.

[0095] Memory consumption: If the computation times are not significantly different, prioritize the path with lower memory consumption.

[0096] Bottleneck analysis: If the bottleneck points of a certain path are significantly higher than those of other paths, the system will avoid this path and select a path with a smaller bottleneck.

[0097] The path selection process is based on the time and memory consumption data provided by the symbolic computation complexity analysis module. By comprehensively evaluating the performance of different paths, a preliminary computation path is selected.

[0098] Path adjustment unit

[0099] After the path selection unit makes a preliminary path selection, the path adjustment unit will dynamically adjust the path based on the incremental optimization algorithm and real-time computation feedback. During the symbolic computation process, the path adjustment unit dynamically adjusts the path according to the actual execution situation of each computation step, thus avoiding redundant computations and unnecessary resource consumption.

[0100] In the incremental optimization algorithm, the path adjustment unit will collect the time increment and memory increment data of each computation step in real time. These increment data are used to determine whether the current path needs to be adjusted. Specifically:

[0101] Time increment: The time change when each subtask is executed. If the computation time of a certain subtask is longer than expected, the path adjustment unit will consider switching to another computation path based on the incremental analysis.

[0102] Memory increment: The memory consumption change when each subtask is executed. If the memory consumption of a certain step exceeds the predetermined threshold, the path adjustment unit will select a computation path that optimizes memory consumption, or implement a memory optimization strategy, such as releasing unnecessary memory or switching to a path with low memory consumption.

[0103] For example, if it is found during the computation process that the memory consumption of a certain computation step is too high, the path adjustment unit will select a path with lower memory consumption, or adopt an optimization strategy to reduce the memory occupancy, thus avoiding the occurrence of a memory bottleneck.

[0104] Mathematical model in the path selection and adjustment process

[0105] To ensure the accuracy of path selection and adjustment, this embodiment uses a mathematical model to quantitatively evaluate the time consumption and memory consumption of each computation path.

[0106] Evaluation formula for time consumption:

[0107]

[0108] Among them, T path represents the total time consumption of the path, and T i represents the time consumption of the i-th calculation step on the path. n is the number of calculation steps in the calculation path. The time consumption of each calculation step is determined by factors such as the operation type of the step and the number of variables involved. For example, basic arithmetic operations such as addition, subtraction, multiplication, and division have relatively low time consumption, while complex operations such as differentiation and integration have relatively high time consumption.

[0109] Evaluation formula for memory consumption:

[0110]

[0111] Among them, M path represents the total memory consumption of the path, and M i is the memory consumption of the i-th calculation step on the path. The evaluation of memory consumption takes into account the variables used in each calculation step, the memory required to store intermediate results, and other resource occupations.

[0112] Through these formulas, the path selection unit and the path adjustment unit can accurately evaluate the time and memory consumption of each calculation path, and thus make the best choice.

[0113] Real-time nature of dynamic feedback and path adjustment

[0114] The path adjustment of the optimal path selection module not only depends on the preliminary path selection data, but also needs to be dynamically optimized according to the real-time data during the symbolic calculation process. During the symbolic calculation process, the path adjustment unit continuously monitors the execution situation of each step and makes adjustments according to the feedback results.

[0115] Specifically, when the calculation time or memory consumption of a certain step is significantly different from the expectation, the path adjustment unit will immediately perform optimization. For example, when the memory consumption is too high, the path adjustment unit may select a more efficient calculation path or optimize the memory usage through a memory management algorithm. In this way, the optimal path selection module ensures the flexibility during the calculation process and continuously optimizes the symbolic calculation path according to the real-time calculation results.

[0116] Through precise path selection and dynamic adjustment, the optimal path selection module can select the optimal calculation path according to the complexity data generated by the symbolic calculation complexity analysis module. During the entire calculation process, the optimal path selection module not only makes path selection based on the initial complexity data, but also dynamically optimizes the calculation path through real-time feedback, minimizing the calculation time and memory consumption to the greatest extent.

[0117] This path selection and adjustment mechanism enables the system to flexibly respond to changes in different calculation conditions during the symbolic calculation process, avoiding the inefficiency and resource waste that may be caused by static calculation paths. Through the precise control of this module, the present invention can significantly improve the efficiency of symbolic calculation and achieve the optimal utilization of resources.

[0118] Incremental optimization algorithm module

[0119] In the present invention, the incremental optimization algorithm module, as an important part of the adaptive optimization mathematical mechanization symbolic calculation system, is responsible for analyzing the intermediate results in the calculation process in real time at each step of the symbolic calculation and making optimization adjustments based on the incremental data of calculation time and memory consumption. By dynamically optimizing the calculation path, the incremental optimization algorithm module can avoid redundant calculations and unnecessary resource waste, thereby improving the overall efficiency of symbolic calculation.

[0120] The incremental optimization algorithm module works closely with the symbolic calculation complexity analysis module and the optimal path selection module. The symbolic calculation complexity analysis module first provides the calculation complexity data of the symbolic calculation, including time consumption, memory consumption, etc. The optimal path selection module selects a suitable preliminary calculation path based on these data, and the incremental optimization algorithm module is responsible for providing real-time feedback and adjusting the calculation path during the calculation process to ensure that the calculation remains optimal at each stage.

[0121] In this embodiment, the specific implementation of the incremental optimization algorithm module includes the following key steps:

[0122] Real-time analysis of calculation incremental data

[0123] The main task of the incremental optimization algorithm module is to analyze the incremental data in the symbolic calculation process in real time. This incremental data includes calculation time increment and memory increment. For each calculation step executed, the system records the actual calculation time and memory consumption of this step and compares them with the preset threshold. If it is found that the calculation time or memory consumption exceeds the expectation, the incremental optimization algorithm module will make adjustments.

[0124] Time increment analysis: The incremental optimization algorithm module will calculate the calculation time difference of each subtask in real time. If the actual calculation time of a certain calculation step exceeds the predetermined time threshold, the system considers that the calculation efficiency of this step is low and may need to adjust the calculation path. The time increment calculation formula for incremental optimization is:

[0125] ΔT i =T actual (i)-T expected (i);

[0126] where, ΔT i represents the time increment of the i-th calculation task, Tactual (i) represents the actual execution time, T expected (i) represents the expected time. If ΔT i exceeds a predetermined threshold, it is considered that the execution efficiency of this calculation step is insufficient and the path may need to be adjusted.

[0127] Memory increment analysis: The incremental optimization algorithm module also tracks the memory consumption of each subtask. When the memory consumption of a certain step exceeds the predetermined threshold, the system optimizes this calculation step. The calculation formula for memory increment is:

[0128] ΔM i = M actual (i) - M expected (i);

[0129] where, ΔM i represents the memory increment of the i-th calculation task, M actual (i) represents the actual memory consumption, M expected (i) represents the expected memory consumption. If the memory increment ΔM i exceeds the predetermined threshold, it indicates that this calculation step may cause a memory bottleneck and the system needs to take optimization measures, such as switching the calculation path or optimizing the memory occupancy.

[0130] Dynamic path adjustment based on incremental data

[0131] When the incremental optimization algorithm module detects that the time increment or memory increment exceeds the predetermined threshold, path adjustment will be initiated. The incremental optimization algorithm module adjusts the calculation path based on real-time incremental data to reduce the calculation time and memory consumption and maintain the calculation efficiency.

[0132] In some embodiments, the process of path adjustment can be carried out in the following two ways:

[0133] Path switching: If the time or memory consumption of a certain calculation path exceeds the preset threshold, the incremental optimization algorithm module uses the optimal path selection module to select another calculation path. The new path attempts to reduce the calculation time or memory occupancy. Specifically, the goal of path switching is to select a path that meets the optimization criteria in terms of both calculation time and memory consumption.

[0134] Calculation optimization: The incremental optimization algorithm module not only makes adjustments during path selection, but can also optimize each step in the path. For example, for a calculation step with a large memory consumption, the system can optimize the storage method of intermediate results or reduce the memory occupancy by streamlining operations. In this way, the system does not necessarily completely switch the path, but reduces the resource consumption by adjusting some details of the current path.

[0135] Feedback mechanism of the incremental optimization algorithm

[0136] One of the cores of the incremental optimization algorithm module is its feedback mechanism. After each calculation step is completed, the system will collect time increment and memory increment data in real time and feed them back to the incremental optimization algorithm module. These feedback data are used to adjust the current calculation path.

[0137] Specifically, the working process of the feedback mechanism is as follows:

[0138] During the symbolic calculation process, the system will continuously monitor the performance of each calculation step and analyze whether the resource consumption of each step meets the expectations through incremental data analysis.

[0139] Once the time increment or memory increment of a certain step exceeds the threshold, the incremental optimization algorithm module will immediately adjust the path to reduce the calculation time or memory consumption.

[0140] This real-time feedback mechanism can ensure that the system always maintains the best path selection during the calculation process, avoiding performance bottlenecks and resource waste.

[0141] For example, during the calculation of a high-dimensional integral, the system may find that the calculation time of a certain step far exceeds the expectation. At this time, the incremental optimization algorithm module can adjust the path and select a path with lower time consumption for subsequent calculations, thereby optimizing the efficiency of the entire symbolic calculation.

[0142] Further optimization strategies for incremental optimization

[0143] The incremental optimization algorithm not only relies on the monitoring of time increment and memory increment, but can also make predictions based on the historical data of each calculation step. For example, some steps may frequently have problems of excessive time consumption or memory consumption. The incremental optimization algorithm module can predict the calculation bottlenecks of these steps in advance by learning historical data and take targeted optimization measures, such as selecting the appropriate operation order and adjusting the subtask division.

[0144] Through the implementation of the incremental optimization algorithm module, the present invention can significantly improve the efficiency of symbolic calculation, reduce redundant calculations and unnecessary resource consumption during the calculation process. By analyzing the incremental data of each subtask in the calculation process in real time, the incremental optimization algorithm module can dynamically adjust the calculation path according to real-time feedback to ensure that the calculation always remains in the optimal state.

[0145] Specifically, the incremental optimization algorithm module of the present invention has the following advantages:

[0146] Improve calculation efficiency: By dynamically optimizing the path, the incremental optimization algorithm avoids redundant steps and inefficient paths in the calculation, thereby improving the calculation efficiency.

[0147] Saving computational resources: By monitoring and optimizing the resource consumption of each computational step in real time, the incremental optimization algorithm can reduce the time and memory required for computation, thus saving computational resources.

[0148] Flexibly adapting to complex computational tasks: The incremental optimization algorithm can adjust the computational path according to the real-time results of symbolic computation, flexibly handle complex tasks, and ensure that the computation is always in an optimal state.

[0149] Through these optimization measures, the present invention can ensure efficient computational path selection and real-time adjustment during the process of symbolic computation, making symbolic computation not only more efficient, but also able to adapt to changing computational requirements under different conditions, providing a flexible and powerful computational framework.

[0150] Multi-dimensional computational model and distributed computing module

[0151] In the present invention, the multi-dimensional computational model and the distributed computing module are the core components of the self-adaptive optimization mathematical mechanization symbolic computation system. Its main task is to solve the computational complexity brought by high-dimensional problems in symbolic computation, and by applying multi-dimensional computational technologies (such as Laplace transform, Fourier transform, etc.), transform high-dimensional problems into low-dimensional problems, reduce the amount of computation, and optimize the computational performance. At the same time, through the distributed computing architecture, divide the symbolic computation task into multiple subtasks and assign them to multiple computing nodes for parallel execution, thereby accelerating the entire computational process.

[0152] This module closely cooperates with the previous symbolic computation complexity analysis module, optimal path selection module, and incremental optimization algorithm module. After the symbolic computation complexity analysis module evaluates the complexity of the computation and provides data support, the optimal path selection module determines the initial path based on these complexity data, and the incremental optimization algorithm module makes real-time path adjustments during the computation process. The multi-dimensional computational model and the distributed computing module are responsible for handling high-dimensional computational problems and accelerating the overall symbolic computation process through parallel computing.

[0153] In this embodiment, the specific implementation method of the multi-dimensional computational model and the distributed computing module includes the following key parts:

[0154] Application of the multi-dimensional computational model

[0155] Many problems involved in symbolic computation belong to high-dimensional computations, especially when dealing with problems such as multi-variable integrals and higher-order differentials, the computational complexity increases significantly. To reduce the computational complexity, the present invention adopts a multi-dimensional computational model, and transforms high-dimensional problems into low-dimensional problems by using mathematical transformation techniques, thus greatly simplifying the computational process.

[0156] Common transformation methods include:

[0157] Fourier transform: Commonly used in the field of signal processing, it transforms complex time-domain signals into frequency-domain signals, reducing their computational complexity.

[0158] Laplace transform: Mainly used to handle high-order differential equations, converting them into algebraic equations to simplify the solution process.

[0159] Multidimensional integral: By decomposing high-dimensional integral problems into multiple one-dimensional integrals for solution, the computational difficulty is reduced.

[0160] Generally, the Laplace transform and Fourier transform are the most commonly used transformation methods. Especially when dealing with integrals or differentials involving multiple variables, the transformation can convert multi-dimensional problems into low-dimensional problems, thereby reducing the required computational dimension.

[0161] Specifically, the Laplace transform can convert complex differential equations into algebraic equations, greatly simplifying the solution process. For example, assuming that a high-dimensional integral problem is involved in symbolic computation, it can be transformed into a low-dimensional problem through the Fourier transform, thus avoiding the computational pressure brought by directly calculating high-dimensional integrals.

[0162] Mathematical formulas in the multi-dimensional calculation model

[0163] To understand these transformation methods more clearly, the following are common transformation formulas:

[0164] Formula for Fourier transform:

[0165] In symbolic computation, if the calculation involves a multi-dimensional integral problem, the Fourier transform can be used to convert the high-dimensional problem into a low-dimensional problem.

[0166] The Fourier transform formula is as follows:

[0167]

[0168] Among them, I is the result after the Fourier transform, f(x) is the input symbolic function, e -i2πkx is the basis function of the Fourier transform, and k is the frequency variable. In this way, the high-dimensional integral problem can be transformed into a one-dimensional problem in the frequency domain, significantly reducing the computational complexity.

[0169] Formula for Laplace transform:

[0170] The Laplace transform is used to convert high-order differential equations into algebraic equations, and the common formula is:

[0171]

[0172] Among them, F(s) is the result of Laplace transform, f(t) is the input symbolic function, and e -st is the basis function of the transform, and s is the complex frequency variable. Through this transform, the system can convert high-order differential equations into algebraic equations, greatly simplifying the calculation process.

[0173] Implementation of Distributed Computing Architecture

[0174] High-dimensional problems usually involve a large amount of computation, and a single computing node may not be able to complete these tasks within a reasonable time. Therefore, to accelerate the computing process, the present invention adopts a distributed computing architecture. By decomposing the computing tasks into multiple subtasks and distributing these subtasks to multiple computing nodes for parallel computing, the total time required for computing can be significantly reduced.

[0175] In this embodiment, the distributed computing module includes a task decomposition unit and a distributed scheduling unit:

[0176] The task decomposition unit is responsible for decomposing the input symbolic computing problem into multiple subtasks and reasonably allocating them to different computing nodes according to the computing resource requirements and complexity of each subtask.

[0177] The distributed scheduling unit is responsible for coordinating the allocation of computing tasks among multiple computing nodes to ensure load balancing of each computing node. The scheduling unit dynamically adjusts the task allocation according to the resource status of the computing nodes to avoid overloading of some nodes.

[0178] Mathematical Models for Task Decomposition and Scheduling

[0179] Task decomposition and scheduling are achieved through mathematical models to achieve load balancing and resource optimization. The following are common mathematical models:

[0180] Task Decomposition Model:

[0181]

[0182] Among them, T total is the total computing time of symbolic computing, T i is the computing time of the i-th subtask, and n is the total number of subtasks. The task decomposition unit reasonably allocates tasks to computing nodes by analyzing the computing time and resource requirements of each subtask.

[0183] Distributed Scheduling Model:

[0184]

[0185] Among them, L node is the load of each computing node, T totalis the total computing time, and N is the number of computing nodes. This model ensures the balanced allocation of computing resources by balancing the load of each node, thereby improving the overall computing efficiency.

[0186] Acceleration effect of parallel computing

[0187] The multi-dimensional computing model and the distributed computing architecture effectively accelerate the computing process by parallelizing computing tasks. Especially when dealing with complex high-dimensional symbolic computing problems, the distributed computing architecture can significantly reduce the total computing time. For example, assume that the symbolic computing involves a complex multi-dimensional integral. The distributed computing can decompose this problem into multiple sub-problems and perform parallel computing on multiple computing nodes. Each computing node only needs to handle a part of it, thus greatly accelerating the computing.

[0188] The multi-dimensional computing model and the distributed computing module in the present invention can significantly improve the efficiency of the symbolic computing process. Especially when dealing with high-dimensional problems, by transforming the computing tasks into low-dimensional problems and performing parallel computing, the computing complexity is significantly reduced and the computing time is reduced. Specifically, the implementation of this module brings the following technical effects:

[0189] Reduce computing complexity: Through mathematical transformations (such as Fourier transform, Laplace transform, etc.) in the multi-dimensional computing model, high-dimensional problems are transformed into low-dimensional problems, reducing the dimensions required for computing, thereby reducing the computing complexity.

[0190] Accelerate the computing process: Through the distributed computing architecture, computing tasks are decomposed into multiple sub-tasks and executed in parallel, greatly accelerating the computing process. Especially when facing complex mathematical problems, the distributed computing can significantly shorten the computing time.

[0191] Optimize the utilization of computing resources: The distributed computing module optimizes the task allocation of computing nodes through a load balancing algorithm, avoiding the generation of computing bottlenecks, thereby realizing the efficient utilization of computing resources.

[0192] Through these optimizations, the present invention can effectively improve the efficiency of symbolic computing, especially in high-dimensional symbolic computing tasks, ensuring that the system can efficiently and flexibly handle various computing tasks while reducing the waste of computing resources.

[0193] The present invention also provides a method for implementing an adaptive optimization mathematical mechanization symbolic computing system. The following will describe the specific implementation manners of each step in combination with the working process of the implementation method of the present invention.

[0194] S1. Receive the input mathematical symbol expression, perform symbolic computing complexity analysis on it, evaluate the computing time, memory consumption of the symbol expression, and possible bottleneck points in the computing process, and generate computing complexity data;

[0195] S2. Based on the generated complexity data, select the most suitable calculation path through the optimal path selection module, and dynamically adjust the calculation path according to the intermediate results during the symbolic calculation process to optimize the calculation process;

[0196] S4. Based on the incremental optimization algorithm, analyze the incremental data of each subtask in the calculation process in real time, adjust the calculation path to avoid redundant calculations, and maximize the calculation efficiency;

[0197] S4. Perform dimensionality reduction processing on the input problem, use Laplace transform or Fourier transform to convert the high-dimensional problem into a low-dimensional problem, and allocate tasks to multiple computing nodes for parallel processing through a distributed computing architecture. The distributed computing architecture coordinates and allocates tasks through a task decomposition unit and a scheduling unit.

[0198] In step S1, evaluate the calculation complexity through the number of variables, order, operation type, and number of operations in the symbolic expression, generate an optimization strategy based on complexity, and select a suitable calculation algorithm.

[0199] In step S2, select the optimal path according to the complexity data of the symbolic calculation. If the memory or time consumption of the calculation path exceeds a predetermined threshold, the system automatically adjusts the path, and the adjustment is based on the incremental optimization algorithm.

[0200] In step S3, the incremental optimization algorithm adjusts the path in real time and optimizes the calculation process by calculating incremental data. The incremental data includes time increment, memory increment, and the calculated results fed back.

[0201] The implementation method of this embodiment can be used to execute the above system embodiment, and its principle and technical effects are similar, so they will not be elaborated here.

[0202] The present invention also provides a device for an adaptive optimization mathematical mechanization symbolic calculation system, including:

[0203] A symbolic calculation complexity analysis unit, configured to receive an input mathematical problem, analyze the number of variables, order, and operation operations of the symbolic expression, and generate calculation complexity data;

[0204] An optimal path selection unit, which selects a calculation path according to the data provided by the symbolic calculation complexity analysis unit and makes dynamic adjustments during the calculation process;

[0205] An incremental optimization unit, configured to analyze the time increment and memory increment of each calculation task in real time, and dynamically adjust the calculation path to optimize the calculation process;

[0206] A multi-dimensional calculation unit and a distributed calculation unit, configured to perform dimensionality reduction processing on high-dimensional symbolic calculation problems, and allocate tasks to multiple computing nodes for parallel processing through a distributed computing architecture.

[0207] The device of this embodiment can be used to implement the above system embodiment, and its principle and technical effects are similar, so they will not be elaborated here.

[0208] Although the embodiments of the present invention have been shown and described, those of ordinary skill in the art can understand that various changes, modifications, substitutions, and variations can be made to these embodiments without departing from the principle and spirit of the present invention. The scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. An adaptively optimized mathematical mechanization symbolic calculation system, characterized in that Including: A symbolic calculation complexity analysis module, which is used to receive an input mathematical symbolic expression, evaluate the calculation complexity of the symbolic expression, and generate complexity data for symbolic calculation; An optimal path selection module, which selects the most suitable calculation path according to the complexity data generated by the symbolic calculation complexity analysis module, and dynamically adjusts the calculation path according to the real-time feedback calculation results; An incremental optimization algorithm module, which is used to gradually optimize the calculation path according to the intermediate calculation results at each step of symbolic calculation, avoid redundant calculations, and reduce calculation time and resource consumption; A multi-dimensional calculation model and a distributed calculation module, which are used to handle high-dimensional problems during symbolic calculation, transform high-dimensional symbolic problems into low-dimensional problems through multi-dimensional integration, Laplace transform or Fourier transform, and use a distributed calculation architecture to allocate calculation tasks to multiple calculation nodes for parallel calculation, thereby accelerating the calculation process.

2. An adaptively optimized mathematical mechanization symbolic calculation system according to claim 1, characterized in that The symbolic calculation complexity analysis module determines the calculation complexity of symbolic calculation by evaluating the number of variables, order, operation type and number of operations of the symbolic expression in the input problem. The calculation complexity includes calculation time, memory consumption and the critical path in the calculation task, and generates corresponding calculation optimization strategies through a preset complexity model. The complexity model includes a time complexity model and a memory consumption model based on the big O notation.

3. An adaptively optimized mathematical mechanization symbolic calculation system according to claim 1, characterized in that, The optimal path selection module includes: A path selection unit, which is used to calculate and compare the time consumption and memory consumption of multiple possible calculation paths, and the time consumption and memory consumption are obtained by real-time monitoring the performance data of each calculation step in the calculation process; A path adjustment unit, which adjusts the symbolic calculation path according to the feedback data and the intermediate results in the calculation process to minimize the calculation time and memory consumption. The adjustment process is based on an incremental analysis algorithm, and new time and memory consumption data are fed back for optimization after each calculation is completed.

4. An adaptively optimized mathematical mechanization symbolic calculation system according to claim 1, characterized in that, The incremental optimization algorithm module dynamically adjusts the calculation path by real-time analyzing the time and memory increments of each step task in the calculation process. The incremental optimization algorithm module is optimized according to the following incremental data: Time increment: Calculate the time difference when each subtask is executed. If the calculation time of the current task exceeds the preset time threshold, the path is automatically adjusted; Memory increment: Analyze the memory consumption of each subtask in the calculation process, and switch to a memory optimization strategy when the memory threshold is reached. The strategy includes adjusting the calculation module with large memory occupancy or using a memory management algorithm for optimization.

5. An adaptively optimized mathematical mechanization symbolic calculation system according to claim 1, characterized in that The multi-dimensional calculation model and the distributed calculation module adopt a variety of mathematical transformation technologies to reduce the dimension of the symbolic calculation task through Laplace transform and Fourier transform, simplify the calculation complexity of high-dimensional problems, and achieve distributed calculation in the following ways: A task decomposition unit divides the input problem into multiple subtasks, and allocates them to multiple calculation nodes for execution according to the scale, calculation resource requirements and complexity analysis results of the subtasks. A distributed scheduling unit coordinates the allocation of computing tasks among multiple computing nodes, optimizes the utilization of computing resources, reduces computing bottlenecks, and the scheduling unit adjusts the task allocation scheme in real time through computing resource monitoring.

6. The implementation method of an adaptively optimized mathematical mechanization symbolic calculation system according to any one of claims 1 to 5, characterized in that, It includes the following steps: S1. Receive the input mathematical symbol expression, perform symbolic calculation complexity analysis on it, evaluate the calculation time, memory consumption, and possible bottleneck points in the calculation process of the symbol expression, and generate calculation complexity data; S2. According to the generated complexity data, select the most suitable calculation path through the optimal path selection module, and dynamically adjust the calculation path according to the intermediate results during the symbolic calculation process to optimize the calculation process; S3. Based on the incremental optimization algorithm, analyze the incremental data of each subtask in the calculation process in real time, adjust the calculation path to avoid redundant calculations, and maximize the calculation efficiency; S4. Perform dimensionality reduction processing on the input problem, use Laplace transform or Fourier transform to convert the high-dimensional problem into a low-dimensional problem, and allocate tasks to multiple computing nodes for parallel processing through a distributed computing architecture. The distributed computing architecture coordinates and allocates tasks through a task decomposition unit and a scheduling unit.

7. The implementation method of an adaptively optimized mathematical mechanization symbolic calculation system according to claim 6, characterized in that, In step S1, the calculation complexity is evaluated through the number of variables, order, operation type, and number of operations in the symbol expression, and an optimization strategy based on complexity is generated to select a suitable calculation algorithm.

8. The implementation method of an adaptively optimized mathematical mechanization symbolic calculation system according to claim 6, characterized in that, In step S2, the optimal path is selected according to the complexity data of the symbolic calculation. If the memory or time consumption of the calculation path exceeds a predetermined threshold, the system automatically adjusts the path, and the adjustment is based on the incremental optimization algorithm.

9. The implementation method of an adaptively optimized mathematical mechanization symbolic calculation system according to claim 6, characterized in that, In step S3, the incremental optimization algorithm adjusts the path in real time and optimizes the calculation process by calculating incremental data. The incremental data includes time increment, memory increment, and the calculated results fed back.

10. An apparatus for implementing the system according to any one of claims 1 to 5, characterized in that, It includes: A symbolic calculation complexity analysis unit for receiving the input mathematical problem and analyzing the number of variables, order, and operation operations of the symbol expression to generate calculation complexity data; An optimal path selection unit for selecting a calculation path according to the data provided by the symbolic calculation complexity analysis unit and making dynamic adjustments during the calculation process; An incremental optimization unit for analyzing the time increment and memory increment of each calculation task in real time and dynamically adjusting the calculation path to optimize the calculation process; A multi-dimensional calculation unit and a distributed calculation unit for performing dimensionality reduction processing on high-dimensional symbolic calculation problems and allocating tasks to multiple computing nodes for parallel processing through a distributed computing architecture.

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