A physical constraint runoff prediction method based on multi-scale smooth gating

Abstract

The application discloses a physical constraint runoff prediction method based on a multi-scale smooth gate, first constructs a runoff prediction model based on an Inception parallel architecture and a GELU-GLU multi-scale time convolution network, then constructs a model loss function, and finally inputs real-time runoff time series data into the runoff prediction model to complete runoff prediction. The method introduces an Inception type multi-branch parallel time series convolution structure, realizes synchronous modeling of different time scale hydrological characteristics, and designs a GELU-GLU asymmetric gate unit through a smooth nonlinear mapping and an adaptive feature screening mechanism, effectively suppresses high-frequency noise interference in a non-stationary hydrological sequence, enhances the prediction stability and generalization ability of the model in complex scenes such as the alternation of dry seasons and wet seasons, and introduces a global non-negative physical constraint mechanism at the network output end, so that the model prediction result strictly meets the hydrological physical boundary condition, and the reliability and engineering applicability of the model in actual hydrological prediction and water management application are improved.

Description

Technical Field

[0001] This invention belongs to the field of hydrological prediction technology, specifically relating to a physical constraint runoff prediction method based on multi-scale smooth gating. Background Technology

[0002] With the intensification of climate change and the increasing impact of human activities, watershed hydrological processes are exhibiting significant nonlinearity, nonstationarity, and multi-scale coupling characteristics. The frequency and intensity of events such as extreme rainfall, sudden floods, and snowmelt runoff are continuously rising, placing higher demands on flood control early warning, water resource allocation, and refined watershed management. Against this backdrop, existing hydrological models based on experience or simplified physical assumptions are gradually revealing their insufficient adaptability in high spatiotemporal resolution prediction and real-time applications, driving the rapid development of data-driven hydrological prediction technologies, represented by deep learning. These methods, with their powerful nonlinear mapping capabilities, have demonstrated excellent predictive potential in modeling complex rainfall-runoff relationships and have become an important direction in current intelligent hydrological prediction research.

[0003] Existing hydrological forecasting methods, especially deep learning models based on convolutional neural networks and sequence modeling structures, have made significant progress in characterizing the complex nonlinear relationship between rainfall input and runoff response. However, most of these models rely on pure data fitting mechanisms and lack explicit physical constraints, which may cause the prediction results to violate basic hydrological physical laws such as mass conservation in some scenarios, limiting the reliability and interpretability of the models. Furthermore, existing convolutional structures typically employ a single, fixed-scale kernel design, making it difficult to effectively represent both sudden flood peak responses caused by short-duration heavy rainfall and slowly varying processes such as long-term snowmelt and groundwater recharge at the same feature level. In addition, commonly used activation functions have a uniform nonlinear mapping form in signal response, lacking the ability to adaptively distinguish between weak hydrological signals and random noise. This can easily introduce accumulated errors in high-noise, highly non-stationary hydrological time series, thus affecting the model's generalization performance.

[0004] In summary, existing hydrological forecasting technologies still have significant shortcomings in terms of physical consistency, multi-scale feature representation capabilities, and noise robustness, making it difficult to simultaneously meet the application requirements of high-precision prediction and physical interpretability. Therefore, there is an urgent need to propose a novel hydrological forecasting method that integrates physical constraint mechanisms, multi-scale feature extraction structures, and adaptive nonlinear mapping capabilities. This would improve the model's stability, generalization ability, and physical reliability under complex hydrological scenarios, thereby providing more reliable technical support for watershed flood early warning and refined water resource management. Summary of the Invention

[0005] To address the aforementioned technical problems, this invention provides a physical constraint runoff prediction method based on multi-scale smooth gating, which avoids non-physical prediction phenomena that may occur in purely data-driven methods, thereby improving the reliability and engineering applicability of the model in practical hydrological forecasting and water management applications.

[0006] The technical solution adopted in this invention is: a physical constraint runoff prediction method based on multi-scale smoothing gating, the specific steps of which are as follows:

[0007] S1. Construct a runoff prediction model based on the Inception parallel architecture and the GELU-GLU multi-scale temporal convolutional network;

[0008] The runoff prediction model includes: one TCN residual module, one ReLU global nonnegative constraint layer, and one linear projection layer.

[0009] The TCN residual module includes a multi-scale feature extraction module and an adaptive residual constraint module. The multi-scale feature extraction module is the Inception-GELU-GLU module.

[0010] (1) The multi-scale feature extraction module includes three convolutional branches based on the Inception parallel topology architecture, which correspond to different convolutional kernel sizes K, namely K1, K2 and K3, and are used to extract runoff features at short, medium and long time scales simultaneously.

[0011] Among them, the one-dimensional dilatational convolution with kernel size K1 has a small receptive field and is used to capture the characteristics of sudden floods caused by instantaneous rainfall. The one-dimensional dilatational convolution with kernel size K2 has a moderate receptive field and is used to extract the mid-term lag characteristics during the soil saturation runoff process. The one-dimensional dilatational convolution with kernel size K3 has the largest receptive field and is used to summarize the long-term evolution trend of snowmelt runoff and groundwater baseflow.

[0012] Each of the convolutional branches independently embeds an improved gated convolutional unit, namely the smooth nonlinear gated unit GELU-GLU. This unit performs nonlinear feature filtering through a dual-gate mechanism including the GELU activation function and a Dropout layer. The outputs of the three convolutional branches are ultimately concatenated and fused along the channel dimension. The fusion expression is as follows:

[0013] ;

[0014] in, Indicates the characteristics after fusion. This represents the output of convolution kernel K1. This represents the output of convolution kernel K2. This represents the output of convolution kernel K3. Indicates dimension.

[0015] (2) The adaptive residual constraint module is configured with a channel dimension matching detection mechanism. When the dimensions of the input features and the output features are inconsistent, linear projection alignment is performed through 1*1 convolution to construct residual connections of identity mapping or projection mapping.

[0016] S2. Based on step S1, construct the loss function of the runoff prediction model, that is, the target loss function of physical-data coupling;

[0017] To construct a hybrid loss function based on the Lagrange multiplier method, the physical constraints of water balance are first defined, i.e., the physical residuals are defined according to the law of conservation of watershed mass. The expression is as follows:

[0018] ;

[0019] in, Indicates rainfall. Indicates snow melting. Indicates the predicted runoff volume. This indicates the amount of evaporation. Indicates water storage capacity.

[0020] Then, by mixing and optimizing the loss function, the total loss function of the runoff prediction model is obtained. The expression is defined as follows:

[0021] ;

[0022] Where MSE represents the data-driven mean squared error. Indicates the actual runoff volume. This represents the physical constraint weight coefficient.

[0023] S3. Input the real-time runoff time series data into the runoff prediction model based on the Inception parallel architecture and GELU-GLU multi-scale temporal convolutional network to complete the runoff prediction;

[0024] Real-time runoff time series data, i.e., tensors After being input into the TCN residual module, the data stream is copied and split into two paths, entering the multi-scale feature extraction module and the adaptive residual constraint module respectively. The fused output of the multi-scale feature extraction module and the output of the adaptive residual constraint module are added element-wise, and finally processed by the ReLU global non-negative constraint layer and the linear projection layer to output a runoff prediction value that conforms to physical laws.

[0025] Furthermore, step S3 is specifically as follows:

[0026] S31, Real-time runoff time series data input multi-scale feature extraction module;

[0027] Will The data is input into the three convolutional branches of the multi-scale feature extraction module, which are based on the Inception parallel topology architecture. The data flows sequentially through the GELU-GLU in each of the convolutional branches, performing layer-by-layer abstraction and refinement of features.

[0028] After the data enters the multi-scale feature extraction module, it is first distributed in parallel to three independent convolutional branches. The specific process of the data within each branch is as follows:

[0029] 1) Within any convolutional branch, the input data is divided into two paths: the content stream of path a and the gated stream of path b.

[0030] First, a dual-path convolution mapping is performed to convert the input of the branch into a single path. Content streams are generated through two independent one-dimensional convolutional layers. and gated flow The expression is as follows:

[0031] ;

[0032] ;

[0033] in, Indicates the expansion rate Convolution operation, , Indicates the corresponding weight. , This indicates the corresponding bias.

[0034] Then perform causal pruning. and Slice the output to remove excess material at the end. The data for each time step is expressed as follows:

[0035] ;

[0036] in, Indicates the expansion rate. This indicates the kernel size of the convolution branch, and .

[0037] Then perform smooth content activation, that is, for the content stream Apply the Gaussian error linear unit (GELU) activation function, as shown in the following expression:

[0038] ;

[0039] ;

[0040] in, The cumulative distribution function represents the standard normal distribution. Represents the Gaussian error function. Indicates content characteristics, It represents the independent variable.

[0041] Finally, noise suppression gating is performed on the gated flow. Applying the Sigmoid activation function strictly limits the output to the interval (0, 1). When the input contains observation noise or irrelevant perturbations, the gate value tends to 0, as shown in the following expression:

[0042] ;

[0043] Where B represents the gating coefficient, This represents the Sigmoid activation function.

[0044] 2) Perform gating filtering to obtain the output of the current convolutional branch;

[0045] The content feature tensor A of path a is multiplied element-wise with the gating coefficient tensor B of path b, and Dropout is introduced into path a to complete feature filtering at the current scale, thus obtaining the final output of the current convolutional branch. The expression is as follows:

[0046] ;

[0047] in, .

[0048] Finally, multi-scale feature fusion is performed. The output tensors from the three convolutional branches are converged to the concatenation layer, and a lossless concatenation along the channel dimension is achieved through a Concat operation with dim=1, forming a comprehensive feature tensor containing short, medium, and long-scale information. .

[0049] S32. Real-time runoff time series data is input into the adaptive residual constraint module for aggregation and correction;

[0050] The original input data in parallel with step S31 The input adaptive residual constraint module performs adaptive matching after traversing the residual path, i.e., it judges the input data. Whether the number of channels is consistent with the number of channels of the output tensor of the multi-scale feature extraction module.

[0051] If the data matches, it is directly transmitted as is through an identity mapping. If the data does not match, it is linearly projected onto the original physical features through a 1*1 convolutional layer to adjust its channel dimensions to match the output tensor of the multi-scale feature extraction module.

[0052] S33. Based on steps S31 and S32, the comprehensive feature tensor output in step S31 is added element by element to the residual path data to achieve lossless gradient flow and retention of historical information.

[0053] By introducing residual connections, the features fused from the multi-scale feature extraction module are integrated. Input with adaptive residual constraint module Perform element-wise addition, apply the ReLU activation function to the sum, and denote the output as... The expression is as follows:

[0054] ;

[0055] in, This represents the residual join processing function.

[0056] Then aggregate the data Force the input of the ReLU global nonnegative constraint layer and truncate all negative values ​​to 0.

[0057] S34. The model loss function constructed based on step S2 By utilizing adaptive residual constraints and multi-scale parallel paths, gradients are accurately backpropagated, driving the model to collaboratively optimize gating parameters at each scale while adhering to physical laws.

[0058] S35. Based on steps S31-S34, the output feature tensor of the ReLU global non-negativity constraint layer is input into the linear projection layer to map the high-dimensional feature space back to the target runoff numerical space, completing the linear projection result prediction and generating the final runoff prediction value. .

[0059] The beneficial effects of this invention are as follows: The method of this invention first constructs a runoff prediction model based on the Inception parallel architecture and a GELU-GLU multi-scale temporal convolutional network, then constructs the model loss function, and finally inputs real-time runoff time-series data into the runoff prediction model to complete runoff prediction. This invention, by introducing an Inception-style multi-branch parallel temporal convolutional structure, achieves simultaneous modeling of hydrological features at different time scales without significantly increasing network depth and computational complexity. It breaks through the existing TCN modeling method that relies on stacking single-scale convolutional kernels layer by layer. By using differentiated convolutional kernels within the same layer, it achieves parallel extraction of features at multiple time scales, enhancing the model's ability to express the multi-scale dynamic features of complex hydrological processes. It can effectively characterize the rapid response process of rainstorm peaks and the gradual evolution of the receding stage, significantly reducing the temporal phase deviation of runoff prediction; and the design... The GELU-GLU asymmetric gated unit effectively suppresses high-frequency noise interference in non-stationary hydrological sequences through smooth nonlinear mapping and adaptive feature selection mechanisms, enhancing the model's prediction stability and generalization ability under complex scenarios such as alternating dry and wet seasons. Furthermore, a global non-negative physical constraint mechanism is introduced at the network output to ensure that the model's prediction results strictly meet the hydrological physical boundary conditions, achieving an organic integration of data-driven modeling and physical consistency constraints. This avoids non-physical prediction phenomena that may occur with purely data-driven methods, improving the reliability and engineering applicability of the model in practical hydrological forecasting and water management applications. Attached Figure Description

[0060] Figure 1 This is a flowchart of a physical constraint runoff prediction method based on multi-scale smooth gating according to the present invention.

[0061] Figure 2 This is a structural diagram of the multi-scale feature extraction module (Inception-GELU-GLU module) in an embodiment of the present invention.

[0062] Figure 3 This is a structural diagram of GELU-GLU in an embodiment of the present invention.

[0063] Figure 4 This is a runoff prediction diagram of the TCN model in an embodiment of the present invention.

[0064] Figure 5 This is a runoff prediction diagram of a single-layer GELU-GLU-TCN model in an embodiment of the present invention.

[0065] Figure 6 This is a runoff prediction diagram of the 3-layer GELU-GLU-TCN model in an embodiment of the present invention. Detailed Implementation

[0066] The method of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0067] like Figure 1 The flowchart of a physical constraint runoff prediction method based on multi-scale smoothing gating of the present invention is shown below. The specific steps are as follows:

[0068] S1. Construct a runoff prediction model based on the Inception parallel architecture and the GELU-GLU multi-scale temporal convolutional network;

[0069] This embodiment aims to establish a temporal feature extraction framework that combines multi-scale perception capabilities, dynamic gating mechanisms, and cross-scale consistent reconstruction, in order to overcome the significant shortcomings of Temporal Convolutional Networks (TCNs) in capturing non-stationary hydrological signals and under cross-timescale dependent structure conditions.

[0070] The runoff prediction model includes: one TCN residual module, one ReLU global nonnegative constraint layer, and one linear projection layer.

[0071] The TCN residual module includes a multi-scale feature extraction module and an adaptive residual constraint module (residual path module). The multi-scale feature extraction module is the Inception-GELU-GLU module.

[0072] (1) such as Figure 2 As shown, the multi-scale feature extraction module includes three convolutional branches based on the Inception parallel topology architecture (abandoning the single convolutional layer design in the standard TCN module and constructing an Inception-style parallel architecture), which correspond to different convolutional kernel sizes K, namely K1, K2, and K3, respectively, to simultaneously extract runoff features at short, medium, and long time scales and capture temporal dependencies in various situations.

[0073] In this embodiment, a one-dimensional dilatational convolution with a kernel size of K1=3 is used, which has a small receptive field and is specifically designed to capture the characteristics of sudden floods caused by instantaneous rainfall. A one-dimensional dilatational convolution with a kernel size of K2=5 is used, which has a moderate receptive field and is used to extract the mid-term lag characteristics during the soil saturation runoff process. A one-dimensional dilatational convolution with a kernel size of K3=7 is used, which has the largest receptive field and is used to summarize the long-term evolution trends of snowmelt runoff and groundwater baseflow.

[0074] like Figure 3As shown, each of the convolutional branches independently embeds an improved gated convolutional unit, namely the smooth nonlinear gated unit GELU-GLU (using GELU-GLU to replace the dilated convolution + ReLU structure in TCN). This unit performs nonlinear feature filtering through a dual-gate mechanism including the GELU activation function and a Dropout layer, and the outputs of the three convolutional branches are finally concatenated and fused along the channel dimension. The fusion expression is as follows:

[0075] ;

[0076] in, Indicates the characteristics after fusion. This represents the output of convolution kernel K1. This represents the output of convolution kernel K2. This represents the output of convolution kernel K3. Indicates dimension.

[0077] The multi-scale feature extraction module breaks through the limitations of the existing single receptive field. It uses parallel collaboration from multiple granular perspectives to simultaneously capture instantaneous flood peak mutations (high frequency) and long-term baseflow trends (low frequency). Combined with GELU's smooth nonlinearity and gating screening mechanism, it effectively enhances the model's ability to fit random fluctuations in non-stationary runoff data and its noise robustness.

[0078] (2) The adaptive residual constraint module is configured with a channel dimension matching detection mechanism, which is used to perform linear projection alignment through 1*1 convolution when the dimensions of the input features and the output features are inconsistent, so as to construct residual connections of identity mapping or projection mapping;

[0079] Adaptive residual constraints construct a physics-guided deep learning architecture. This architecture ensures stable gradient propagation in deep networks through adaptive residual paths and completely eliminates the "negative runoff" phenomenon that violates physical principles from the bottom layer of the algorithm through hard physical boundary constraints at the end. This significantly guarantees the physical reliability of the model in practical water conservancy engineering applications.

[0080] S2. Based on step S1, construct the loss function of the runoff prediction model, that is, the target loss function of physical-data coupling;

[0081] To ensure that the prediction results conform to basic hydrological principles, a hybrid loss function based on the Lagrange multiplier method is constructed. First, physical constraints on water balance are defined, i.e., physical residuals are defined according to the law of conservation of watershed mass. The expression is as follows:

[0082] ;

[0083] in, Indicates rainfall. Indicates snow melting. Indicates the predicted runoff volume. This indicates the amount of evaporation. Indicates water storage capacity.

[0084] Then, by mixing and optimizing the loss function, the total loss function of the runoff prediction model is obtained. The expression is defined as follows:

[0085] ;

[0086] Where MSE represents the data-driven mean squared error. Indicates the actual runoff volume. This represents the weighting coefficients of the physical constraints. This loss function forces the model to search the parameter space that satisfies the water balance equation while minimizing the prediction error.

[0087] S3. Input the real-time runoff time series data (hydrological data and meteorological data, both of which are publicly available datasets) into the runoff prediction model based on the Inception parallel architecture and GELU-GLU multi-scale temporal convolutional network to complete the runoff prediction.

[0088] Real-time runoff time series data, i.e., tensors After being input into the TCN residual module, the data stream is copied and split into two paths, entering the multi-scale feature extraction module and the adaptive residual constraint module respectively. The fused output of the multi-scale feature extraction module and the output of the adaptive residual constraint module are added element-wise, and finally processed by the ReLU global non-negative constraint layer and the linear projection layer to output a runoff prediction value that conforms to physical laws.

[0089] In this embodiment, step S3 is specifically as follows:

[0090] S31, Real-time runoff time series data input multi-scale feature extraction module;

[0091] Will The data is input into the three convolutional branches of the multi-scale feature extraction module, which are based on the Inception parallel topology architecture. The data flows sequentially through the GELU-GLU in each of the convolutional branches, performing layer-by-layer abstraction and refinement of features.

[0092] After the data enters the multi-scale feature extraction module, it is first distributed in parallel to three independent convolutional branches. The specific process of the data within each branch is as follows:

[0093] 1) Within any convolutional branch, the input data is divided into two paths: the content stream of path a and the gated stream of path b.

[0094] First, a dual-path convolution mapping is performed to convert the input of the branch into a single path. Content streams are generated through two independent one-dimensional convolutional layers. Content Stream and Gated Stream (Gate Stream), the expression is as follows:

[0095] ;

[0096] ;

[0097] in, Indicates the expansion rate Convolution operation, , Indicates the corresponding weight. , This indicates the corresponding bias.

[0098] Due to the use of dilated convolution and padding, the length of the output sequence increases. To ensure causality (i.e., the prediction at time t depends only on data at time t and before, and the use of future information is strictly prohibited), the outputs of the two streams are sliced, i.e., causal pruning is performed. and Slice the output to remove excess material at the end. The data for each time step is expressed as follows:

[0099] ;

[0100] in, Indicates the expansion rate. This indicates the kernel size of the convolution branch, and .

[0101] Then perform smooth content activation, that is, for the content stream Apply the Gaussian error linear unit (GELU) activation function, as shown in the following expression:

[0102] ;

[0103] ;

[0104] in, The cumulative distribution function represents the standard normal distribution. Represents the Gaussian error function. Indicates content characteristics, Let represent the independent variable. GELU is approximately linear on the positive half-axis, preserving the advantage of the non-negative physical properties of hydrological variations; it has a smooth, non-monotonic curvature near zero on the negative half-axis, allowing for small negative gradient backpropagation. This enables the model to achieve refined capture of low-flow processes when dealing with weak signals during the dry season.

[0105] Finally, noise suppression gating is performed on the gated flow. Applying the Sigmoid activation function strictly limits the output to the (0, 1) interval. When the input contains observation noise or irrelevant perturbations, the gate value tends to 0, thus "shutting off" the transmission of that part of the information, achieving hard filtering and enhancing the model's robustness. The expression is as follows:

[0106] ;

[0107] Where B represents the gating coefficient, This represents the Sigmoid activation function.

[0108] 2) Perform gating filtering to obtain the output of the current convolutional branch;

[0109] The content feature tensor A of path a is multiplied element-wise with the gating coefficient tensor B of path b. Dropout is introduced into path a to prevent overfitting. This completes the feature selection at the current scale and yields the final output of the current convolutional branch. The expression is as follows:

[0110] ;

[0111] in, .

[0112] Path a (content flow): The data is processed sequentially through dilated convolution to extract features, GELU activation function for non-linear mapping, and Dropout layer for regularization to generate content feature tensors.

[0113] Path b (gated flow): The data is sequentially processed by dilated convolution and sigmoid activation function of the same dimension to generate a gated coefficient tensor with values ​​in the interval (0, 1).

[0114] Then, multi-scale feature fusion is performed. The output tensors obtained after processing the three convolutional branches are converged to the concatenation layer. The concatenation is lossless along the channel dimension using the Concat operation with dim=1, forming a comprehensive feature tensor containing short, medium, and long-scale information. .

[0115] S32. Real-time runoff time series data is input into the adaptive residual constraint module for aggregation and correction;

[0116] The original input data in parallel with step S31 The input adaptive residual constraint module performs adaptive matching after traversing the residual path, i.e., it judges the input data. Whether the number of channels is consistent with the number of channels of the output tensor of the multi-scale feature extraction module.

[0117] If they match, the data is directly transmitted as is through an identity mapping. If they do not match, the data undergoes a 1x1 convolutional layer for linear projection of the original physical features, adjusting its channel dimensions to match the output tensor of the multi-scale feature extraction module. By preserving the linear components of the data, the loss of fundamental physical trend information is prevented due to the nonlinear transformations of deep networks.

[0118] S33. Based on steps S31 and S32, the comprehensive feature tensor output in step S31 is added element by element to the residual path data to achieve lossless gradient flow and retention of historical information.

[0119] To address the degradation problem of deep networks and maintain the non-negative physical properties of features, residual connections are introduced to fuse the features obtained from the multi-scale feature extraction module at multiple scales. Input with adaptive residual constraint module Element-wise summation is performed, and to ensure that the higher-order hydrological features output at each layer strictly satisfy non-negativity, a ReLU activation function is applied to the summed result. The output result is denoted as... The expression is as follows:

[0120] ;

[0121] in, This represents the residual join processing function.

[0122] Then aggregate the data Force the input of the ReLU global nonnegative constraint layer and truncate all negative values ​​to 0.

[0123] S34. The model loss function constructed based on step S2 By utilizing adaptive residual constraints and multi-scale parallel paths, gradients are accurately backpropagated, driving the model to collaboratively optimize gating parameters at each scale while adhering to physical laws.

[0124] S35. Based on steps S31-S34, the output feature tensor of the ReLU global non-negativity constraint layer is input into the linear projection layer to map the high-dimensional feature space back to the target runoff numerical space, completing the linear projection result prediction and generating the final runoff prediction value. .

[0125] To verify the effectiveness of the method of this invention, this embodiment selects hydrological and meteorological data of Nuleke Dam from 2005 to 2017 as experimental samples. The dataset covers nine feature variables, including daily rainfall, daily temperature (including average, maximum, and minimum temperatures), daily surface soil volumetric water content, daily total evapotranspiration, daily snowmelt, daily snowfall, and daily runoff, with a total of 42,696 data entries. The experiment strictly followed a 6:2:2 ratio to divide the dataset into training, validation, and test sets. Simultaneously, this embodiment constructs a TCN and single-layer and multi-layer GELU-GLU models (the runoff prediction model described in this invention) for training, and the final prediction results are as follows: Figure 4 , 5 As shown in Figures 6 and 7, the Nash efficiency coefficients of the three models are 0.8825, 0.8917, and 0.9016, respectively. Experimental results demonstrate that the method proposed in this invention has higher accuracy and effectiveness in runoff prediction tasks.

[0126] In summary, regarding network structure, this invention proposes an improved temporal convolutional network that integrates the Inception parallel convolutional architecture with smooth nonlinear gated units (GELU-GLU). On one hand, the Inception parallel convolutional architecture is constructed to cover hydrological patterns across long, medium, and short-term scales; on the other hand, a novel GELU-GLU smooth gated mechanism is proposed to replace traditional units. This mechanism effectively overcomes the physical uninterpretability problems of neuron death and negative outputs, thus achieving refined capture of weak hydrological signals while preserving non-negative physical constraints. Regarding physical constraints, this invention constructs a physical constraint loss term based on the law of conservation of hydrological quality and employs the Lagrange multiplier method and data-driven loss to jointly solve it, forming a hybrid optimization objective that couples physical and data. This invention not only achieves high-precision prediction of key variables in complex time-series data but also significantly enhances the robustness and generalization performance of the model under abrupt changes, non-stationary characteristics, and noise interference.

[0127] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Various modifications and variations can be made to the invention by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the invention should be included within the scope of the claims of the invention.

Claims

1. A physical constraint runoff prediction method based on multi-scale smoothing gating, the specific steps of which are as follows: S1. Construct a runoff prediction model based on the Inception parallel architecture and the GELU-GLU multi-scale temporal convolutional network; The runoff prediction model includes: One TCN residual module, one ReLU global nonnegativity constraint layer, and one linear projection layer; The TCN residual module includes a multi-scale feature extraction module and an adaptive residual constraint module; the multi-scale feature extraction module is the Inception-GELU-GLU module. (1) The multi-scale feature extraction module includes three convolutional branches based on the Inception parallel topology architecture, which correspond to different convolutional kernel sizes K, namely K1, K2, and K3, and are used to extract runoff features at short, medium, and long time scales simultaneously. Among them, the one-dimensional dilatational convolution with kernel size K1 has a small receptive field and is used to capture the characteristics of sudden floods caused by instantaneous rainfall; the one-dimensional dilatational convolution with kernel size K2 has a moderate receptive field and is used to extract the mid-term lag characteristics in the soil saturation runoff process; the one-dimensional dilatational convolution with kernel size K3 has the largest receptive field and is used to summarize the long-term evolution trend of snowmelt runoff and groundwater baseflow. Each of the convolutional branches independently embeds an improved gated convolutional unit, namely the smooth nonlinear gated unit GELU-GLU. This unit performs nonlinear feature filtering through a dual-gate mechanism including the GELU activation function and a Dropout layer. The outputs of the three convolutional branches are finally concatenated and fused along the channel dimension; the fusion expression is as follows: ； in, Indicates the characteristics after fusion. This represents the output of convolution kernel K1. This represents the output of convolution kernel K2. This represents the output of convolution kernel K3. Indicates dimension; (2) The adaptive residual constraint module is configured with a channel dimension matching detection mechanism. When the dimensions of the input features and the output features are inconsistent, linear projection alignment is performed through 1*1 convolution to construct residual connections of identity mapping or projection mapping. S2. Based on step S1, construct the loss function of the runoff prediction model, that is, the target loss function of physical-data coupling; To construct a hybrid loss function based on the Lagrange multiplier method, the physical constraints of water balance are first defined, i.e., the physical residuals are defined according to the law of conservation of watershed mass. The expression is as follows: ； in, Indicates rainfall. Indicates snow melting. Indicates the predicted runoff volume. This indicates the amount of evaporation. Indicates water storage capacity; Then, by mixing and optimizing the loss function, the total loss function of the runoff prediction model is obtained. The expression is defined as follows: ； Where MSE represents the data-driven mean squared error. Indicates the actual runoff volume. Indicates the physical constraint weight coefficient; S3. Input the real-time runoff time series data into the runoff prediction model based on the Inception parallel architecture and GELU-GLU multi-scale temporal convolutional network to complete the runoff prediction; Real-time runoff time series data, i.e., tensors After being input into the TCN residual module, the data stream is copied and split into two paths, which enter the multi-scale feature extraction module and the adaptive residual constraint module respectively. The fusion output of the multi-scale feature extraction module and the output of the adaptive residual constraint module are added element by element, and finally processed by the ReLU global non-negative constraint layer and the linear projection layer to output the runoff prediction value that conforms to the physical laws.

2. The physical constraint runoff prediction method based on multi-scale smooth gating according to claim 1, characterized in that, Step S3 is as follows: S31, Real-time runoff time series data input multi-scale feature extraction module; Will The input multi-scale feature extraction module consists of three convolutional branches based on the Inception parallel topology architecture; Data flows sequentially through GELU-GLU in each of the convolutional branches, performing layer-by-layer abstraction and refinement of features; After the data enters the multi-scale feature extraction module, it is first distributed in parallel to three independent convolutional branches; the specific process of the data within each branch is as follows: 1) Within any convolutional branch, the input data is divided into two paths: the content stream of path a and the gated stream of path b. First, a dual-path convolution mapping is performed to convert the input of the branch into a single path. Content streams are generated through two independent one-dimensional convolutional layers. and gated flow The expression is as follows: ； ； in, Indicates the expansion rate Convolution operation, , Indicates the corresponding weight. , Indicates the corresponding bias; Then perform causal pruning. and Slice the output to remove excess material at the end. The data for each time step is expressed as follows: ； in, Indicates the expansion rate. This indicates the kernel size of the convolution branch, and ; Then perform smooth content activation, that is, for the content stream Apply the Gaussian error linear unit (GELU) activation function, as shown in the following expression: ； ； in, The cumulative distribution function represents the standard normal distribution. Represents the Gaussian error function. Indicates content characteristics, Indicates the independent variable; Finally, noise suppression gating is performed on the gated flow. Applying the Sigmoid activation function strictly limits the output to the interval (0, 1). When the input contains observation noise or irrelevant perturbations, the gate value tends to 0, as shown in the following expression: ； Where B represents the gating coefficient, This represents the Sigmoid activation function; 2) Perform gating filtering to obtain the output of the current convolutional branch; The content feature tensor A of path a is multiplied element-wise with the gating coefficient tensor B of path b, and Dropout is introduced into path a to complete feature filtering at the current scale, thus obtaining the final output of the current convolutional branch. The expression is as follows: ； in, ; Finally, multi-scale feature fusion is performed. The output tensors from the three convolutional branches are converged to the concatenation layer, and a lossless concatenation along the channel dimension is achieved through a Concat operation with dim=1, forming a comprehensive feature tensor containing short, medium, and long-scale information. ; S32. Real-time runoff time series data is input into the adaptive residual constraint module for aggregation and correction; The original input data in parallel with step S31 The input adaptive residual constraint module performs adaptive matching after traversing the residual path, i.e., it judges the input data. Whether the number of channels is consistent with the number of channels of the output tensor of the multi-scale feature extraction module; If they are consistent, the data is transmitted directly through the identity mapping, maintaining its original state; if they are inconsistent, the data is linearly projected onto the original physical features through a 1*1 convolutional layer, and its channel dimensions are adjusted to be consistent with the output tensor of the multi-scale feature extraction module. S33. Based on steps S31 and S32, the comprehensive feature tensor output in step S31 is added element by element to the residual path data to achieve lossless gradient flow and retention of historical information. By introducing residual connections, the features fused from the multi-scale feature extraction module are integrated. Input with adaptive residual constraint module Perform element-wise addition, apply the ReLU activation function to the sum, and denote the output as... The expression is as follows: ； in, This represents the residual join processing function; Then aggregate the data Force the input of the ReLU global nonnegativity constraint layer and truncate all negative values ​​to 0; S34. The model loss function constructed based on step S2 By utilizing adaptive residual constraints and multi-scale parallel paths, gradients are accurately backpropagated, driving the model to collaboratively optimize gating parameters at each scale while adhering to physical laws. S35. Based on steps S31-S34, the output feature tensor of the ReLU global non-negativity constraint layer is input into the linear projection layer to map the high-dimensional feature space back to the target runoff numerical space, completing the linear projection result prediction and generating the final runoff prediction value. .

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