Method for predicting physical quantity through gaussian distribution learning, and system and computer program for executing same

Abstract

According to the present invention, disclosed are a method for predicting a physical quantity through Gaussian distribution learning and a system for executing same. A method for predicting a physical quantity through Gaussian distribution learning according to one disclosed embodiment is a method for predicting a physical quantity through Gaussian distribution learning, which is performed by a system including at least one processor, and comprises: a candidate kernel setting process of declaring a plurality of prediction positions for points in inputted flow field data and setting a plurality of candidate kernels based on Gaussian distribution through data sampling at the plurality of prediction positions; a physical quantity prediction process of predicting a physical quantity on the basis of a Gaussian property of each candidate kernel and a probability value of Gaussian for each prediction position; a Gaussian property learning process of learning Gaussian properties including a size, a rotation, a center position, and a physical quantity for the Gaussian distribution of each candidate kernel; a Gaussian adjustment process of adjusting Gaussian properties and the number of the Gaussian distribution of each candidate kernel on the basis of an error value calculated in consideration of physical constraints so as to select whether the physical quantity prediction for a point to which each candidate kernel belongs is accurate; and a kernel application process of selecting the candidate kernel Gaussian-adjusted through the Gaussian adjustment process as a final kernel and storing the learned Gaussian distribution and Gaussian properties for the selected kernel.

Description

Method for predicting physical quantities through Gaussian distribution learning, and a system and computer program for executing the same

[0001] The disclosed invention relates to a method for predicting physical quantities through Gaussian distribution learning for high-resolution prediction of physical quantities and a system for implementing the same.

[0002] The content described in this section merely provides background information regarding the present embodiment and does not constitute prior art.

[0003] A flow field represents a function or mapping that assigns a vector to each point in space, and signifies a collection of vectors having direction and magnitude at each point. Such flow fields are applied in various fields, such as electromagnetic fields, gravitational fields, or fluid dynamics; in particular, they can be utilized in designing shelves, airplanes, or vehicles based on flow velocity or volume, in the hardware design of wind power generation, and in the diagnosis of cardiovascular diseases.

[0004] However, technologies that visualize physical data of flow fields and measure them at high resolution have the disadvantage of requiring significant time and cost, as well as being susceptible to noise. Methods for analyzing flow fields using Computational Fluid Dynamics (CFD) face problems such as the high computational cost required to calculate high-resolution physical properties from low-resolution data, and the inevitably limited basis for determining whether the analyzed results are valid.

[0005] To address these problems, AI-based technologies for predicting and analyzing high-resolution physical data with fast estimation speeds are being researched.

[0006] While general neural networks rely entirely on data without considering physical laws, the Physics-Informed Neural Network (PINN) is a method that incorporates physical information inherent in the governing equations (physical equations) into the neural network to satisfy them. General neural networks learn using only training data, and their loss function is trained to minimize the discrepancy between the original data and the data predicted by the training model; however, PINN utilizes the physical equations themselves in the loss function to train the network so that the sampled data satisfies physical laws.

[0007] Due to their flexibility and powerful modeling capabilities, these PINNs are playing an increasingly important role in various fields of science and engineering. For example, in the field of fluid dynamics, modeling and predicting complex systems related to fluid flow has traditionally been a difficult task; however, PINNs enable more accurate and efficient fluid flow prediction by integrating the fundamental laws of fluid dynamics into models. In climate science, since climate models must simulate highly complex physical processes and accurate predictions are essential for critical decision-making, PINNs can improve the accuracy of climate change predictions by combining climate data with physical laws. In structural engineering, where predicting stress and deformation in buildings and other structures is a critical part of the field, PINNs allow for a better understanding and prediction of the physical behavior of structures. In the field of medical imaging, where accurate imaging is key to diagnosis and treatment planning, PINNs can be used to interpret medical images and model complex biological systems, thereby providing better diagnostic and treatment strategies. In the energy sector, as the optimization and management of renewable energy systems are critical steps toward a sustainable future, PINNs can play an important role in understanding and predicting complex patterns of energy production and consumption.

[0008] As such, PINN is a model that predicts internal data by learning physical constraints, and unlike existing deep learning models, it utilizes only physical constraints as the loss function during the learning process. However, PINN has the problem that accuracy decreases as it moves further away from the boundary conditions because it does not utilize data within the boundary conditions, and training time inevitably increases as the number of training locations is increased to improve accuracy.

[0009] Learning and predicting physical data using PINN requires a significant amount of training time. Furthermore, retraining is essential when learning data with different physical properties. In addition, there are limitations, such as difficulties in optimizing and training PINN, particularly when utilizing low-resolution data, and the limitation that predictions are only possible within the range of the training data. Moreover, PINN, which solves partial differential equations (PDEs) based on physical information, faces the problem of requiring long training times to learn solution operators for arbitrary PDEs or demanding large amounts of high-resolution data for high-resolution processing.

[0010] To solve these problems, the disclosed embodiment provides a method for predicting physical quantities through Gaussian distribution learning and a system for executing the same, wherein a kernel based on a Gaussian distribution can be set at multiple prediction locations within the flow field data, Gaussian properties including the magnitude, rotation, center position, and physical quantity of each kernel's Gaussian distribution are learned considering physical constraints, and efficient learning of the Gaussian distribution through Gaussian adjustment can be performed, thereby enabling high-resolution prediction of physical quantity data based on the Gaussian distribution.

[0011] In particular, the method for predicting physical quantities through Gaussian learning and the system for executing it may include all or part of the Gaussian magnitude, rotation, center position, and physical quantity as learnable parameters, and by fixing the axis, the calculation process of the rotation matrix is ​​omitted, thereby enabling faster learning speeds than existing PINNs, physical information operators, and computational fluid dynamics.

[0012] A method for predicting a physical quantity through Gaussian distribution learning according to a disclosed embodiment is a method for predicting a physical quantity through Gaussian distribution learning performed by a system including at least one processor, comprising: a candidate kernel setting process of declaring a plurality of prediction positions for points within input flow field data and setting a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of prediction positions; a physical quantity prediction process of predicting a physical quantity based on the Gaussian properties and probability values ​​of each candidate kernel for each prediction position; a Gaussian property learning process of learning Gaussian properties including magnitude, rotation, center position, and physical quantity for the Gaussian distribution of each candidate kernel; a Gaussian adjustment process of selecting whether the prediction of a physical quantity for the point to which each candidate kernel belongs is accurate by adjusting the Gaussian properties and number of the Gaussian distribution of each candidate kernel based on an error value calculated considering physical constraints; and a kernel application process of selecting the candidate kernel that has been Gaussian-adjusted through the Gaussian adjustment process as the final kernel and storing the Gaussian distribution and Gaussian properties learned for the selected kernel.

[0013] Alternatively, prior to the above-mentioned Gaussian property learning process, it further includes a data sampling process that provides additional candidate kernels by applying the physical quantity assumption governing equation and sampling data from prediction locations other than those declared in the above-mentioned candidate kernel setting process.

[0014] Alternatively, the data sampling module uses one of a plurality of sampling techniques, including grid sampling, random sampling, and loss-weighted sampling.

[0015] Alternatively, the Gaussian property learning process described above involves acquiring the additional candidate kernel and learning the Gaussian properties of the Gaussian distribution of the acquired additional candidate kernel.

[0016] Alternatively, the above candidate kernel setting process determines the size, rotation, and position of the Gaussian distribution of multiple candidate kernels.

[0017] Alternatively, the above candidate kernel setting process determines the magnitude or rotation of the Gaussian distribution of each candidate kernel using either the distance set by user input or the distance set based on a shortest distance algorithm that calculates the minimum distance.

[0018] Alternatively, the physical quantity prediction module calculates a Gaussian probability value using any one of a probability-based normalization technique based on a Gaussian probability distribution, a transparency-based multiplication technique, and a normalization technique that multiplies by a constant value.

[0019] Alternatively, the Gaussian property learning module is trained by applying a loss-weighted sampling technique that considers the physical error of the candidate kernel at each prediction position.

[0020] Alternatively, the above Gaussian property learning process will obtain the Gaussian properties of each candidate kernel's Gaussian distribution through the backpropagation process of the loss function.

[0021] Alternatively, the Gaussian property learning process is based on a non-linear optimization technique that optimizes the Gaussian property using one of a plurality of algorithms including ADAM and LBFGS.

[0022] Alternatively, the above Gaussian adjustment process stores a preset threshold for Gaussian adjustment and performs Gaussian adjustment through the replication, splitting, removal, or merging of the Gaussian distribution for each candidate kernel based on the stored threshold.

[0023] Alternatively, the above Gaussian adjustment process is such that among the Gaussian properties of each candidate kernel, the error of the center of the Gaussian distribution is a first threshold (τ p If it is greater than ), Gaussian adjustment is performed, and if the error in the center of the Gaussian distribution is less than or equal to the first threshold, Gaussian adjustment is not performed.

[0024] Alternatively, in the Gaussian adjustment process, if the error in the center of the Gaussian distribution of the candidate kernel is greater than the first threshold, the magnitude of the Gaussian distribution of the candidate kernel is the second threshold (τ s If it is greater than ), the corresponding Gaussian distribution is split, and if the size of the corresponding Gaussian distribution is less than or equal to the second threshold, the Gaussian distribution is duplicated.

[0025] Alternatively, the Gaussian adjustment process described above involves the cosine similarity of the Gaussian distribution of the new candidate kernel, in which the partitioning or replication of the Gaussian distribution of the candidate kernel is completed, reaching a third threshold (τ). m If it is greater than ), it merges the corresponding Gaussian distribution.

[0026] Alternatively, the Gaussian adjustment process is such that the size of the Gaussian distribution of the new candidate kernel, in which the splitting or replication of the Gaussian distribution of the candidate kernel is completed, is a fourth threshold (τ). L If it is greater than ), the corresponding candidate kernel is removed.

[0027] A system for predicting a physical quantity through Gaussian distribution learning according to a disclosed embodiment includes: a memory for storing a physical quantity prediction model with a kernel based on a Gaussian distribution applied; A processor that trains the physical quantity prediction model and predicts the physical quantity of the flow field for each point of the input flow field data through the trained physical quantity prediction model; wherein the processor declares a plurality of prediction positions for points within the input flow field data, sets a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of prediction positions, predicts the physical quantity based on the Gaussian properties and probability values ​​of each candidate kernel for each prediction position, learns the Gaussian properties including magnitude, rotation, center position, and physical quantity for the Gaussian distribution of each candidate kernel, adjusts the Gaussian properties and number of the Gaussian distribution of each candidate kernel based on error values ​​calculated considering physical constraints to select whether the prediction of the physical quantity for the point to which each candidate kernel belongs is accurate, selects the Gaussian-adjusted candidate kernel as the final kernel through the Gaussian adjustment process, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

[0028] A computer program according to a disclosed embodiment is a computer program stored on a computer-readable storage medium, wherein, when executed on one or more processors, the computer program performs operations for predicting physical quantities through Gaussian distribution learning, and the operations include: a candidate kernel setting operation for declaring a plurality of prediction positions for points within input flow field data and setting a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of prediction positions; a physical quantity prediction operation for predicting physical quantities based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction position; a Gaussian property learning operation for learning Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel; and a Gaussian adjustment operation for selecting whether the prediction of physical quantities for the point to which each candidate kernel belongs is accurate by adjusting the Gaussian properties and number of the Gaussian distribution of each candidate kernel based on an error value calculated considering physical constraints. and a kernel application operation that selects a Gaussian-tuned candidate kernel through the above Gaussian tuning process as the final kernel, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

[0029] A user terminal according to a disclosed embodiment comprises: a data receiving unit for receiving flow field data; a processor for predicting physical quantities based on the received flow field data and learning and adjusting Gaussian properties for each point; and an output unit for predicting physical quantities for new flow field data based on the results learned by the processor; wherein the processor comprises: a physical quantity prediction module that declares a plurality of prediction positions for points within the input flow field data, sets a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of prediction positions, and predicts physical quantities based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussian for each prediction position; and a Gaussian property learning module that learns Gaussian properties including magnitude, center position, and physical quantities for the Gaussian distribution of each candidate kernel, excluding rotational properties. It includes a Gaussian adjustment module that selects whether each candidate kernel accurately predicts physical quantities for the point to which it belongs by adjusting the Gaussian properties and number of Gaussian distributions of each candidate kernel based on error values ​​calculated considering physical constraints, and selects the Gaussian-adjusted candidate kernel as the final kernel through the Gaussian adjustment process, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

[0030] The above physical quantity prediction module can provide additional candidate kernels by sampling data at prediction locations other than the prediction locations declared in the candidate kernel setting process prior to the Gaussian property learning process.

[0031] The above physical quantity prediction module may use any one of a plurality of sampling techniques including grid sampling, random sampling, and loss-weighted sampling.

[0032] The above Gaussian property learning module can acquire the additional candidate kernel and learn the Gaussian properties of the Gaussian distribution of the acquired additional candidate kernel.

[0033] The above physical quantity prediction module can fix the rotation axis and determine the size and position of the Gaussian distribution of a plurality of candidate kernels.

[0034] The above physical quantity prediction module can determine the magnitude of the Gaussian distribution of each candidate kernel by using either of the distances set based on a shortest distance algorithm that calculates the distance or minimum distance set by user input.

[0035] The above physical quantity prediction module can calculate a Gaussian probability value by using any one of a probability-based normalization technique based on a Gaussian probability distribution, a transparency-based multiplication technique, and a normalization technique that multiplies by a constant value.

[0036] The above Gaussian property learning module can be trained by applying a loss-weighted sampling technique that considers the physical error of the candidate kernel at each prediction position.

[0037] The above Gaussian property learning module can learn the Gaussian properties of the Gaussian distribution of each candidate kernel through the backpropagation process of the loss function.

[0038] The above Gaussian property learning module can learn based on a non-linear optimization technique that optimizes the Gaussian property using any one of a plurality of algorithms including SGD, RMSProp, ADAM, and LBFGS.

[0039] The above Gaussian adjustment module calculates a total error value of a Gaussian distribution formed by a weighted sum of a first error value based on the difference between a predicted physical quantity and an actual value and a second error value based on the physical constraints, and among the Gaussian properties of each candidate kernel, if the total error value is greater than a first threshold, Gaussian adjustment is performed, and if the total error value at the center of the Gaussian distribution is less than or equal to the first threshold, Gaussian adjustment may not be performed.

[0040] The above Gaussian adjustment module can split the Gaussian distribution if the total error value is greater than the first threshold and the size of the Gaussian distribution of the corresponding candidate kernel is greater than the second threshold, and can replicate the Gaussian distribution if the size of the Gaussian distribution is less than or equal to the second threshold.

[0041] The above Gaussian adjustment module can connect the Gaussian distributions within a graph and merge the connected Gaussian distributions if the similarity of the Gaussian distribution of a new candidate kernel, in which the splitting or replication of the Gaussian distribution of the candidate kernel is completed, is greater than a third threshold.

[0042] The above Gaussian adjustment module can remove a candidate kernel if the size of the Gaussian distribution of a new candidate kernel, in which the splitting or replication of the Gaussian distribution of the candidate kernel is completed, is greater than the fourth threshold.

[0043] A system according to another disclosed embodiment comprises: a data receiving unit for receiving flow field data; a processor for predicting physical quantities based on the received flow field data and learning and adjusting Gaussian properties for each point; and an output unit for predicting physical quantities for new flow field data based on the results learned by the processor. The processor declares a plurality of predicted positions for points within the input flow field data, sets a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of predicted positions, predicts physical quantities based on the Gaussian properties and probability values ​​of each candidate kernel for each predicted position, learns Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel, calculates a total error value of the Gaussian distribution formed by a weighted sum of a first error value based on the difference between the predicted physical quantity and the actual value and a second error value based on the physical constraints, and performs Gaussian adjustment if the total error value among the Gaussian properties of each candidate kernel is greater than a first threshold.

[0044] A computer program stored on a computer-readable storage medium according to another disclosed embodiment, wherein the computer program, when executed on one or more processors, performs operations for predicting physical quantities through Gaussian learning, the operations comprising: a candidate kernel setting operation of declaring a plurality of prediction positions for points within input flow field data and setting a plurality of candidate kernels based on a Gaussian distribution through data sampling at the plurality of prediction positions; a physical quantity prediction operation of predicting physical quantities based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction position; a Gaussian property learning operation of learning Gaussian properties including the magnitude, center position, and physical quantity for the Gaussian distribution of each candidate kernel, excluding rotation matrices; and a Gaussian adjustment operation of adjusting the Gaussian properties and number of the Gaussian distribution of each candidate kernel based on an error value calculated considering physical constraints to determine whether the prediction of physical quantities for the point to which each candidate kernel belongs is accurate. and a kernel application operation that selects a Gaussian-tuned candidate kernel through the above Gaussian tuning process as the final kernel, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

[0045] The method for predicting physical quantities through Gaussian distribution learning and the system for executing the same according to the disclosed embodiment can predict physical quantities from low-resolution physical quantity data through a model applying a kernel based on a Gaussian distribution, and has the effect of upgrading physical quantity data to high resolution with a faster learning speed than existing PINNs, physical information operators, and computational fluid dynamics.

[0046] A method for predicting physical quantities through Gaussian distribution learning according to a disclosed embodiment and a system for executing the same predict physical quantities using a kernel based on a Gaussian distribution through a probability-based normalization technique at multiple prediction locations within input fluidity data, and since the Gaussian properties and number of Gaussian distributions of each kernel can be adjusted, it has the effect of not only accurately predicting physical quantity data but also enhancing learning stability.

[0047] In addition, the method for predicting physical quantities through Gaussian learning according to the disclosed embodiment and the system for executing the same enable data resolution at a faster speed than existing physical information artificial neural networks, physical information artificial operators, and computational fluid dynamics through rapid resolution through physical quantity prediction, and through this technology, data required for medical and fluid research can be rapidly synthesized.

[0048] The method for predicting physical quantities through Gaussian learning according to the disclosed embodiment and the system for executing the same can be utilized more directly for analysis, unlike existing artificial intelligence models for predicting physical quantities which are Black-box problems, and through this, is much more amenable to the analysis of physical quantities, such as detailed cardiovascular diagnosis through detailed analysis of blood flow.

[0049] FIG. 1 is a diagram illustrating a system for predicting physical quantities through Gaussian distribution learning according to a disclosed embodiment and data analyzed by the system.

[0050] FIG. 2 is a control block diagram of a user terminal that executes a method for predicting physical quantities through disclosed Gaussian distribution learning.

[0051] FIG. 3 is a block diagram specifically illustrating the configuration of a processor for executing a method of predicting physical quantities through disclosed Gaussian distribution learning.

[0052] Figure 4 is a flowchart explaining a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0053] Figure 5 is a diagram illustrating the process of predicting physical quantities using a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0054] FIG. 6 is a flowchart illustrating the process of learning the Gaussian properties of a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0055] Figure 7 is a diagram that visualizes the learning process of Gaussian properties of a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0056] Figure 8 is an example diagram comparing the Gaussian properties before and after learning for the disclosed candidate kernel.

[0057] Figure 9 is a flowchart illustrating the Gaussian adjustment process of a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0058] Figure 10 is a diagram visualizing the Gaussian adjustment process of a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0059] Figure 11 is an example diagram showing the result of applying a Gaussian adjustment process to each disclosed candidate kernel.

[0060] Figure 12 is an example diagram showing the prediction results for actual high-resolution data through a method of predicting physical quantities through the disclosed Gaussian distribution learning.

[0061] Figure 13 is an example diagram showing the results of a comparison of the training time between the disclosed method for predicting physical quantities through Gaussian distribution learning and existing physical artificial neural network models.

[0062] Figure 14 is an example diagram showing the accuracy according to training time of a method for predicting physical quantities through the disclosed Gaussian distribution learning and existing physical artificial neural network models.

[0063] FIG. 15 is a flowchart illustrating an overall method for predicting physical quantities through Gaussian learning according to another embodiment.

[0064] Figure 16 is a diagram visually illustrating the method of Figure 16.

[0065] FIG. 17 is a flowchart for further explaining in detail the operation method of a physical quantity prediction module according to another embodiment.

[0066] FIG. 18 is a flowchart specifically describing the operation process of a Gaussian property learning module according to another embodiment.

[0067] FIG. 19 is a flowchart specifically describing the operation process of a Gaussian adjustment module according to another embodiment.

[0068] FIG. 20 is a diagram illustrating the effect of a physical quantity prediction method using a disclosed Gaussian distribution.

[0069] Figure 21 shows the results of experimentally verifying the essentiality of each component.

[0070] Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the attached drawings. However, the technical concept of the present invention is not limited to the embodiments described herein and may be embodied in other forms. Rather, the embodiments introduced herein are provided to ensure that the disclosed content is thorough and complete and to sufficiently convey the concept of the present invention to those skilled in the art.

[0071] In this specification, when a component is described as being on another component, it means that it may be formed directly on the other component or that a third component may be interposed between them. Additionally, in the drawings, shapes and sizes are exaggerated for the effective illustration of the technical content.

[0072] Additionally, although terms such as first, second, third, etc., have been used to describe various components in the various embodiments of this specification, these components should not be limited by such terms. These terms are used merely to distinguish one component from another. Accordingly, what is referred to as the first component in one embodiment may be referred to as the second component in another embodiment. Each embodiment described and illustrated herein also includes its complementary embodiment. Furthermore, in this specification, "and / or" is used to mean including at least one of the components listed before and after it.

[0073] In the specification, singular expressions include plural expressions unless the context clearly indicates otherwise. Furthermore, terms such as "include" or "have" are intended to specify the existence of the features, numbers, steps, components, or combinations thereof described in the specification, and should not be understood as excluding the existence or addition of one or more other features, numbers, steps, components, or combinations thereof. Additionally, in this specification, "connection" is used to include both indirectly connecting multiple components and directly connecting them.

[0074] Furthermore, in describing the present invention below, if it is determined that a detailed description of related known functions or configurations could unnecessarily obscure the essence of the invention, such detailed description will be omitted.

[0075] FIG. 1 is a diagram illustrating a system for predicting physical quantities through Gaussian distribution learning according to a disclosed embodiment and data analyzed by the system.

[0076] Referring to FIG. 1, a system (1) that predicts physical quantities through Gaussian distribution learning can collect various flow field data from the outside. Specifically, the data that the system (1) can collect may include various data such as flow field data for wind (3), flow field data for blood flow (4), or various other wave fields (5).

[0077] Flow field data is data utilized in various fields, such as wind power generation, design of automobiles and aircraft, climate change analysis, and blood flow change analysis based on MRI image data. As an example, flow field data may be a set of four-dimensional point data, such as points included in the flow field, for example, x, y, z, and t. The disclosed system (1) can predict the predicted values ​​of the flow field change at each point of the flow field data, for example, velocity (u, v) and pressure (p) at each point, and further calculate the total physical quantity of the flow field data through the predicted values. As another example, the predicted values ​​of the flow field change at each point may include various physical quantities such as density.

[0078] The system (1) can collect fluid field data through a communication network (2) or receive input from a user. Specifically, the system (1) may include a user terminal (10) that can be implemented as a computer or portable terminal capable of connecting to the communication network (2), and a server (20) that trains a large-capacity artificial intelligence model that is difficult to store or train due to the hardware limitations of the user terminal (10).

[0079] A computer, which is one example of a user terminal (10), may include, for example, a laptop, desktop, laptop, tablet PC, slate PC, etc. equipped with a web browser. A portable terminal, which is another example of a user terminal (10), may include, for example, a wearable device such as a PCS (Personal Communication System), GSM (Global System for Mobile communications), PDC (Personal Digital Cellular), PHS (Personal Handyphone System), PDA (Personal Digital Assistant), IMT (International Mobile Telecommunication)-2000, CDMA (Code Division Multiple Access)-2000, W-CDMA (W-Code Division Multiple Access), WiBro (Wireless Broadband Internet) terminal, smartphone, etc., as a wireless communication device that ensures portability and mobility.

[0080] The communication network (2) includes various short-range, wired, and wireless networks. The communication network (2) can communicate by a communication module included in a user terminal (10) or a server (20).

[0081] Specifically, the short-range communication module of the user terminal (10) may include various short-range communication modules that transmit and receive signals using a wireless communication network at a short range, such as a Bluetooth module, an infrared communication module, an RFID (Radio Frequency Identification) communication module, a WLAN (Wireless Local Access Network) communication module, an NFC communication module, and a Zigbee communication module.

[0082] The wired communication module of the user terminal (10) may include various wired communication modules such as a Local Area Network (LAN) module, a Wide Area Network (WAN) module, or a Value Added Network (VAN) module, as well as various cable communication modules such as USB (Universal Serial Bus), HDMI (High Definition Multimedia Interface), DVI (Digital Visual Interface), RS-232 (recommended standard 232), power line communication, or POTS (plain old telephone service).

[0083] The wireless communication module of the user terminal (10) may include a wireless communication module that supports various wireless communication methods, such as GSM (global System for Mobile Communication), CDMA (Code Division Multiple Access), WCDMA (Wideband Code Division Multiple Access), UMTS (universal mobile telecommunications system), TDMA (Time Division Multiple Access), and LTE (Long Term Evolution), in addition to a Wi-Fi module and a WiBro (Wireless broadband) module.

[0084] The server (20) may include at least one processor and a communication module, and may train an artificial intelligence model described below on behalf of the user terminal (10) or transmit the trained artificial intelligence model to the user terminal (10). As another example, the server (20) may receive flow field data (3, 4, 5), calculate a prediction value, and transmit it to the user terminal (10).

[0085] Meanwhile, the disclosed system (1) does not necessarily need to include both a user terminal (10) and a server (20). It is sufficient for the system (1) to be configured to calculate a predicted value or a total physical quantity using various flow field data (3, 4, 5) as input.

[0086] FIG. 2 is a control block diagram of a user terminal that executes a method for predicting physical quantities through disclosed Gaussian distribution learning.

[0087] Referring to FIG. 2, a user terminal (10) includes a data receiving unit (11) for receiving a plurality of flow field data, a processor (12) for predicting the physical quantity of the flow field for each point of the flow field data by appropriately dividing the received flow field data and inputting the divided flow field data into a pre-trained physical quantity prediction model, a memory (memory, 13) for storing the received flow field data and a physical quantity prediction model that applies at least one artificial intelligence model or a kernel based on a Gaussian distribution, and an output unit (14) for outputting the prediction result. Here, the physical quantity prediction model may be a multi-layer perceptron (MLP) model utilizing a Gaussian distribution.

[0088] Specifically, the data receiving unit (11) can receive not only a communication module that receives various fluid field data from the communication network (2) described in FIG. 1, but also input commands from a user and various signals input by a user through a hardware configuration such as a USB (Universal Serial Bus). Specifically, the data receiving unit (11) may include hardware devices such as various buttons or switches, pedals, keyboards, mice, trackballs, various levers, handles or sticks to receive user input, and may include at least one of a short-range communication module, a wired communication module, and a wireless communication module capable of communicating with the communication network (2).

[0089] The memory (13) can store not only the flow field data that the data receiving unit (11) intends to predict, but also multiple artificial intelligence models operated by the processor (12) and training data required for the training of the multiple artificial intelligence models. To this end, the memory (13) may be implemented as at least one of a non-volatile memory device such as a cache, ROM (Read Only Memory), PROM (Programmable ROM), EPROM (Erasable Programmable ROM), EEPROM (Electrically Erasable Programmable ROM), and flash memory, a volatile memory device such as RAM (Random Access Memory), or a storage medium such as a hard disk drive (HDD) and CD-ROM, but is not limited thereto. As shown in FIG. 2, the memory (13) is implemented as a separate chip from the processor (12), but may be implemented as a single chip with the processor (12) as needed.

[0090] The output unit (14) outputs the result predicted by the processor (12), that is, the predicted value for each point in the prediction area or the result of visualizing the total physical quantity of the flow field data calculated from the predicted value. To this end, the output unit (14) may include various hardware devices such as a Digital Light Processing (DLP) panel, a Plasma Display Panel, a Liquid Crystal Display (LCD) panel, an Electro Luminescence (EL) panel, an Electrophoretic Display (EPD) panel, an Electrochromic Display (ECD) panel, a Light Emitting Diode (LED) panel, or an Organic Light Emitting Diode (OLED) panel.

[0091] Meanwhile, the output unit (14) may include a device that is a GUI (Graphical User Interface), i.e., software, such as a touch pad, for receiving user input commands. The touch pad may be implemented as a touch screen panel (TSP) and may form a mutual layer structure with the data receiving unit (11).

[0092] The specific method by which the processor (12) predicts physical quantities through Gaussian distribution learning will be described in more detail later through other drawings below.

[0093] The processor (12) may be implemented as a processor that executes an algorithm or a program that reproduces an algorithm for controlling the operation of each component (data receiving unit, memory and output unit, etc.) of the user terminal (10). The processor (12) may refer to a data processing device embedded in hardware having a physically structured circuit to perform a function expressed by code or instructions included in the program. Examples of such data processing devices embedded in hardware may include, but are not limited to, processing devices such as a microprocessor, a central processing unit (CPU), a processor core, a multiprocessor, an application-specific integrated circuit (ASIC), a field programmable gate array (FPGA), and a Graphics Processing Unit (GPU). The processor (12) may include one or more processors.

[0094] Meanwhile, the user terminal (10) may include other configurations in addition to the configuration described in FIG. 2.

[0095] FIG. 3 is a block diagram specifically illustrating the configuration of a processor for executing a method of predicting physical quantities through disclosed Gaussian distribution learning.

[0096] Specifically, the processor (12) includes, but is not limited to, a candidate kernel setting module (121), a physical quantity prediction module (122), an error calculation module (123), a data sampling module (124), a Gaussian property learning module (125), a Gaussian adjustment module (126), and a kernel application module (127).

[0097] The candidate kernel setting module (121) sets a candidate kernel based on a Gaussian distribution for calculating the weight of the observed data for one or more points among the points in the input flow field data. At this time, the candidate kernel setting module (121) determines the size, rotation, and position of the Gaussian distribution of each candidate kernel, and can specify the candidate kernel using sampling techniques such as random sampling, grid sampling, or techniques utilizing image features of the data. The candidate kernel setting module (121) may use all points included in the flow field data, but may also use only some points.

[0098] The candidate kernel setting module (121) may arbitrarily set the distance to determine the size and rotation of the Gaussian distribution of each candidate kernel, but may also automatically set the distance based on a shortest distance algorithm that calculates the minimum distance.

[0099] At this time, the physical quantity observed in the candidate kernel set by the candidate kernel setting module (121) can be used directly as observation data or calculated through interpolation and used as observation data, and the physical quantity properties of each candidate kernel can be used as vector values ​​as well as scalar values.

[0100] The candidate kernel setting module (121) can declare multiple prediction locations for points within the flow field data and set candidate kernels by sampling data from the multiple prediction locations. Since the weight of the observed data changes depending on the prediction location, the candidate kernel can be defined as a Gaussian distribution for calculating the weight of the observed data.

[0101] Generally, there is an assumption that physical quantities must satisfy the governing equation at all locations within physical constraints. Therefore, the data sampling module (124) samples training data for learning additional physical properties (or characteristics), and by applying the physical quantity assumption governing equation, it randomly samples predicted locations within the flow field that are previously unknown so that they can be used additionally for learning physical constraints. The data sampling module (124) may use any one of various sampling techniques, including grid sampling, random sampling, and loss-weighted sampling.

[0102] The physical quantity prediction module (122) predicts physical quantities based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction location. To increase the stability and accuracy of physical quantity prediction through the Gaussian probability distribution, this physical quantity prediction module (122) may use various normalization methods, such as probability-based normalization techniques, transparency-based multiplication techniques, and multiplication by a constant, and may also adjust the region of interest based on the probability values ​​of the Gaussians calculated through the probability-based normalization technique. At this time, the physical quantity prediction module (122) may also obtain the probability values ​​of the Gaussians multiplied to the physical quantity properties of each candidate kernel by normalization or by multiplying by a constant value.

[0103] The physical quantity prediction module (122) can use a valid range of physical quantities for each candidate kernel specified by the user, and the partial derivative values ​​for calculating the governing equation can include both numerical calculation methods through software and analytical calculation methods through mathematical calculation methods.

[0104] The Gaussian property learning module (125) learns the Gaussian properties of each candidate kernel, and may use a loss-weighted sampling method that considers the physical error of each point during the learning process. At this time, the Gaussian properties of each candidate kernel may include data on the magnitude, rotation, center position, and physical quantity of the Gaussian distribution of each candidate kernel. The Gaussian property learning module (125) may also learn the Gaussian properties of each candidate kernel for additional predicted positions sampled by the data sampling module (124).

[0105] The error calculation module (123) calculates the error value by considering physical constraints, and the error value used in the learning process of the Gaussian property learning module (125) can use not only an automatic differentiation engine (orch. autograd) that supports neural network learning but also mathematically calculated partial derivative values.

[0106] At this time, the Gaussian property learning module (125) performs learning through the backpropagation process of the loss function and can learn based on a non-linear optimization technique that can optimize Gaussian properties using various algorithms such as ADAM and LBFGS. At this time, the Gaussian property learning module (125) may apply various governing equations such as the Navier-Stokes equation and the Burgers equation as loss functions, and may apply loss functions for initial conditions and boundary conditions of flow field data, loss functions for predicted values, etc.

[0107] The Gaussian adjustment module (126) can adjust the error value or the gradient of the error value to select inaccurate candidate kernels for an efficient Gaussian distribution within the flow field data, and can perform Gaussian adjustment through a process of duplication, splitting, removal, or merging for each candidate kernel.

[0108] The Gaussian adjustment module (126) may use an error value and a derivative of the error value to determine whether each candidate kernel accurately predicts the corresponding point, and a threshold value (τ) for Gaussian adjustment in memory (). p , τ s , τ m , τ L After saving ), the process of duplicating or splitting candidate kernels based on a threshold can be performed. Additionally, the Gaussian adjustment module (126) can remove or merge unnecessary candidate kernels, and the merging process may include a graph construction method utilizing cosine similarity.

[0109] The system (1) may use the size, transparency, or similarity of the Gaussian distribution of the candidate kernel as criteria for determining that the candidate kernel is unnecessary for predicting physical quantities.

[0110] The kernel application module (127) selects a candidate kernel that has undergone the replication, splitting, merging, or removal process by the Gaussian adjustment module (126) as the final kernel, applies it to the physical quantity prediction model, and stores the Gaussian distribution and Gaussian properties learned for the kernel.

[0111] Each of the modules described above is merely an example for explaining the present invention and is not limited thereto, and may be implemented in various modifications. Additionally, the modules described above are stored in memory as a computer-readable recording medium that can be controlled by a processor (12). Furthermore, at least some of the modules described above may be implemented as software, firmware, hardware, or a combination of at least two of these, and may include a module, program, routine, instruction set, or process for performing one or more functions.

[0112] Figure 4 is a flowchart explaining a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0113] A method for predicting a physical quantity through Gaussian distribution learning performed by the disclosed system (1) comprises a candidate kernel setting process (S10), a physical quantity prediction process (S20), an error calculation process (S30), a data sampling process (S40), a Gaussian property learning process (S50), a Gaussian adjustment process (S60), and a kernel application process (S70).

[0114] In the candidate kernel process (S10), multiple candidate kernels are set based on a Gaussian distribution for calculating the weight of the observed data for at least one point among the points in the input flow field data. The candidate kernel setting module (121) declares multiple predicted locations for the points in the flow field data and sets candidate kernels through data sampling at the multiple predicted locations.

[0115] In the physical quantity prediction process (S20), physical quantities are predicted based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction location.

[0116] Figure 5 is a diagram illustrating the process of predicting physical quantities using a method for predicting physical quantities through the disclosed Gaussian distribution learning.

[0117] As illustrated in FIG. 5, the physical quantity prediction process (S20) can predict physical quantities at four-dimensional points of x, y, z, and t at predicted locations P1, P2, and P3 using a probability-based normalization formula as shown in Equation 1 below, in order to increase the stability and accuracy of the physical quantity prediction through a Gaussian probability distribution.

[0118]

[0119] In mathematical formula 1, μ represents the average value at any point i.

[0120] As shown in mathematical formulas 2 and 3, in the physical quantity prediction process (S20), partial derivative values ​​for calculating the governing equation can be obtained using an analytical calculation method with mathematical formulas.

[0121]

[0122]

[0123]

[0124]

[0125]

[0126]

[0127] To explain Fig. 4 again, in the error calculation process (S30), the error value is calculated by considering physical constraints, and mathematically calculated partial derivative values ​​can be used.

[0128] In the data sampling process (S40), candidate kernels for prediction locations within the flow field that are not initially declared, which are unknown, are randomly sampled by applying the governing equations for physical quantity assumptions and are additionally used for learning physical constraints.

[0129] The Gaussian property learning process (S50) learns Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel. At this time, the Gaussian property learning process (S50) can also learn the properties of each additional candidate kernel for additional sampled prediction positions.

[0130] The Gaussian adjustment process (S60) adjusts the flow field data to select inaccurate candidate kernels using error values ​​or the gradient of error values ​​for an efficient Gaussian distribution.

[0131] In the kernel application process (S70), after performing replication, splitting, merging, or removal processes on the Gaussian distribution of each candidate kernel through the Gaussian adjustment process (S60), the candidate kernel with completed Gaussian adjustment is selected as the final kernel, and the selected kernel is applied to the physical quantity prediction model while storing the Gaussian distribution and properties learned for the kernel.

[0132] FIG. 6 is a flowchart explaining the process of learning Gaussian properties of a method for predicting physical quantities through the disclosed Gaussian distribution learning, FIG. 7 is a diagram visualizing the process of learning Gaussian properties of a method for predicting physical quantities through the disclosed Gaussian distribution learning, and FIG. 8 is an example diagram comparing the state before and after learning Gaussian properties for a disclosed candidate kernel.

[0133] The Gaussian property learning process (S50) obtains the predicted value of the physical quantity predicted in the physical quantity prediction process (S20) (S510), and calculates the error value using the difference between the obtained predicted value and the actual value (S520).

[0134] In the Gaussian property learning process (S50), the calculated error value or the slope of the error value is calculated (S530), and the Gaussian property of each candidate kernel is updated using the calculated error value or the slope of the error value (S540).

[0135] As illustrated in FIG. 7, in the Gaussian property learning process (S50), the predicted value (u p By calculating the partial differential equation (PDE) for ) and applying both PDE loss and data loss, each Gaussian property is learned for the physical quantity data and additional sampled prediction locations through the backpropagation process of the loss function, and the Gaussian property can be learned based on a nonlinear optimization technique that can optimize using various algorithms such as ADAM and LBFGS.

[0136] As shown in Fig. 8, it can be seen that the candidate kernel, which has undergone the Gaussian property learning process (S50), enables high resolution of physical quantity data.

[0137] FIG. 9 is a flowchart explaining the Gaussian adjustment process of a method for predicting physical quantities through the disclosed Gaussian distribution learning, FIG. 10 is a diagram visualizing the Gaussian adjustment process of a method for predicting physical quantities through the disclosed Gaussian distribution learning, and FIG. 11 is an example diagram showing the result of applying the Gaussian adjustment process to each disclosed candidate kernel.

[0138] In the Gaussian adjustment process (S60), Gaussian properties including the magnitude, rotation, center position, and physical quantity of the Gaussian distribution for each candidate kernel are obtained (S610).

[0139] First, in the Gaussian adjustment process (S60), an error value and a derivative of the error value are used to determine whether each candidate kernel accurately predicts the corresponding point. First, among the Gaussian properties of each candidate kernel, the error of the center of the Gaussian distribution is the first threshold (τ p If it is greater than ), Gaussian adjustment is performed, and if the error of the center of the Gaussian distribution is less than or equal to the first threshold, Gaussian adjustment is not performed (S620).

[0140] The Gaussian adjustment process (S60) is performed such that the error in the center of the Gaussian distribution of the corresponding candidate kernel is greater than the first threshold, and the magnitude of the Gaussian distribution is greater than the second threshold (τ). s If it is greater than ), the corresponding Gaussian distribution is split (S630, S640), and if the size of the Gaussian distribution is less than or equal to the second threshold, the Gaussian distribution is duplicated (S630, S650).

[0141] The Gaussian adjustment process (S60) stores the Gaussian properties of the new candidate kernel formed by splitting or duplicating in memory (S660). The Gaussian adjustment process (S60) sets the cosine similarity of the Gaussian distribution for the new candidate kernel to a third threshold (τ). m If it is greater than ), the corresponding Gaussian distribution is merged (S670, S671). Meanwhile, in the Gaussian adjustment process (S60), among the Gaussian properties of the new candidate kernel, the magnitude of the Gaussian distribution is the fourth threshold (τ L If it is greater than ), the corresponding candidate kernel is removed (S680, S681). The fourth threshold can be set to have a pre-set valid range so that it can be meaningful data.

[0142] As illustrated in FIG. 11, when a Gaussian adjustment process (S60) is applied to candidate kernels based on a Gaussian distribution for all initially declared prediction locations, it can be seen that the number of candidate kernels (or Gaussian distributions) decreases as Gaussian adjustment is performed, but maintains an appropriate number once it reaches a certain level.

[0143] FIG. 12 is an example diagram showing the prediction results for actual high-resolution data through the disclosed method of predicting physical quantities through Gaussian distribution learning, FIG. 13 is an example diagram showing the results of comparing the training time of the disclosed method of predicting physical quantities through Gaussian distribution learning with existing physical artificial neural network models, and FIG. 14 is an example diagram showing the accuracy according to the training time of the disclosed method of predicting physical quantities through Gaussian distribution learning with existing physical artificial neural network models.

[0144] As illustrated in FIGS. 12 to 14, the disclosed method can rapidly increase the resolution of physical quantity data compared to existing physical artificial neural network models, thereby saving costs and time for high-resolution data measurement in the medical and fluid fields. Above all, it can be seen that the disclosed method can increase the resolution of physical quantity data with a faster learning speed (~10 m) than PINN, physical information operators, and computational fluid dynamics. The disclosed method can help design efficient structures through detailed analysis of flow field data during the design of automobiles and airplanes, and can contribute to cardiovascular diagnosis prediction through detailed analysis of blood flow fields in the medical field.

[0145] Although FIGS. 4, 6, and 9 describe each process as being executed sequentially, this is merely an illustrative explanation of the technical concept of one embodiment of the present invention. In other words, a person skilled in the art to which one embodiment of the present invention belongs can apply various modifications and variations by changing the order described in each figure or executing one or more of the processes in parallel, as long as they do not deviate from the essential characteristics of one embodiment of the present invention. Therefore, FIGS. 4, 6, and 9 are not limited to a chronological order.

[0146] In the following, a method for predicting physical quantities through Gaussian learning according to another embodiment is described.

[0147] FIG. 15 is a flowchart illustrating an overall method for predicting physical quantities through Gaussian learning according to another embodiment. FIG. 16 is a diagram visually representing the method of FIG. 15. To avoid redundant descriptions, they are described together below.

[0148] Referring to FIG. 15, the processor (12) receives flow field data (S1100), predicts an initial Gaussian setting and an initial physical quantity for each point location (S1200), learns Gaussian properties for the predicted physical quantity data and additional sampled locations respectively (S1300), and selects inaccurate candidate kernels or adjusts the Gaussian by cloning, splitting, removing, or merging for each candidate kernel (S1400).

[0149] Referring to FIG. 16, the processor (12), in particular the physical quantity prediction module (122), generates a point sampling and an initial Gaussian map (15) for predicting physical quantities based on flow field data (3, 4, 5). In the initial Gaussian map, the physical quantity prediction module (122) predicts Gaussian distributions for each sampled point (P).

[0150] Meanwhile, the physical quantity prediction module (122) predicts a physical quantity for each sampled point, and rotation (R i Physical quantities can be predicted while fixing the vector value for ). Referring to FIG. 17, the physical quantity prediction module (122) rotates (R i Fix the vector value for ) statically, and other physical quantities, for example, the center (u i ), velocity(v i ), pressure(s i ) can be predicted (dynamic).

[0151] The system (1) initiated through this is the center (u) of each Gaussian candidate kernel. i ), diagonal covariance( ), physical quantity vector v i (e.g.: [v x , v y , v z By training only , p]), the rotation matrix R i (Variables that are difficult to optimize in high dimensions) are completely removed, and the scale h for each axisij Only the diagonal matrix needs to be adjusted. As a result, even in 4D (3 spaces + 1 time), only the diagonal matrix needs to be handled, so the number of parameters is reduced (e.g., 10 → 4, based on 1 Gaussian), and learning can be simplified, stable, and fast.

[0152] Referring again to FIGS. 15 and FIGS. 16, the physical quantity prediction module (122) sets candidate kernels and samples training data for additional physical characteristic learning in the process of predicting physical quantities (S1200).

[0153] Specifically, the physical quantity prediction module (122) sets a candidate kernel based on a Gaussian distribution for calculating the weight of the observed data for one or more points among the points in the input flow field data.

[0154] The physical quantity prediction module (122) determines the size and location of the Gaussian distribution of each candidate kernel, and can specify the candidate kernels using sampling techniques such as random sampling and grid sampling, or techniques utilizing image features of the data. The physical quantity prediction module (122) can use all points included in the flow field data, but may also use only some points.

[0155] The physical quantity prediction module (122) determines the size (or center position) of the Gaussian distribution of each candidate kernel, and while it may use a distance value arbitrarily set by the user, it may also automatically set the distance based on a shortest distance algorithm that calculates the minimum distance.

[0156] The physical quantity prediction module (122) can use physical quantities observed in the set candidate kernels, for example, velocity (u, v) and pressure (p), directly as observation data or calculated through interpolation and used as observation data, and the physical quantity properties of each candidate kernel can use vector values ​​as well as scalar values.

[0157] The physical quantity prediction module (122) can declare multiple prediction locations for points within the flow field data and set candidate kernels through data sampling at the multiple prediction locations. Since the weight of the observed data changes depending on the prediction location, the candidate kernels can be defined as a Gaussian distribution for calculating the weight of the observed data.

[0158] Generally, there is an assumption that physical quantities must satisfy the governing equation at all locations within physical constraints. Therefore, the data physical quantity prediction module (122) samples training data for learning additional physical properties (or characteristics), randomly samples predicted locations within the flow field that are previously unknown by applying the physical quantity assumption governing equation, and allows them to be used additionally for learning physical constraints. The physical quantity prediction module (122) may use any one of various sampling techniques, including grid sampling, random sampling, and loss-weighted sampling.

[0159] The physical quantity prediction module (122) predicts physical quantities based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction location. To increase the stability and accuracy of physical quantity prediction through the Gaussian probability distribution, the physical quantity prediction module (122) may use various normalization methods, such as probability-based normalization techniques, transparency-based multiplication techniques, and multiplication by a constant, and may also adjust the region of interest based on the probability values ​​of the Gaussians calculated through the probability-based normalization technique. At this time, the physical quantity prediction module (122) may also obtain the probability values ​​of the Gaussians multiplied to the physical quantity properties of each candidate kernel by normalization or by multiplying by a constant value.

[0160] The physical quantity prediction module (122) can use a valid range of physical quantities for each candidate kernel specified by the user, and the partial derivative values ​​for calculating the governing equation can include both numerical calculation methods through software and analytical calculation methods through mathematical calculation methods.

[0161] After predicting the initial physical quantity, the processor (100), specifically the Gaussian property learning module (125), learns the Gaussian properties of each candidate kernel.

[0162] During the learning process, the Gaussian property learning module (125) may use a loss-weighted sampling method that considers the physical error of each point. At this time, the Gaussian property of each candidate kernel may include the magnitude, center location, and physical quantity data for the Gaussian distribution of each candidate kernel.

[0163] The disclosed Gaussian property learning module (125) can learn Gaussian properties through two embodiments. According to one embodiment, each Gaussian property learned by the Gaussian property learning module (125) may include a physical quantity, magnitude, rotation, and the position of the center.

[0164] In another embodiment, the Gaussian property learning module (125) can learn Gaussian properties including magnitude, center position, and physical quantity for the Gaussian distribution of each candidate kernel, excluding Gaussian properties for rotation.

[0165] Specifically, the Gaussian property learning module (125) is the center (u) of each candidate kernel. i ), diagonal covariance( ), physical quantity vector v i (e.g.: [v x , v y , v z It can learn only , p]). That is, the Gaussian property learning module (125) is a rotation matrix R i(Variables that are difficult to optimize in high dimensions) are completely removed, and the scale for each axis (h ij Only ) can be adjusted.

[0166] The Gaussian property learning module (125) can also learn the Gaussian properties of each candidate kernel for additional predicted locations sampled from the physical quantity prediction module (122).

[0167] The Gaussian property learning module (125) calculates an error value by considering physical constraints, and the error value used in the learning process can be a mathematically calculated partial derivative value as well as an automatic differentiation engine (orch. autograd) that supports neural network learning. At this time, the Gaussian property learning module (125) performs learning through the backpropagation process of the loss function and can learn based on a non-linear optimization technique that can optimize Gaussian properties using various algorithms such as SGD, RMSProp, ADAM, and LBFGS.

[0168] The Gaussian property learning module (125) may have various governing equations such as the Navier-Stokes equation and the Burgers equation applied as loss functions, and may have loss functions for initial conditions and boundary conditions of flow field data, loss functions for predicted values, etc.

[0169] Once the Gaussian properties have been learned to some extent, the processor (12), i.e., the Gaussian adjustment module (126), can be adjusted to select inaccurate candidate kernels using the error value or the gradient of the error value for an efficient Gaussian distribution within the flow field data. The Gaussian adjustment module (126) can perform Gaussian adjustment through a process of duplication, splitting, removal, or merging for each candidate kernel.

[0170] The Gaussian adjustment module (126) may use an error value and a derivative of the error value to determine whether each candidate kernel accurately predicts the corresponding point, and after storing a threshold for Gaussian adjustment (see FIG. 20) in memory (13), it may perform a process of duplicating or splitting candidate kernels based on the threshold. Additionally, the Gaussian adjustment module (126) may remove or merge unnecessary candidate kernels, and the merging process may include a graph construction method utilizing similarity.

[0171] The Gaussian adjustment module (126) may use the magnitude, transparency, or similarity of the Gaussian distribution of the candidate kernel as a criterion for the system (1) to determine that the candidate kernel is unnecessary for predicting physical quantities.

[0172] The processor (100) selects a candidate kernel that has undergone the replication, splitting, merging, or removal process by the Gaussian adjustment module (126) as the final kernel and applies it to a physical quantity prediction model, and stores the Gaussian distribution and Gaussian properties learned for the kernel (S1500 of FIG. 16).

[0173] After storing the learned Gaussian distribution and Gaussian properties for each kernel, the processor (100) predicts physical quantities for newly input flow field data based on the stored Gaussian distribution and properties (S1600).

[0174] In the inference process (S1600), the processor (100) loads a stored Gaussian distribution and properties (parameters) corresponding to a target point and generates a physical quantity (161) corresponding thereto. Additionally, the processor (100) can output a Gaussian distribution (162) corresponding thereto through an output unit (14).

[0175] Meanwhile, FIG. 16 illustrates a method for predicting physical quantities while keeping the physical quantity for rotation fixed, but it is not necessarily limited to having a fixed rotation value. That is, the disclosed system (1) may use all physical quantities, such as magnitude, rotation, position, and other physical quantities for the Gaussian distribution of each candidate kernel, for learning Gaussian properties, and may also include and use rotation values ​​in the Gaussian adjustment process.

[0176] FIG. 17 is a flowchart for further explaining in detail the operation method of a physical quantity prediction module according to another embodiment.

[0177] The physical quantity prediction module (122) consists of a candidate kernel setting process (S1110), a physical quantity prediction process (S1120), and a data sampling process (S1130).

[0178] In the candidate kernel process (S1110), the physical quantity prediction module (122) sets multiple candidate kernels based on a Gaussian distribution for calculating the weight of the observed data for at least one of the points in the input flow field data (3, 4, 5). That is, the physical quantity prediction module (122) declares multiple prediction locations for the points in the flow field data and sets candidate kernels through data sampling at the multiple prediction locations.

[0179] In the physical quantity prediction process (S1120), the physical quantity prediction module (122) predicts the physical quantity based on the Gaussian properties of each candidate kernel and the probability values ​​of the Gaussians for each prediction location.

[0180] As illustrated in FIG. 5, the physical quantity prediction module (122) can predict physical quantities at four-dimensional points of x, y, z, and t at predicted locations P1, P2, and P3 using a probability-based normalization formula such as the mathematical formula 1 described above, in order to increase the stability and accuracy of the physical quantity prediction through a Gaussian probability distribution.

[0181] As shown in the above-described mathematical formulas 2 and 3, the physical quantity prediction module (122) can obtain partial derivative values ​​for the calculation of the governing equations using an analytical calculation method using mathematical formulas.

[0182] Referring again to FIG. 5, in the data sampling process (113), the physical quantity prediction module (122) applies the physical quantity assumption governing equation to randomly sample candidate kernels for prediction locations within the flow field that are initially not declared, which are unknown in advance, and uses them additionally for learning physical constraints.

[0183] FIG. 18 is a flowchart specifically describing the operation process of a Gaussian property learning module according to another embodiment.

[0184] The Gaussian property learning module (125) obtains the predicted value of the physical quantity predicted by the physical quantity prediction module (122) (S1210) and calculates the error value considering physical constraints (S1220).

[0185] Specifically, the Gaussian property learning module (125) refers to the process of learning the properties of each Gaussian for additional locations sampled from the physical quantity prediction module (122). To this end, the Gaussian property learning module (125) calculates a learning error through the predicted value of the physical quantity and physical constraints. Here, the Gaussian property learning module (125) may use mathematically calculated partial derivative values.

[0186] Referring to FIG. 7, according to one example, the Gaussian property learning module (125) uses flow field data v(x,y,z,t) = [v x , v y , v z ] T It can be expressed as an incompressible Newtonian fluid. Therefore, the following mathematical equations 4 and 5 are used as learning constraints.

[0187]

[0188]

[0189] Here, ρ is the fluid density, v is the kinematic viscosity, p is the pressure, and g is the gravitational term.

[0190] Equation 4 is the momentum conservation equation, indicating that the change in velocity of the flow field is determined by the pressure gradient, viscous diffusion, and gravity, and Equation 5 is the mass conservation equation (continuity equation), and since it is an incompressible fluid, the divergence is zero.

[0191] When an error value is calculated, the Gaussian property learning module (125) calculates the gradient of the error value through backpropagation (123) and updates the Gaussian properties of each candidate kernel (124). At this time, the Gaussian property learning module (125) can learn based on a non-linear optimization technique that can optimize Gaussian properties using various algorithms such as SGD, RMSProp, ADAM, LBFGS.

[0192] Referring again to FIG. 7, the Gaussian property learning module (125) predicts the value (u p By calculating the partial differential equation (PDE) for ) and applying both PDE loss and data loss, each Gaussian property is learned for the physical quantity data and additional sampled prediction positions through the backpropagation process of the loss function.

[0193] Loss L is the data error L data and physical constraints L PDE It is a combination (λ=1.0) and can be defined by the following mathematical formulas 6, 7, and 8.

[0194]

[0195]

[0196]

[0197] Here λ is the PDE residual term derived from Equation 6 and Equation 6, which measures the degree of violation of the Navier-Stokes and continuity equations. The value of λ can be adjusted between 0 and 1. If the value of λ is 0, learning proceeds using only the first error value (data loss), and if the value of λ is greater than 0, learning proceeds using both physical quantities and data values. If the value of λ is set to 0, learning can also proceed using only data loss. ω is a binary vector that masks pressure terms that are not directly measured by a device collecting flow field data (e.g., MRI).

[0198] The disclosed Gaussian property learning module (125) is a physical quantity v of each Gaussian. i This is trained to satisfy this equation, and simultaneously enforces fluid dynamic consistency with data fit. Unlike conventional PINN, the Gaussian property learning module (125) expresses the velocity field in an explicit Gaussian form, so the derivatives of the PDE terms (∂ / ∂x, ∂ / ∂t, etc.) can be calculated analytically without automatic differentiation. This significantly reduces the computational complexity of the Navier-Stokes residual calculation, thereby greatly improving the training speed compared to PINN. In addition, it can be confirmed from the output result (see FIG. 8) that the Gaussian distribution and physical quantity data for the candidate kernels that have undergone the disclosed Gaussian property learning process (S1340) can be made high resolution.

[0199] Meanwhile, the disclosed Gaussian property learning module (125) can update the Gaussian properties of the Gaussian distribution of each candidate kernel by 1) including magnitude, center position, rotation and physical quantity (S1250), and 2) including magnitude, center position and physical quantity (S1260).

[0200] That is, the disclosed Gaussian property learning module (125) may perform Gaussian property learning by excluding rotation values ​​while fixing the rotation axis (e.g., Euclidean) according to the user's choice, or may learn Gaussian properties by including rotation values.

[0201] The Gaussian property learning module (125) estimates the accuracy of the Gaussian properties (magnitude, rotation, physical quantity, position) of each candidate kernel (S1270). The accuracy estimated in this way can then be used as the error value of the Gaussian adjustment module (126).

[0202] FIG. 19 is a flowchart specifically describing the operation process of a Gaussian adjustment module according to another embodiment.

[0203] Referring to FIG. 19, the Gaussian adjustment module (126) obtains Gaussian properties including the magnitude, center position, and physical quantity (or rotation) of the Gaussian distribution for each candidate kernel (S1310).

[0204] Specifically, the Gaussian adjustment module (126) uses an error value and a derivative of the error value to determine whether each candidate kernel accurately predicts the corresponding point. First, among the Gaussian properties of each candidate kernel, the total error of the Gaussian distribution is a first threshold (τ). P If it is greater than ), Gaussian adjustment is performed, and the total error of the Gaussian distribution is the first threshold (τ P If ) or less, Gaussian adjustment is not performed (S1330).

[0205] Here, the total error of each candidate kernel is calculated as a weighted sum of an error value (hereinafter referred to as the first error value) calculated using the difference between the predicted physical quantity and the actual value, and an error value (second error value) calculated considering physical constraints. In addition, the first threshold (τ P ) is calculated based on one of the multiple statistical values ​​(average or median) of the total errors of each candidate kernel.

[0206] The Gaussian adjustment module (126) determines that the total error of the Gaussian distribution of the corresponding candidate kernel is a first threshold (τ). P While being greater than ), the magnitude of the Gaussian distribution is the second critical value (τ S If it is greater than ), the corresponding Gaussian distribution is partitioned (S1340), and the magnitude of the Gaussian distribution is the second threshold (τ S If ) or less, replicate the Gaussian distribution (S1350).

[0207] The Gaussian adjustment module (126) stores the Gaussian properties of the new candidate kernel formed by splitting or duplicating in memory (S1360).

[0208] The Gaussian adjustment module (126) has a Gaussian distribution similarity to a new candidate kernel at a third threshold (τ m If greater than ), merge the corresponding Gaussian distributions (S1370, S1390).

[0209] There may be various methods for merging Gaussian distributions. The disclosed Gaussian adjustment module (126) has a similarity of each Gaussian distribution at a third threshold (τ). m For Gaussian distributions greater than ), they can be connected within the graph, and the connected Gaussian distributions can be merged into a single Gaussian distribution.

[0210] Referring to FIG. 10, a Gaussian adjustment module (126) according to one example can calculate the similarity between each Gaussian distribution (G(x)1, G(x)2) and the predicted values ​​of physical quantities (P1, P2) corresponding thereto. For example, based on the compared similarity, the Gaussian adjustment module (126) can generate each physical quantity in the form of a matrix, and as shown in FIG. 11, among the matrix values ​​other than the diagonal of the matrix, a third threshold (τ) m A Gaussian distribution (G1, ..., G) containing values ​​(B) greater than or equal to ) n ) can be selected. The Gaussian adjustment module (126) selects the selected Gaussian distribution (G1, ..., G nYou can connect the graphs of ) and merge the connected Gaussian distributions into a single Gaussian.

[0211] Meanwhile, the Gaussian adjustment module (126) has a Gaussian distribution magnitude among the Gaussian properties of the new candidate kernel that is a fourth threshold (τ). L If it is greater than ), the corresponding candidate kernel is removed (S1380, S1400). The fourth threshold can be set to have a pre-set valid range so that it can be meaningful data.

[0212] FIG. 20 is a diagram illustrating the effect of the disclosed method for predicting physical quantities using a Gaussian distribution, and FIG. 21 is the result of experimentally verifying the necessity of each component.

[0213] Figure 20 shows a side-by-side comparison of the prediction results of the conventional PINN, Siren, and PIG and the disclosed invention in three 2D flow fields (Lid-driven cavity, Y-shaped channel, L-shaped channel) with the Ground Truth (actual CFD results) and absolute error map. As the color becomes lighter, it indicates an area with a larger error, and the color scale was clipped to the mean error based on PINN for visual comparison.

[0214] As can be seen in FIG. 20, the error map of the disclosed system (1) is generally dark (low error) and shows that the shape is well restored even near complex vortices or branches. In conventional PINN or Siren, errors are concentrated near the boundary layer and an over-smoothing phenomenon occurs. This visually demonstrates that the combination of Normalized Gaussian Splatting + Axes Alignment of the disclosed system (1) enables stable and detailed flow reproduction.

[0215] Referring to FIG. 21, it can be seen that the disclosed invention (PINGS-X) converges normally with Lid-driven, Y-shaped, and L-shaped, and has higher accuracy compared to the prior art. In addition, the disclosed system (1) applies normalization, Axes Alignment, and Merging techniques to achieve guaranteed convergence, verification of theoretical stability, reduced training time, and memory efficiency. Furthermore, the disclosed system (1) reduces training time by 3 to 4 hours compared to the prior art, and reduces GPU memory amplification and training instability.

[0216] Meanwhile, the operation processes of the disclosed system (1) can be implemented as computer-readable code on a computer-readable recording medium. A computer-readable recording medium includes all types of recording devices in which data that can be read by a computer system is stored. That is, a computer-readable recording medium includes storage media such as magnetic storage media (e.g., ROM, floppy disk, hard disk, etc.) and optical reading media (e.g., CD-ROM, DVD, etc.). In addition, the computer-readable recording medium can be distributed across networked computer systems, and computer-readable code can be stored and executed in a distributed manner.

Claims

1. A method for predicting a physical quantity through Gaussian distribution learning, performed by a system comprising at least one processor, wherein A candidate kernel setting process for declaring multiple predicted locations for points within input flow field data and setting multiple candidate kernels based on a Gaussian distribution through data sampling from the multiple predicted locations; A physical quantity prediction process that predicts physical quantities based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel for each prediction location; A Gaussian property learning process for learning Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel; A Gaussian adjustment process for selecting whether each candidate kernel accurately predicts physical quantities for the point to which it belongs by adjusting the Gaussian properties and number of Gaussian distributions of each candidate kernel based on error values ​​calculated considering physical constraints; and A kernel application process that selects a Gaussian-tuned candidate kernel as the final kernel through the above Gaussian tuning process, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel; A method that includes 2. In Paragraph 1, A method comprising, prior to the above-mentioned Gaussian property learning process, a data sampling process that provides additional candidate kernels by applying a governing equation for physical quantity assumptions and sampling data at prediction locations other than those declared in the above-mentioned candidate kernel setting process.

3. In Paragraph 2, The above data sampling module is, A method of using any one of a plurality of sampling techniques including grid sampling, random sampling, and loss-weighted sampling.

4. In Paragraph 2, The above Gaussian property learning process is, A method of obtaining the above additional candidate kernels and learning the Gaussian properties of the Gaussian distribution of the obtained additional candidate kernels.

5. In Paragraph 1, The above candidate kernel configuration process is, A method for determining the magnitude, rotation, and position of a Gaussian distribution of multiple candidate kernels.

6. In Paragraph 1, The above candidate kernel configuration process is, A method for determining the magnitude or rotation of a Gaussian distribution of each candidate kernel using either of the distances set based on a shortest distance algorithm that calculates a distance or minimum distance set by user input.

7. In Paragraph 1, The above physical quantity prediction module is, A method for calculating Gaussian probability values ​​using any one of a probability-based normalization technique based on a Gaussian probability distribution, a transparency-based multiplication technique, and a normalization technique that multiplies by a constant value.

8. In Paragraph 1, The above Gaussian property learning module is, A method of learning by applying a loss-weighted sampling technique that considers the physical error of the candidate kernel at each prediction position.

9. In Paragraph 1, The above Gaussian property learning process is, A method of learning the Gaussian properties of the Gaussian distribution of each candidate kernel through the backpropagation process of the loss function.

10. In Paragraph 9, The above Gaussian property learning process is, A method of learning the above Gaussian properties based on a non-linear optimization technique that optimizes the properties using any one of a plurality of algorithms including ADAM and LBFGS.

11. In Paragraph 1, The above Gaussian adjustment process is, A method for Gaussian adjustment that stores a preset threshold for Gaussian adjustment and performs Gaussian adjustment through the process of replication, splitting, removal, or merging of the Gaussian distribution for each candidate kernel based on the stored threshold.

12. In Paragraph 11, The above Gaussian adjustment process is, Among the Gaussian properties of each candidate kernel, the error of the center of the Gaussian distribution is the first threshold (τ p A method in which Gaussian adjustment is performed if the error in the center of the Gaussian distribution is greater than ), and Gaussian adjustment is not performed if the error is less than or equal to the first threshold.

13. In Paragraph 12, The above Gaussian adjustment process is, If the error in the center of the Gaussian distribution of the above candidate kernel is greater than the first threshold, the magnitude of the Gaussian distribution of the said candidate kernel is greater than the second threshold (τ s A method in which the Gaussian distribution is split if the size is greater than ) and the Gaussian distribution is duplicated if the size of the Gaussian distribution is less than or equal to a second threshold.

14. In Paragraph 13, The above Gaussian adjustment process is, The cosine similarity of the Gaussian distribution of the new candidate kernel, after the splitting or replication of the Gaussian distribution of the above candidate kernel is completed, is the third threshold (τ m A method that merges the corresponding Gaussian distributions if it is greater than ).

15. In Paragraph 13, The above Gaussian adjustment process is, The size of the Gaussian distribution of the new candidate kernel, after the splitting or replication of the Gaussian distribution of the above candidate kernel is completed, is the fourth threshold (τ L A method of removing the corresponding candidate kernel if it is greater than ).

16. As a system for predicting physical quantities through Gaussian distribution learning, Memory for storing a physical quantity prediction model with a kernel based on a Gaussian distribution; A processor that trains the above-mentioned physical quantity prediction model and predicts the physical quantity of the flow field for each point of the input flow field data through the trained physical quantity prediction model; The above processor is, Declare multiple prediction locations for points within the input flow field data, and set multiple candidate kernels based on a Gaussian distribution through data sampling from the multiple prediction locations, Predict physical quantities based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel for each predicted location, and Learn Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel, and Based on error values ​​calculated considering physical constraints, the Gaussian properties and number of Gaussian distributions of each candidate kernel are adjusted to determine whether each candidate kernel accurately predicts physical quantities for the point to which it belongs, and A system that selects a Gaussian-tuned candidate kernel as the final kernel through the above Gaussian tuning process, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

17. A computer program stored on a computer-readable storage medium, wherein the computer program, when executed on one or more processors, performs operations to predict a physical quantity through learning a Gaussian distribution, and The above operations are, Candidate kernel setting operation for declaring multiple prediction locations for points within input flow field data and setting multiple candidate kernels based on a Gaussian distribution through data sampling at the multiple prediction locations; Physical quantity prediction operation that predicts physical quantities based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel for each prediction location; A Gaussian property learning operation that learns Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel; A Gaussian adjustment operation that selects whether each candidate kernel accurately predicts physical quantities for the point to which it belongs by adjusting the Gaussian properties and number of Gaussian distributions of each candidate kernel based on error values ​​calculated considering physical constraints; and A computer program comprising: a kernel application operation that selects a Gaussian-tuned candidate kernel through the above Gaussian tuning process as the final kernel, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

18. A data receiving unit that receives fluid field data; A processor that predicts physical quantities based on received flow field data and learns and adjusts Gaussian properties for each point; and The above processor includes an output unit that predicts physical quantities for new flow field data based on the learned results; The above processor is, A physical quantity prediction module that declares multiple prediction locations for points within input flow field data, sets multiple candidate kernels based on a Gaussian distribution through data sampling at the multiple prediction locations, and predicts physical quantities based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel for each prediction location; A Gaussian property learning module that learns Gaussian properties including magnitude, center location, and physical quantities for the Gaussian distribution of each candidate kernel, excluding rotational properties; and A Gaussian adjustment module that selects whether each candidate kernel accurately predicts physical quantities for the point to which it belongs by adjusting the Gaussian properties and number of Gaussian distributions of each candidate kernel based on error values ​​calculated considering physical constraints; A user terminal that selects a Gaussian-tuned candidate kernel through the above Gaussian tuning process as the final kernel, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel.

19. In Paragraph 18, The above physical quantity prediction module is, A user terminal that provides additional candidate kernels through data sampling at prediction locations other than the prediction locations declared in the candidate kernel setting process prior to the above Gaussian property learning process.

20. In Paragraph 19, The above physical quantity prediction module is, A user terminal using any one of a plurality of sampling techniques including grid sampling, random sampling, and loss-weighted sampling.

21. In Paragraph 19, The above Gaussian property learning module is, A user terminal that acquires the above additional candidate kernels and learns the Gaussian properties of the Gaussian distribution of the acquired additional candidate kernels.

22. In Paragraph 18, The above physical quantity prediction module is, Fix the rotation axis, A user terminal determining the size and location of a Gaussian distribution of multiple candidate kernels.

23. In Paragraph 18, The above physical quantity prediction module is, A user terminal that determines the size of the Gaussian distribution of each candidate kernel using either of the distances set based on a shortest distance algorithm that calculates the distance or minimum distance set by user input.

24. In Paragraph 18, The above physical quantity prediction module is, A user terminal that calculates a Gaussian probability value using any one of a probability-based normalization technique based on a Gaussian probability distribution, a transparency-based multiplication technique, and a normalization technique that multiplies by a constant value.

25. In Paragraph 18, The above Gaussian property learning module is, A user terminal trained by applying a loss-weighted sampling technique that considers the physical error of candidate kernels at each prediction location.

26. In Paragraph 18, The above Gaussian property learning module is, A user terminal that learns the Gaussian properties of the Gaussian distribution of each candidate kernel through the backpropagation process of the loss function.

27. In Paragraph 26, The above Gaussian property learning module is, A user terminal that learns based on a non-linear optimization technique that optimizes the above Gaussian properties using any one of a plurality of algorithms including SGD, RMSProp, ADAM, and LBFGS.

28. In Paragraph 18, The above Gaussian adjustment module is, Calculate the total error value of a Gaussian distribution formed by the weighted sum of a first error value based on the difference between the predicted physical quantity and the actual value and a second error value based on the physical constraints, and A user terminal that performs Gaussian adjustment if the total error value among the Gaussian properties of each candidate kernel is greater than a first threshold, and does not perform Gaussian adjustment if the total error value of the Gaussian distribution is less than or equal to the first threshold.

29. In Paragraph 28, The above Gaussian adjustment module is, If the above total error value is greater than the above first threshold and the magnitude of the Gaussian distribution of the corresponding candidate kernel is greater than the second threshold, the corresponding Gaussian distribution is partitioned, and A user terminal that replicates the Gaussian distribution if the magnitude of the above Gaussian distribution is less than or equal to a second threshold.

30. In Paragraph 29, The above Gaussian adjustment module is, If the similarity of the Gaussian distribution of the new candidate kernel, after the splitting or replication of the Gaussian distribution of the above candidate kernel is completed, is greater than the third threshold, the above Gaussian distribution is connected within the graph, and A method of merging the above-mentioned connected Gaussian distributions.

31. In Paragraph 30, The above Gaussian adjustment module is, A method in which the Gaussian distribution of a new candidate kernel, after the splitting or replication of the Gaussian distribution of the above candidate kernel is completed, is removed if the size of the Gaussian distribution of the new candidate kernel is greater than a fourth threshold.

32. Data receiving unit for receiving fluid field data; A processor that predicts physical quantities based on received flow field data and learns and adjusts Gaussian properties for each point; and The above processor includes an output unit that predicts physical quantities for new flow field data based on the learned results; The above processor is, For points within the input flow field data, multiple prediction locations are declared, multiple candidate kernels based on a Gaussian distribution are set through data sampling from the multiple prediction locations, and for each prediction location, physical quantities are predicted based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel. Learn Gaussian properties including magnitude, rotation, center position, and physical quantities for the Gaussian distribution of each candidate kernel, and A system for calculating a total error value of a Gaussian distribution formed by a weighted sum of a first error value based on the difference between a predicted physical quantity and an actual value and a second error value based on the physical constraints, and for performing Gaussian adjustment if the total error value is greater than a first threshold among the Gaussian properties of each candidate kernel.

33. In Paragraph 32, The above processor is, The above total error value is greater than the above first threshold, and the magnitude of the Gaussian distribution of the corresponding candidate kernel is the second threshold (τ s If it is greater than ), partition the corresponding Gaussian distribution, and A system that replicates a Gaussian distribution when the magnitude of the above Gaussian distribution is less than or equal to a second threshold.

34. In Paragraph 33, The above processor is, The similarity of the Gaussian distribution of the new candidate kernel, after the partitioning or replication of the Gaussian distribution of the above candidate kernel is completed, is the third threshold (τ m If it is greater than ), connect the above Gaussian distribution within the graph, and A system for merging the above-mentioned connected Gaussian distributions.

35. In Paragraph 34, The above processor is, The size of the Gaussian distribution of the new candidate kernel, after the splitting or replication of the Gaussian distribution of the above candidate kernel is completed, is the fourth threshold (τ L A system that removes the corresponding candidate kernel if it is greater than ).

36. A computer program stored on a computer-readable storage medium, wherein the computer program, when executed on one or more processors, performs operations to predict physical quantities through Gaussian learning, and The above operations are, Candidate kernel setting operation for declaring multiple prediction locations for points within input flow field data and setting multiple candidate kernels based on a Gaussian distribution through data sampling at the multiple prediction locations; Physical quantity prediction operation that predicts physical quantities based on the Gaussian properties and Gaussian probability values ​​of each candidate kernel for each prediction location; Excluding the rotation matrix, a Gaussian property learning operation that learns Gaussian properties including magnitude, center position, and physical quantities for the Gaussian distribution of each candidate kernel; A Gaussian adjustment operation that selects whether each candidate kernel accurately predicts physical quantities for the point to which it belongs by adjusting the Gaussian properties and number of Gaussian distributions of each candidate kernel based on error values ​​calculated considering physical constraints; and A kernel application operation that selects a Gaussian-tuned candidate kernel through the above Gaussian tuning process as the final kernel, and stores the Gaussian distribution and Gaussian properties learned for the selected kernel; A computer program that includes

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