Runoff prediction method based on lstm-kan and physical guidance mechanism

Abstract

The application discloses a runoff prediction method based on LSTM-KAN and a physical guiding mechanism, and comprises the following steps: a time sequence feature extraction network is used to encode a historical meteorological forcing sequence, and a high-dimensional dynamic feature vector is generated; the historical meteorological forcing sequence is input into a multi-physical mechanism state model, and a multi-physical mechanism state vector at a current moment is calculated and output; the high-dimensional dynamic feature vector and a historical runoff observation sequence are input into a parallelly arranged extreme runoff representation network and a normal runoff representation network, and an extreme runoff prediction component and a normal runoff prediction component are respectively generated; a physical guiding fusion weight is calculated according to the multi-physical mechanism state vector, and the extreme runoff prediction component and the normal runoff prediction component are weighted and fused according to the physical guiding fusion weight, so that a final runoff prediction result is generated. The application effectively solves the problems of single runoff generation mechanism, static definition of extreme events and redundant representation features in the prior art, and improves the precision and physical interpretability of runoff prediction.

Description

Technical Field

[0001] This invention belongs to the field of hydrological forecasting, and in particular to a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms. Background Technology

[0002] As global climate change intensifies, watershed runoff processes are exhibiting stronger nonlinear and nonstationary characteristics, posing a severe challenge to accurately capturing flood peaks and low water levels. Traditional purely physical models are complex to calibrate, while purely data-driven methods, although capable of fitting historical patterns, often lack explanatory power regarding physical mechanisms and are ill-suited to constantly changing environmental conditions.

[0003] Currently, deep learning methods incorporating physical mechanisms are becoming a research hotspot. Existing mainstream research often employs Long Short-Term Memory (LSTM) networks to mine meteorological time-series features and attempts to introduce simple physical constraints, such as embedding a single water balance equation into a neural network, or using static statistical thresholds to distinguish between extreme and normal events. These methods attempt to find a balance between data mining capabilities and physical laws, but they still rely on relatively crude processing logic when dealing with complex watershed runoff differentiation and dynamic extreme scenarios.

[0004] However, existing technologies still have significant limitations in handling complex hydrological processes, mainly in the oversimplification of physical runoff generation mechanisms and the rigidity of extreme event identification. Existing physical guidance methods typically reduce watershed runoff generation to a single soil moisture state evolution, failing to effectively decouple physical mechanisms with different response rates, such as surface runoff, interflow, and baseflow recharge. This results in models being unable to adaptively match the dominant runoff generation process when facing different rainfall patterns, such as short-duration torrential rains or prolonged droughts. Furthermore, for the identification of extreme hydrological events, existing methods largely rely on static thresholds based on historical flow statistics (such as the top 10% quantile), ignoring the decisive influence of watershed internal physical states, such as soil moisture saturation, on runoff generation. This leads to an inability to distinguish between fundamentally different physical scenarios, such as floods caused by high-intensity rainfall and drought-induced soil absorption of heavy rainfall. In addition, when using dual-channel networks to predict extreme and normal values ​​separately, the lack of structural constraints in the feature space often results in the two networks learning highly overlapping redundant features. This makes it difficult for the model to truly capture the unique long-tail distribution patterns of extreme events, limiting further improvements in forecast accuracy. Summary of the Invention

[0005] The purpose of this invention is to provide a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms to solve the aforementioned problems in the existing technology.

[0006] The technical solution, a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms, includes:

[0007] Receive historical meteorological forcing sequences and historical runoff observation sequences of the watershed;

[0008] A time-series feature extraction network is used to encode historical meteorological forced sequences, generating high-dimensional dynamic feature vectors that reflect the evolution of meteorological elements over time.

[0009] Input the historical meteorological forcing sequence into a multi-physical mechanism state model that includes surface runoff, soil runoff and baseflow recharge mechanisms, calculate and output the multi-physical mechanism state vector at the current moment;

[0010] High-dimensional dynamic feature vectors and historical runoff observation sequences are input into parallel extreme runoff characterization networks and normal runoff characterization networks to generate extreme runoff forecast components and normal runoff forecast components, respectively.

[0011] The physical guidance fusion weight is calculated based on the state vector of the multi-physics mechanism. The extreme runoff forecast component and the normal runoff forecast component are then weighted and fused to generate the final runoff forecast result.

[0012] Beneficial effects: This invention effectively solves the problems of single runoff generation mechanism characterization, static definition of extreme events, and redundant characterization features in the prior art, thereby improving the accuracy and physical interpretability of runoff forecasting. Attached Figure Description

[0013] Figure 1 A flowchart illustrating the steps of a runoff forecasting method based on LSTM-KAN and physical guidance mechanism provided in this application embodiment.

[0014] Figure 2 A flowchart illustrating the steps for calculating and outputting the multiphysics mechanism state vector at the current moment, as provided in this application embodiment.

[0015] Figure 3 A flowchart illustrating the steps for calculating the physical-guided fusion weights provided in this application embodiment.

[0016] Figure 4 A flowchart illustrating the steps for receiving historical meteorological forcing sequences and historical runoff observation sequences of a watershed, as provided in this application embodiment. Detailed Implementation

[0017] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0018] It should be noted that the terms include and have, and any variations thereof, are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or device that includes a series of steps or units is not necessarily limited to those steps or units that are explicitly listed, but may include other steps or units that are not explicitly listed or that are inherent to such process, method, product, or device.

[0019] like Figure 1 As shown, a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms includes the following steps:

[0020] It receives historical meteorological forcing sequences and historical runoff observation sequences of the watershed.

[0021] Alternatively, one can receive historical meteorological forcing sequences and historical runoff observation sequences from the watershed, perform preprocessing including missing value imputation, outlier removal, and data standardization, and obtain preprocessed historical meteorological forcing sequences and historical runoff observation sequences.

[0022] In this embodiment, the historical meteorological forcing sequence refers to a series of meteorological observation data arranged in chronological order, which can serve as input variables to drive the hydrological model. Specifically, the meteorological forcing sequence can include observed values ​​of various meteorological elements such as rainfall, temperature, evaporation, relative humidity, and wind speed. The historical runoff observation sequence refers to the sequence of measured flow data at the corresponding watershed outlet section. To ensure the effectiveness of subsequent model training and prediction, these sequences need to cover a sufficiently long time span, such as several years or even decades. In practical implementation, the data can be automatically collected by rain gauges, meteorological stations, and hydrological stations deployed within the watershed and transmitted to the data center via a telemetry system.

[0023] For example, the received data is stored and processed in the form of a multidimensional matrix. Taking a historical meteorological forcing sequence as an example, if it contains P meteorological elements and the total number of time steps is T, then the sequence can be represented as a matrix of length T multiplied by P. Similarly, a historical runoff observation sequence can be represented as a vector of length T. Preferably, after receiving the data, data preprocessing operations are performed, such as missing value imputation, outlier removal, and data standardization, to ensure that the quality of the input data meets the requirements of the deep learning model.

[0024] A time-series feature extraction network is used to encode historical meteorological forced sequences, generating high-dimensional dynamic feature vectors that reflect the evolution of meteorological elements over time.

[0025] In this embodiment, a temporal feature extraction network is used to extract deep-seated temporal dependencies and dynamic evolution patterns from raw meteorological data. For example, the temporal feature extraction network can be implemented using a Long Short-Term Memory (LSTM) network. LSTM, by introducing gating mechanisms including input gates, forget gates, and output gates, can effectively solve the gradient vanishing or exploding problem in long sequence training, thereby capturing long-distance temporal dependencies.

[0026] Specifically, the processed historical meteorological forcing sequence is fed into an LSTM network. At each time step, the LSTM unit receives the current meteorological input and the hidden state from the previous time step, updates the cell state through internal gating operations, and outputs the current hidden state. This set of hidden state vectors output over time steps constitutes a high-dimensional dynamic feature vector. This feature vector maps the original low-dimensional meteorological data to a high-dimensional feature space, enabling a richer expression of the nonlinear driving effect of meteorological elements on watershed hydrological processes.

[0027] The historical meteorological forcing sequence is input into a multi-physical mechanism state model that includes surface runoff, soil runoff, and baseflow recharge mechanisms. The multi-physical mechanism state vector at the current moment is calculated and output.

[0028] In this embodiment, hydrophysical mechanisms are introduced to simulate the water movement process within the watershed by constructing a multi-physical mechanism state model. Unlike purely data-driven black-box models, this model decouples the watershed runoff process into physical processes of surface runoff, subsurface runoff, and baseflow recharge. Surface runoff mainly describes the process of rainfall forming runoff on the soil surface, which is usually related to rainfall intensity and soil infiltration capacity; subsurface runoff describes the process of water flowing laterally in soil pores; and baseflow recharge describes the process of water infiltrating into the groundwater layer and slowly recharging the river channel.

[0029] In a preferred implementation, the multi-physics mechanism state model can consist of a set of coupled differential equations or their discretized forms. For each time step, the model receives meteorological forcing data such as rainfall as input, combines it with the physical state from the previous time step, and calculates the state variable values ​​corresponding to each physical process at the current time step according to the law of conservation of mass and the runoff generation physics equation. For example, surface runoff state can correspond to surface water storage, subsurface runoff state can correspond to soil moisture content, and baseflow recharge state can correspond to groundwater storage. Combining the state values ​​of these three components forms the multi-physics mechanism state vector for the current time step. This vector reflects the hydrophysical state of the watershed at the current time step, providing physical constraints and prior information for subsequent runoff forecasting.

[0030] High-dimensional dynamic feature vectors and historical runoff observation sequences are input into parallel extreme runoff characterization networks and normal runoff characterization networks to generate extreme runoff forecast components and normal runoff forecast components, respectively.

[0031] In this embodiment, to address the challenge of traditional models simultaneously achieving high accuracy in predicting extreme floods and normal flow rates, a hierarchical decoupled representation learning strategy is employed. Two parallel neural networks are constructed: an extreme runoff representation network and a normal runoff representation network. Structurally, these networks can adopt the Kolmogorov-Arnold Network (KAN), which, based on the Kolmogorov-Arnold representation theorem, utilizes learnable univariate activation functions such as B-spline functions to approximate complex nonlinear mapping relationships, exhibiting stronger function fitting capabilities than traditional multilayer perceptrons.

[0032] Specifically, high-dimensional dynamic feature vectors are fused with historical runoff observation sequences, for example, through vector concatenation operations, to construct a joint input vector. This joint input vector is simultaneously fed into the two representation networks mentioned above. The extreme runoff representation network is trained to capture features of extreme hydrological events such as floods and rainstorms, and its output is the extreme runoff forecast component, which can accurately predict extreme flow values ​​far from historical averages. In contrast, the normal runoff representation network focuses on capturing regular hydrological patterns during small and medium-sized floods and dry seasons, and its output is the normal runoff forecast component, which can accurately predict normal flow values ​​close to historical averages. Through this parallel division of labor mechanism, the model can maintain high predictive sensitivity across different flow ranges.

[0033] The physical guidance fusion weight is calculated based on the state vector of the multi-physics mechanism. The extreme runoff forecast component and the normal runoff forecast component are weighted and fused using the physical guidance fusion weight to generate the final runoff forecast result.

[0034] In this embodiment, the prediction results of two parallel networks are dynamically integrated through a physics-guided fusion mechanism. Since extreme events are often accompanied by specific physical states, such as highly saturated soil, the multi-physics mechanism state vector becomes the physical basis for determining whether the current moment leans towards an extreme scenario.

[0035] For example, a mapping function or lightweight neural network can be constructed to map the multi-physics mechanism state vector to normalized weight values, i.e., physics-guided fusion weights. These weights contain two components, corresponding to the contribution ratios of the extreme runoff forecast component and the normal runoff forecast component, respectively. When the physical state vector indicates that the watershed is in a highly saturated, runoff-prone extreme state, the system automatically increases the weight of the extreme runoff forecast component; conversely, when the physical state vector indicates that the watershed is in a drought or steady state, the weight of the normal runoff forecast component is increased. By linearly weighting and summing the two forecast components with their corresponding weights, the final runoff forecast result for the current moment can be obtained. This approach not only utilizes the fitting capabilities of deep learning but also incorporates the causal logic of hydrophysical mechanisms, improving the interpretability and robustness of the forecast results.

[0036] In some possible implementations, evaluation metrics can be introduced to quantitatively assess the model's forecasting performance under different scenarios. For overall forecast accuracy, the root mean square error (RMSE) is used for evaluation. However, for forecasting performance on extreme hydrological events, especially for extreme samples located at the beginning and end of the flow distribution, the symmetric mean absolute percentage error (sMAPE) is preferred for evaluation. Evaluation metrics can objectively reflect the model's relative error level under extreme high or low flow scenarios, verifying the model's ability to capture extreme events.

[0037] like Figure 4 As shown, in one possible implementation, before receiving the historical meteorological forcing sequence and historical runoff observation sequence of the watershed, the following preprocessing steps are included on the raw data:

[0038] Establish a unified time index benchmark, extract the time intersection interval of all original data sources as a common time period, and truncate and align the pre-stored original data sequence based on the common time period to obtain the aligned original data sequence;

[0039] For missing data in the aligned original data sequence, historical year data with similar runoff characteristics are retrieved and used to fill in the missing data, resulting in the filled original data sequence.

[0040] In addition to rainfall, all the filled raw data sequences were standardized and mapped to a standard normal distribution with a mean of 0 and a variance of 1 to obtain historical meteorological forcing sequences and historical runoff observation sequences.

[0041] In practical hydrological modeling, raw data often originates from different observation stations, and time records may have biases or varying lengths. Therefore, a unified time index benchmark needs to be established. Specifically, the system scans the timestamps of all input data sources to identify time periods where all data sources have records, i.e., common time periods. All sequences are cropped into this common time period, ensuring strict alignment of variables in the time dimension during subsequent calculations. For unavoidable missing values ​​in the raw data, a hydrological similarity-based imputation strategy is preferred. Specifically, the system searches the historical database for complete years with similar runoff processes or similar rainfall patterns to the year containing the missing data, and uses contemporaneous data from these similar years to impute the missing values. This method preserves the periodicity and fluctuation characteristics of hydrological processes better than simple linear interpolation. Furthermore, to eliminate numerical differences caused by different physical units and accelerate model convergence, standardization is performed on all meteorological and runoff data except for rainfall elements with obvious physical significance. The Z-Score standardization method can be used, which involves subtracting the historical mean of the data from the raw data and then dividing by its historical standard deviation, transforming the data into a distribution with a mean of 0 and a standard deviation of 1.

[0042] In one exemplary embodiment, a high-dimensional dynamic feature vector reflecting the evolution of meteorological elements over time is generated. Specifically, assuming the current time is t and the input meteorological forcing data is x... t The hidden state at the previous time step was h. t-1 The cell state at the previous moment was C. t-1 Calculate the input gate i t This is used to control the degree to which new information is written into the cell state, and its calculation formula is: i t = σ(W ix * x t + W ih * h t-1 + b i ); Computing the forget gate f t This is used to control the degree to which the cell state from the previous moment is forgotten, and its calculation formula is: f t = σ(W fx * x t + W fh * h t-1 + b f ); Calculate the output gate o t This is used to control the degree of output of the current cell state, and its calculation formula is: o t = σ(W ox * x t + W oh * h t-1 + b o ); Calculate the candidate cell state C at the current time.tilde_t The calculation formula is: C tilde_t = tanh(W Cx * x t + W Ch * h t-1 + b C Update the current cell state C. t The calculation formula is: C t = f t * C t-1 + i t * C tilde_t ; Calculate the hidden state h at the current time. t The calculation formula is: h t = o t * tanh(C t ); where σ is the Sigmoid activation function; x t Forcibly input weather data at the current moment; C t In cellular state; W ix W ih W fx W fh W ox W ho W Cx W Ch b is the corresponding weight matrix; i b f b o b C For the corresponding bias term; * indicates matrix multiplication or element-wise multiplication, h t This is a high-dimensional dynamic feature vector.

[0043] In a preferred embodiment, the multi-physics mechanism state model uses a gated unit-based soil water state equation for state updating, calculates and outputs the multi-physics mechanism state vector at the current moment, including calculating the soil water state S at the current moment based on the following formula. t :

[0044] R st =ReLU(W Rp P t + W Rh h t + W Rs S t-1 +b R );

[0045] i st = σ(W ip P t + W ih h t+ W is S t-1 + b i );

[0046] m int = i st ·P t ;

[0047] S t = m int + R st ·S t-1 -O other ;

[0048] Among them, S t S represents the current soil water state. t-1 The soil water state at the previous moment; P t This represents the rainfall data at the current moment; h t R represents a high-dimensional dynamic feature vector. st i is the mass redistribution factor; st For input gating unit; m int Input for system quality; O other This represents the outflow component containing both the system mass non-closed term and the runoff output term; ReLU() is the column-normalized linear rectified activation function, and σ() is the column-normalized Sigmoid activation function; W Rp W Rh W Rs b R These represent the weights and biases for rainfall, dynamic characteristics, and historical states, respectively, when calculating the mass redistribution coefficient; W ip W ih W is b i These represent the weights and biases for rainfall, dynamic features, and historical states when calculating the input gating unit.

[0049] Specifically, calculate the mass redistribution factor R. st This reflects the water exchange behavior between soil water units at the previous moment. This coefficient is determined by rainfall P. t Meteorological features extracted by LSTM h t and the previous state S t-1 Jointly decided, and through column normalization The activation function is guaranteed to be non-negative and also obeys the law of conservation of mass. The input gating unit i is calculated. st This determines the current rainfall P t The method of inputting into each soil water unit; this gate value is processed using the Sigmoid function and then normalized. The system quality input m is calculated. intThat is, the actual amount of water entering the soil system, which is equal to the input gate i. st With rainfall P t The product of and . Update the current soil water state S. t Its value is equal to the mass m of the new input. int Adding the residual water volume R from the previous moment after adjustment by the redistribution factor st Multiply by S t-1 Subtract the amount of water flowing out of the system, O other ; where O other Taking into account evapotranspiration losses and the resulting runoff output, for example, O other = q1 t + q2 t + E t ;where q1 t For direct runoff, q2 t For super-permeable runoff, E t Evaporation loss can be expressed using formula E. t = k E ×PET t ×S t / S max Calculation, PET t Potential evapotranspiration can be obtained from meteorological forcing sequences, k E The evapotranspiration coefficient has a value range of 0.8-1.2.

[0050] This embodiment mathematically mimics the water balance process in the hydrological cycle.

[0051] In a further embodiment, the multi-physics mechanism state model also includes runoff generation calculation for characterizing the nonlinear generation mechanism of runoff. The runoff generation calculation includes calculating the maximum storage capacity, field capacity, direct runoff, and infiltration excess runoff based on the following formulas:

[0052] S max = f Smax (a s W Smax b Smax );

[0053] S fc = min(f Sfc (a s W Sfc b Sfc ), S max );

[0054] S ret =R st ·S t-1 ;

[0055] q1t = m int *(tanh(λ(S ret - S max ))+1) / 2;

[0056] o t =σ(W op P t + W oh h t + W os S t-1 + b o );

[0057] q2 t = o t *ReLU(S ret - S fc );

[0058] Among them, a s f represents the static parameters of the watershed. Smax and f Sfc For a multilayer perceptron model; S max S represents the maximum water storage capacity. fc S is the field holding capacity; ret The cell state after reallocation; q1 t For direct runoff; q2 t This refers to the infiltration runoff exceeding the field water-holding capacity; λ is the adjustment constant; o t This is an output gate used to regulate moisture output; W Smax W Sfc W op W oh W os and b Smax b Sfc b o represents the corresponding network parameters; tanh is the hyperbolic tangent function.

[0059] In this embodiment, a multilayer perceptron (MLP) is used based on the static attribute parameter a of the watershed. s For example, factors such as topographic slope and soil type are used to estimate the maximum water storage capacity S of the watershed. max Field water holding capacity S fc This allows the model parameters to have physical meaning and adapt to the characteristics of different watersheds. The redistributed unit states S are then calculated. ret This refers to the remaining stock after the redistribution of the state from the previous moment. Calculate the direct runoff q1. t This portion of runoff mainly originates from the newly infiltrated water when the soil is near saturation; the formula uses the tanh function to simulate this nonlinear runoff threshold effect, where λ is a constant that adjusts the steepness of the curve. The output gating is calculated.t Based on this, the excess infiltration runoff q2 is calculated. t Excessive infiltration runoff refers to runoff that occurs when soil moisture content exceeds field capacity (S). fc At that time, the excess water generates runoff under the influence of gravity; the formula uses the ReLU function to ensure that only when S ret Greater than S fc This portion of the runoff only occurs at a certain time. The final total runoff output Q t From q1 t and q2 t Superimposed, for example, Q t =∑ i=1 k (q1 t i + q2 t i ), where q1 t i Let q2 be the direct runoff of the i-th unit at time t. t i Let be the excess runoff of the i-th unit at time t, and k be the total number of units.

[0060] According to one aspect of this application, both the extreme runoff characterization network and the normal runoff characterization network adopt a neural network structure based on the Kolmogorov-Arnold representation theorem, and the calculation formula for the j-th feature in the l-th layer of the network is:

[0061] x l，j =∑ i=1 nl-1 Φ l-1，j，i (x l-1，i );

[0062] Where, Φ l，j，i For a learnable univariate activation function, a B-spline function is used for approximation, and its expression is:

[0063] Φ(x)=∑ k=0 K c k B k (x);

[0064] x l-1，i n is the i-th input feature of the (l-1)-th layer; l-1 B is the input feature dimension of the previous layer; k (x) is a k-order B-spline basis function; c k represents the learnable spline coefficients; K represents the spline order.

[0065] In this embodiment, different from traditional neural networks that apply fixed activation functions to neurons, the KAN network places the activation function on the connection edges, and the activation function Φ is a learnable non-linear function. The B-spline function is used to parameterize Φ. Specifically, any Φ function is represented as a linear combination of K-order B-spline basis functions B k (x), and c k is the corresponding spline coefficient, which is a parameter to be optimized during network training. This allows the network to learn complex univariate mappings, showing higher accuracy and interpretability in physical process modeling. Exemplarily, the KAN architecture is defined by an integer array [n0, n1, …, n l , where n l represents the number of neurons in the l-th layer. The transformation of the j-th neuron in the (l + 1)-th layer is given by: x l+1，j = ∑ i=1 nl Φ l，j，i (x l，i ); j = 1, …, n l+1 .

[0066] According to another aspect of the present application, generating extreme runoff forecast components and normal runoff forecast components respectively further includes: jointly optimizing network parameters based on a loss function that includes a physical consistency constraint term, and the loss function includes an associated distance regularization loss term. The weight calculation formula for the associated distance regularization loss term is:

[0067] w ft = tanh 2 (y t );

[0068] w nt = (1 - |tanh(y t )|); 2 ;

[0069] l1 = RMSE((y* far * w ft ), (y * w ft ));

[0070] l2 = RMSE((y* near * w nt ), (y * w nt ));

[0071] where y t is the runoff observation value at the current moment; w ft is the weight focusing on expressing extreme values; w ntTo emphasize the weights of normal values; l1 and l2 are the correlation distance regularization losses for extreme runoff forecast components and normal runoff forecast components, respectively; RMSE is the root mean square error function, y* far and y* near These are the outputs of extreme and normal runoff forecast components, respectively.

[0072] In this embodiment, a regularization term is defined in the loss function used to train the model, guiding the two KAN networks to focus on extreme and normal values ​​respectively. Specifically, based on the current runoff observation value y t Calculate two dynamic weights. Extreme value weight w ft Using the hyperbolic tangent square function tanh 2 Calculate the property of this function so that when y t When the absolute value is large, w ft It approaches 1; while when y t When it approaches 0, w ft It approaches 0. This perfectly matches the characteristic that extreme values ​​deviate far from the mean. Conversely, the weights of normal values ​​w nt Then in y t The value approaches 1 when it is close to 0. These two weights are used to evaluate the output y* of the extreme runoff characterization network. far and the output y* of the normal runoff characterization network near The error between the prediction and the true value y is weighted. l1 is the weighted prediction error for extreme values, and l2 is the weighted prediction error for normal values. Adding these two terms to the total loss function forces the extreme value network to focus on fitting extreme samples, while the normal value network focuses on fitting normal samples.

[0073] In one possible embodiment, the method further includes constructing a dynamic extremeity determination mechanism, which calculates soil moisture saturation, instantaneous extremeity index, and cumulative extremeity index based on the following formula:

[0074] η t =S re t / S max E t =η t ·g P t + (1-η t )·g ΔS t E* t =α·E t + (1-α)· E* t-1 ;

[0075] Where, η t S represents soil moisture saturation. ret S represents the redistributed soil water state extracted from the multi-physics mechanism state vector; max E represents the maximum water storage capacity of the basin. t g is the instantaneous extremity index. P t The precipitation anomaly is calculated based on historical meteorological forcing sequences; g ΔS t E* represents the anomaly degree of soil water state change calculated using time difference of state vectors based on multiple physics mechanisms. t α is the cumulative extremity index, used to characterize the time-series cumulative effect of consecutive extreme events; α is the time-series decay coefficient.

[0076] In this embodiment, the definition of extremes is transformed from a simple statistical distribution of data to a dynamic determination based on the physical state of the watershed. Specifically, the soil moisture saturation η is calculated. t This index is equal to the current redistributed soil water state S. re t Divide by the maximum water storage capacity S of the basin max For example, if S max For 100 millimeters, the current S re t If it is 80 mm, then η t A value of 0.8 indicates that the soil is nearing saturation. The instantaneous extreme index E is calculated. t This index takes into account both rainfall intensity and soil moisture changes. The g in the formula... P t This refers to rainfall anomaly, which can be defined, for example, as the standardized deviation of the current rainfall relative to the historical mean after being mapped by a Sigmoid algorithm. ΔS t It refers to the anomaly degree of soil water state change. When the soil saturation η t At higher levels, g P t The higher weighting of η indicates that the extreme nature of the soil is primarily determined by rainfall intensity, as saturated soil is extremely sensitive to rainfall and readily generates runoff; conversely, when the soil is dry... t At lower levels, extremes depend more on drastic changes in soil water storage. Calculate the cumulative extremes index E*. t Considering that flood events are often the result of continuous rainfall accumulation, simple instantaneous indicators may be lagging or fluctuating. By introducing a recursive formula with an attenuation coefficient α, for example, 0.7, extreme information from historical moments can be transmitted to the present, smoothing out and enhancing the ability to capture persistent extreme events.

[0077] In some alternative implementations, the instantaneous extremity index E tThe calculation can also be based on the runoff change rate. Specifically, it calculates the runoff Q predicted by the physical module at the current moment. t The rate of change r relative to the previous time step Qt :r Qt =(Q t -Q t-1 ) / (Q t-1 +ε), where ε is a small constant. The absolute value of this rate of change is standardized and mapped to the interval between 0 and 1, as E. t It serves as an alternative or supplementary indicator, providing another basis for judgment in the absence of precise soil parameters.

[0078] In a further embodiment, the physical-guided fusion weights are calculated based on the multi-physics mechanism state vector, including classifying hydrological scenarios based on the cumulative extrema index and soil moisture saturation, and calculating the physical-driven extreme value weights γ according to the following strategy. far t :

[0079] When E* t >θ E And η t >θ η，h When this is determined to be an extreme high-flow scenario, the calculation formula is: γ far t =σ(β1·(E* t -θ E )+β2·(η t -θ η，h ));

[0080] When E* t >θ E And η t <θ η，l When this is determined to be an extremely low flow scenario, the calculation formula is: γ far t =σ(β3·(E* t -θ E )+β4·(θ η，l -η t ));

[0081] Otherwise, it is judged as a normal traffic scenario, and the calculation formula is: γ far t =σ(β5·E* t );

[0082] in θ E θ η，h θ η，lThese represent the extreme value threshold, high saturation threshold, and low saturation threshold, respectively; β1 to β5 are learnable scaling parameters, initialized from -1 to 1; σ() is the Sigmoid activation function; the physics-guided fusion weights are based on the physics-driven extreme value weights γ. far t generate.

[0083] In this embodiment, a hierarchical fusion strategy based on physical scenarios is established. The system presets an extreme event determination threshold θ. E For example, 0.5, high saturation threshold θ η，h For example, 0.8, low saturation threshold θ η，l For example, 0.2. When the cumulative extrema index E* t and soil saturation η t When all values ​​exceed the corresponding threshold, it is judged as an extreme high-flow scenario, such as torrential rain and flooding. In this case, the extreme value weight γ... far t The calculation of E* is positively correlated with the degree to which these two indicators exceed the threshold, maximizing the contribution of the extreme runoff characterization network. t High but soil saturation η t When the flow rate is extremely low, it is classified as an extreme low-flow scenario, such as severe drought. In this case, the weight calculation focuses on the degree of low saturation, and extreme network intervention is still required to capture drought characteristics. In other cases, it is classified as a normal flow scenario, and the weight γ... far t Mainly affected by the slight fluctuations in the cumulative extremity index, which usually remains at a low level, the model mainly relies on the normal runoff characterization network.

[0084] Preferably, to enhance the robustness of the system, a physical simulation confidence correction mechanism can be introduced. The physical simulation confidence ρ is calculated. t Its value is inversely proportional to the degree to which the runoff predicted by the physical module deviates from the historical average. Simultaneously, an auxiliary multilayer sensor directly outputs data based on meteorological characteristics to drive the candidate weights γ'. far t The final adaptive fusion weight w f_t Physically driven weight γ far t and data-driven weights γ' far t Based on confidence level ρ t A weighted combination is applied. That is, when the confidence of the physical model is high, the physical weights are adopted; otherwise, the data-driven weights are reverted to the lower confidence levels.

[0085] In one possible implementation, the physical consistency constraint term includes a physical consistency loss. physicsThe physical consistency loss is used to constrain the extreme degree of the model prediction to be consistent with the extreme degree index of the physical process determination. Its calculation formula is as follows:

[0086] l physics =(1 / T)∑ t=1 T (E* t -σ(|y* t |)) 2 ;

[0087] Where T is the time step of the training samples; E* t For cumulative extrema index; y* t The final runoff forecast result is the model's final predicted runoff; σ() is the Sigmoid activation function, used to map the forecast result to the same range of values ​​as the cumulative extremity index.

[0088] In this embodiment, physical discrimination information is fed back to the neural network through a loss function. Specifically, the calculation model ultimately predicts the runoff y*. t The absolute value of the result after being mapped by the Sigmoid function represents, mathematically, the statistical extremism of the model's output. Physical consistency loss l physics This measures the extreme values ​​of the model output and the extreme values ​​of the physics decision E*. t The difference between them. By minimizing this loss, the neural network's predictions are forced to align with the physical process's judgment on extreme trends, thus preventing the neural network from making predictions that violate physical common sense when data is lacking.

[0089] like Figure 2 As shown, in one embodiment of this application, the multi-physics mechanism state vector is composed of independently updated surface runoff state components, subsurface runoff state components, and baseflow recharge state components; historical meteorological forcing sequences are input into the multi-physics mechanism state model containing surface runoff, subsurface runoff, and baseflow recharge mechanisms, and the multi-physics mechanism state vector at the current moment is calculated and output, including:

[0090] Extract the current moment's rainfall input data from historical meteorological forcing sequences;

[0091] Using the surface state update function, the surface runoff state component at the current moment is calculated based on the rainfall input data at the current moment and the pre-stored surface runoff state component at the previous moment. The surface runoff state component is used to characterize the physical state of surface retention and runoff generation processes in the watershed.

[0092] Using the soil state update function, the soil runoff state component at the current moment is calculated based on the rainfall input data at the current moment and the pre-stored soil runoff state component at the previous moment. The soil runoff state component is used to characterize the physical state of watershed soil moisture content and soil runoff process.

[0093] Using the baseflow state update function, the baseflow recharge state component at the current moment is calculated based on the rainfall input data at the current moment and the pre-stored baseflow recharge state component at the previous moment. The baseflow recharge state component is used to characterize the physical state of the watershed groundwater recharge and baseflow process.

[0094] By concatenating the surface runoff state components, soil runoff state components, and baseflow recharge state components at the current moment, a multi-physical mechanism state vector at the current moment is obtained.

[0095] In a preferred implementation, the multiphysics state vector is computed:

[0096] S phys t =[S surf t S sub t S base t ];S k t = f k (S k t-1 P t );

[0097] Among them, S phys t S is the multiphysics mechanism state vector at time t; surf t S sub t S base t These represent the surface runoff generation, subsurface runoff generation, and baseflow recharge state components in the multi-physics mechanism state model; k∈surf, sub, and base represent the corresponding physical mechanisms, namely the surface runoff generation, subsurface runoff generation, and baseflow recharge mechanisms, respectively; f k S is the learnable nonlinear state update function corresponding to the mechanism; k t S represents the state components of physical mechanism k at time t; k t-1 P represents the state component from the previous time step. t This refers to the current moment's rainfall data extracted from historical meteorological forcing sequences.

[0098] In this embodiment, a multidimensional physical state machine is constructed to replace the single soil moisture state. In actual hydrological cycles, runoff formation is often the result of multiple mechanisms working together. Therefore, the physical state is decoupled into three independent components. Specifically, S phys t The current multi-physics mechanism state vector is composed of three concatenated components. S surf t The surface runoff state component mainly characterizes the physical processes of rainfall filling depressions, being retained, and generating surface runoff on the surface; S sub t The soil runoff state component mainly characterizes the physical processes of water infiltration, storage, and lateral flow formation in soil pores; S base t The baseflow recharge state component primarily characterizes the physical processes of deep groundwater accumulation and the slow release of baseflow into the river channel. For each state component, an independent state update function f is used. k Iterative calculations are performed. In the formula, k takes values ​​from surf, sub, and base, representing the three physical mechanisms mentioned above, respectively; P t The current rainfall input; S k t-1 This represents the state component corresponding to the previous time step. Preferably, f k This can be achieved using recurrent neural network units with gating mechanisms, such as a variant of the gated recurrent unit (GRU), but whose internal weights are designed to reflect the water storage capacity and drainage rate of the corresponding physical layer. In this way, the multi-physical mechanism state vector can comprehensively capture the hydrological response characteristics of the watershed at different vertical levels.

[0099] like Figure 3 As shown, in a further embodiment, calculating the physical guidance fusion weights includes:

[0100] The multi-physics mechanism state vector is concatenated with the high-dimensional dynamic feature vector to construct a mechanism discrimination input vector for identifying the dominant flow generation mechanism;

[0101] The mechanism discrimination input vector is input into a pre-configured mechanism probability calculation network, and the physical mechanism probability vector is calculated through a normalized exponential function. The physical mechanism probability vector contains probability components corresponding to surface runoff generation mechanism, soil runoff generation mechanism and baseflow recharge mechanism, respectively, which are used to quantify the probability that each physical mechanism dominates runoff formation at the current moment.

[0102] Based on the physical mechanism probability vector, a physical guidance fusion weight is generated to regulate the contribution ratio of extreme runoff forecast components and normal runoff forecast components. When the physical mechanism probability vector indicates that the surface runoff generation mechanism is dominant, the generated physical guidance fusion weight increases the weight ratio of the extreme runoff forecast component.

[0103] In one exemplary implementation, the physical guidance fusion weights are calculated:

[0104] π t = Softmax(G(S phys t h t ));W f t =π t ·v map W n t =1-W f t ;

[0105] Where, π t Let G be the probability vector of physical mechanisms, representing the dominant probabilities of surface runoff, subsurface runoff, and baseflow recharge mechanisms at the current moment; G is a pre-defined probability mapping network; h t For high-dimensional dynamic feature vectors; v map W is a mapping vector that maps mechanism probabilities to extreme weights; f t With W n t These are the weight values ​​for the extreme runoff forecast component and the normal runoff forecast component in the physical guidance fusion weights, respectively.

[0106] In this embodiment, different runoff generation mechanisms often correspond to different types of hydrological events. For example, when surface runoff generation mechanisms dominate, they typically correspond to extreme events such as torrential rains and floods, while when baseflow recharge mechanisms dominate, they typically correspond to normal flow during the dry season. Therefore, the competitive relationship between physical mechanisms is used to dynamically determine the weights of extreme and normal forecast components. Specifically, the probability vector π of the physical mechanism is calculated. t In the formula, G is a pre-defined probability mapping network, typically a multilayer perceptron; h t Meteorological features extracted by LSTM. The current physical state vector S... phys t With meteorological characteristics h t Mapped to a set of probability distributions, after normalization using the Softmax function, π t Each element in the matrix represents the probability that surface, subsurface, and baseflow mechanisms dominate runoff formation at the current moment. The weights W of the extreme runoff forecast components are calculated. f tIn the formula, v map The mapping vector is a learnable or pre-defined parameter vector used to convert mechanism probabilities into extreme weights. For example, the mapping coefficient corresponding to surface runoff can be set to a larger value, while the coefficient corresponding to baseflow can be set to a smaller value. The mechanism probabilities are converted into scalar weights through dot product operations. The weights W of the normal runoff forecast components are then calculated. n t Its value is equal to 1 minus W f t This is equivalent to building an expert selector based on physical principles, which can intelligently select whether the prediction network focuses on extreme or normal values ​​based on which hydrophysical process is currently occurring.

[0107] In a further embodiment, extreme runoff forecast components and normal runoff forecast components are generated, including:

[0108] Construct extreme scenario condition vectors and normal scenario condition vectors. The extreme scenario condition vector includes a multi-physics mechanism state vector, a physical mechanism probability vector, and an extreme metric factor calculated based on historical runoff observation sequences. The normal scenario condition vector includes a multi-physics mechanism state vector, a physical mechanism probability vector, and a normal state metric factor calculated based on historical runoff observation sequences.

[0109] The high-dimensional dynamic feature vector, historical runoff observation sequence and extreme scenario condition vector are concatenated and input into the extreme runoff representation network. The intermediate feature matrix of the extreme representation is extracted and the extreme runoff forecast component is output.

[0110] The high-dimensional dynamic feature vector, historical runoff observation sequence and normal scenario condition vector are concatenated and input into the normal runoff representation network. The intermediate feature matrix of the normal representation is extracted and the normal runoff forecast component is output.

[0111] During network training, orthogonal constraints are imposed on the intermediate feature matrices of extreme and normal representations to decouple the extreme runoff representation network from the normal runoff representation network in the feature space.

[0112] In other words, extreme runoff forecast components and normal runoff forecast components are generated separately, including constructing scenario condition vectors based on the following formula and performing representation learning:

[0113] c f t =Concat(S phys t , π t r f t );

[0114] c nt =Concat(S phys t , π t r n t );

[0115] z f t =Concat(h t y l c f t );

[0116] z n t =Concat(h t y l c n t );

[0117] y* far t F far =KAN far (z f t );

[0118] y* near t F near =KAN near (z n t );

[0119] Where Concat() represents the vector concatenation operation; c f t With c n t These are the extreme scenario condition vectors and the normal scenario condition vectors, respectively; r f t With r n t These are the extreme and normal measurement factors calculated based on historical runoff statistical characteristics, respectively; z f t With z n t KAN, an extreme runoff characterization network far KAN, a normal runoff characterization network near The input vector; y* far t With y* near t These are the extreme runoff forecast components and normal runoff forecast components, respectively; F far With F nearThese are the intermediate feature matrices of extreme representations and normal representations extracted by the network, respectively; y l This is a historical runoff observation sequence.

[0120] In this embodiment, to allow the dual KAN networks to better focus on their respective tasks, differentiated scene condition vectors are introduced at the input. Specifically, c f t The extreme scenario condition vector is composed of the multi-physics mechanism state vector S. phys t Physical mechanism probability vector π t and extreme metric r f t It is pieced together. Where r... f t This could be a prior probability derived from historical traffic statistics, indicating that the current timeframe falls within an extreme range. Similarly, c n t This is a normal scene condition vector, containing the normality metric r. n t Construct the network input vector. z f t KAN is an extreme runoff characterization network far The input is determined by meteorological characteristics h. t Historical runoff l With extreme scenario condition vector c f t It is pieced together. This makes KAN far While receiving data, it clearly perceives that the current encoding is based on extreme scenarios. Similarly, z n t It is the normal runoff characterization network KAN near The input is KAN. Both networks perform forward propagation. far Output extreme runoff forecast component y* far t and the extreme representation of the intermediate feature matrix F far ;KAN near Output normal runoff forecast component y* near t and the normal representation intermediate feature matrix F near Intermediate feature matrix F far and F near It is the output of the penultimate layer of the network, containing the high-dimensional feature representation learned by the network, which will be used for orthogonal constraints in the future.

[0121] In a further embodiment, generating extreme runoff forecast components and normal runoff forecast components separately further includes adding a characterizing orthogonal loss term L to a pre-configured loss function. orthoThis achieves the representation of orthogonal constraints, where the formula for calculating the orthogonal loss term is:

[0122] L ortho =|F far T F near | F ;

[0123] Among them, F far T | | represents the transpose of the intermediate feature matrix representing the extreme characteristics; F The Frobenius norm operation represents the orthogonal loss term used to minimize the correlation between extreme and normal features in the feature space.

[0124] Specifically, this approach forcibly decouples the functions of the extreme and normal networks in the feature space. In traditional dual-head networks, the two branches tend to learn similar features, leading to unclear division of labor. This embodiment introduces a representation orthogonal loss term L... ortho To solve this. Among them, F far T This represents the transpose of the intermediate feature matrix representing extreme characteristics; | | F This represents the Frobenius norm operation, which is the square root of the sum of the squares of all elements of a matrix. Calculate F... far T With F near The norm of the product of is essentially about minimizing the cross-correlation between the two characteristic matrices. When L ortho When the value approaches 0, it means that the extreme feature spaces and the normal feature spaces are geometrically orthogonal, meaning that the information they contain does not overlap. By adding this term to the total loss function, KAN is forced to... far Only those that are strongly correlated with extreme events and KAN can be learned. near Uncaptured features, such as abrupt spikes, while KAN near This focuses on learning stable background flow characteristics, improving the model's independent expressive power under different flow regimes. In one possible implementation, the total loss function L... total = l1 + l2 + 0.1 L ortho +0.05 l physics , where 0.1 is the orthogonal constraint weight and 0.05 is the physical consistency loss weight.

[0125] In some alternative implementations, the representation orthogonality constraint can also be implemented using a mutual information minimization algorithm. Specifically, a mutual information estimator can be constructed, for example, using a contrastive learning framework, defining the representation orthogonality loss term as F. far With F nearThe mutual information between them. By minimizing this mutual information, the goal of feature decoupling can also be achieved, allowing the two networks to extract statistically independent extreme and normal features respectively.

[0126] According to another aspect of this application, in watersheds lacking detailed soil hydrological parameters, or in scenarios requiring attention to sudden flood fluctuations, an instantaneous extreme index calculated based on runoff change rate can be used. Specifically, the instantaneous extreme index E... t The calculation formula is: r Qt = (Q t - Q t-1 ) / (Q t-1 + ε); E t =σ((|r Qt | -r Qbar ) / (σ rQ + ε)) * (0.5 + 0.5 * sign(r Qt ) *η t ); where r Qt Q represents the rate of change of runoff at the current moment. t The runoff prediction value output by the physical guidance module; Q t-1 The previous runoff forecast value is given; ε is a small constant to prevent division by zero; r Qbar and σ rQ These are the mean and standard deviation of the absolute values ​​of runoff change rates on the training set, respectively; sign is the sign function; η t σ represents soil moisture saturation; σ is the Sigmoid activation function. The first term in the instantaneous extremity index formula measures the anomalous magnitude of runoff variation, and the second term correlates the direction of change with soil saturation. Specifically, when there is a positive change (i.e., a sharp increase in flow rate) and the soil is at high saturation, or when there is a negative change (i.e., a sharp decrease in flow rate) and the soil is at low saturation, the calculated E... t The value will increase, allowing the model to more accurately capture the extreme characteristics during the rise and fall of flood peaks.

[0127] In a preferred implementation, based on the hierarchical fusion strategy, a physics simulation confidence mechanism is introduced to further prevent the physics module from generating misleading fusion weights under certain extreme or unknown scenarios. Specifically, the system calculates the confidence ρ of the physics simulation at the current moment. t Its calculation formula is: ρ t = exp(-λ ρ * |(Q t - Q bar ) / (Q bar +ε)|); where Q tThe runoff prediction value output by the physical guidance module; Q bar λ is the mean of the physical simulation outputs on the training set. ρ ρ represents the confidence decay coefficient. The further the physics prediction deviates from the historical mean, i.e., when the physics model enters the extrapolation region it is not good at, the lower the confidence level ρ becomes. t The lower the value, the better. Simultaneously, the system constructs a data-driven alternative weight generator in parallel, preferably implemented using a multilayer perceptron (MLP). This MLP receives high-dimensional features h extracted by LSTM. t and physical runoff Q t Output data drives the candidate weights γ' far t The calculation formula is: γ' far t = MLP(Concat(h t Q t The final adaptive fusion weights, i.e., the adaptive fusion weights w ft Weight γ is no longer driven solely by physics far t The decision is not made by the weighted combination of the two factors: w ft =ρ t * γ far t +(1 -ρ t ) *γ' far t ;w nt =1 - w ft ;where w ft The final fusion weights are represented by extreme values; w nt The final fusion weights represent the normal values. When the confidence level of the physical simulation is high, the model fully utilizes the interpretability of the physical processes; while when the confidence level of the physical simulation is low, the model automatically softly switches back to data-driven mode, using the strong fitting capability of the MLP for compensation. This enhances the robustness and generalization ability of the forecast system in complex and variable environments.

[0128] In one possible embodiment, a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms may also be:

[0129] The system receives historical meteorological forcing sequences and historical runoff observation sequences of the watershed; it encodes the historical meteorological forcing sequences using a time-series feature extraction network to generate high-dimensional dynamic feature vectors reflecting the evolution of meteorological elements over time; it constructs a multi-physical mechanism state model including surface runoff, subsurface runoff, and baseflow recharge components, updates the internal state of the model based on the historical meteorological forcing sequences, and outputs the multi-physical mechanism state vector at the current moment; it constructs parallel extreme runoff characterization networks and normal runoff characterization networks, generating extreme runoff forecast components and normal runoff forecast components based on the high-dimensional dynamic feature vectors and historical runoff observation sequences, respectively; it calculates physical guidance fusion weights based on the multi-physical mechanism state vectors, and performs weighted fusion of the extreme runoff forecast components and normal runoff forecast components to generate the final runoff forecast result; it jointly optimizes the network parameters based on a loss function containing a physical consistency constraint term, which is used to ensure that the final runoff forecast result is consistent with the physical state indicated by the multi-physical mechanism state vector.

[0130] In another possible embodiment, a runoff forecasting method based on LSTM-KAN and physical guidance mechanisms may also be:

[0131] Historical hydrological and meteorological data for the study area were collected, cleaned, and preprocessed, and then divided into training and testing sets. Specifically, the collected historical hydrological and meteorological data included meteorological element information recorded by various meteorological stations, including rainfall, air pressure (mean / extreme), relative humidity (mean / minimum), sunshine duration, and temperature (mean / extreme), as well as runoff observation data from forecast stations. To ensure the consistency of time-series data, time alignment was performed by extracting common time periods from each data series. Specifically, a unified time index benchmark was established for each data source, and the time intersection interval of all datasets was extracted as the effective modeling period. The final obtained common time-series data will be used for training and testing the hydrological forecasting model. Missing historical meteorological and hydrological data were supplemented using data from similar runoff years. Data other than rainfall meteorological elements were standardized to eliminate dimensional differences between features and labels. Standardization maps the data to a standard normal distribution with a mean of 0 and a variance of 1, thereby improving numerical stability and convergence efficiency. The formula is: x std=(xu) / σ*; where x is the original data, u is the mean of the data, and σ* is the standard deviation of the data. The standardized data was used for model training. The data was divided into a training set (80%) and a test set (20%) according to the time sequence. The model parameters were tuned on the training set, and the performance of the trained model was evaluated on the test set. LSTM was used to mine the dynamic characteristics of the evolution of meteorological forcing variables over time. KAN was applied to construct the intrinsic correlation between meteorological forcing and runoff, and the representations of extreme and normal values ​​were obtained. The two representations were fused through physics-guided gating. The model parameters were initialized and tuned through parameter optimization algorithms to obtain the runoff forecast model with the best parameters. The training loss was constrained by the data fitting loss and the correlation distance regularization loss function, so that the model not only conforms to the observed data but also learns rich representations of extreme and normal values. The runoff forecast model constructed on the training set was used to verify the model performance on the test set, and its prediction results were systematically evaluated.

[0132] In summary, the runoff forecasting method based on LSTM-KAN and physical guidance mechanisms includes: encoding historical meteorological forcing sequences using a temporal feature extraction network; constructing a multi-physical mechanism state model to decouple the calculation of surface runoff, subsurface runoff, and baseflow recharge states, and generating the dominant probability of physical mechanisms accordingly; simultaneously constructing parallel extreme and normal runoff representation networks, introducing scenario condition vectors and representation orthogonal constraints, and extracting mutually uncorrelated extreme and normal forecast components respectively; constructing a dynamic extremeity determination mechanism based on soil moisture saturation, generating physical guidance weights for adaptive weighted fusion of forecast components; and optimizing the model by incorporating physical consistency loss.

[0133] This invention employs a multi-physics mechanism state model, expanding a single state into a three-dimensional independent state vector encompassing surface, soil, and baseflow. Combined with a mechanism probabilistic routing strategy, the model can intelligently identify and switch to the dominant runoff-generating physical process based on current meteorological conditions. For example, it emphasizes surface runoff during heavy rainfall and baseflow during dry seasons, maintaining the correctness of physical logic under different hydrological scenarios. A dynamic extremity determination mechanism based on soil moisture saturation is introduced. By calculating soil saturation in real time and combining it with rainfall anomalies, the model can dynamically define extremities, accurately identifying flood risks amplified by soil saturation or rainfall processes buffered by soil dryness, achieving a qualitative leap from statistical extremes to physical response extremes. Scene condition vectors and orthogonal constraints on representations (and a mutual information minimization alternative) are introduced into the extreme and normal representation networks. The correlation between extreme and normal features is removed from the feature space, forcing the extreme network to focus on capturing abrupt changes in the long-tail distribution, thus solving the prediction bias problem caused by feature coupling.

[0134] The preferred embodiments of the present invention have been described in detail above. However, the present invention is not limited to the specific details in the above embodiments. Within the scope of the technical concept of the present invention, various equivalent transformations can be made to the technical solutions of the present invention, and these equivalent transformations all fall within the protection scope of the present invention.

Claims

1. A method for runoff prediction based on LSTM-KAN and physical guidance mechanism, characterized in that, The method comprises the following steps: receiving a historical meteorological forcing sequence and a historical runoff observation sequence of a river basin; encoding the historical meteorological forcing sequence by using a time sequence feature extraction network to generate a high-dimensional dynamic feature vector reflecting the evolution of meteorological elements over time; inputting the historical meteorological forcing sequence into a multi-physical mechanism state model comprising surface runoff generation, interflow generation and baseflow recharge mechanism to calculate and output a multi-physical mechanism state vector at the current time; inputting the high-dimensional dynamic feature vector and the historical runoff observation sequence into a parallelly arranged extreme runoff representation network and a normal runoff representation network to generate an extreme runoff prediction component and a normal runoff prediction component respectively; calculating a physical guidance fusion weight according to the multi-physical mechanism state vector, and weighting and fusing the extreme runoff prediction component and the normal runoff prediction component according to the physical guidance fusion weight to generate a final runoff prediction result; calculating the physical guidance fusion weight, comprising: splicing the multi-physical mechanism state vector and the high-dimensional dynamic feature vector to construct a mechanism discrimination input vector for identifying the dominant runoff generation mechanism; inputting the mechanism discrimination input vector into a pre-configured mechanism probability calculation network to obtain a physical mechanism probability vector by using a normalized exponential function, wherein the physical mechanism probability vector comprises probability components corresponding to the surface runoff generation mechanism, the interflow generation mechanism and the baseflow recharge mechanism respectively; generating a physical guidance fusion weight for regulating the contribution proportion of the extreme runoff prediction component and the normal runoff prediction component based on the physical mechanism probability vector; generating the extreme runoff prediction component and the normal runoff prediction component respectively, comprising constructing a scenario condition vector based on the following formula and performing representation learning: c f t = Concat(S phys t , π t , r f t ); c n t = Concat(S phys t , π t , r n t ); z f t = Concat(h t , y l , c f t ); z n t = Concat(h t , y l , c n t ); y* far t , F far = KAN far (z f t ); y* near t , F near = KAN near (z n t ); Where Concat() represents the vector concatenation operation; c f t With c n t These are the extreme scenario condition vectors and the normal scenario condition vectors, respectively; r f t With r n t These are the extreme and normal measurement factors calculated based on historical runoff statistical characteristics, respectively; z f t With z n t KAN, an extreme runoff characterization network far KAN, a normal runoff characterization network near The input vector; y* far t With y* near t These are the extreme runoff forecast components and normal runoff forecast components, respectively; F far With F near These are the intermediate feature matrices of extreme representations and normal representations extracted by the network, respectively; y l Historical runoff observation sequence; S phys t π is the multiphysics mechanism state vector at time t; t h is the probability vector of the physical mechanism. t It is a high-dimensional dynamic feature vector.

2. The method of claim 1, wherein, calculating and outputting the multi-physical mechanism state vector at the current time, comprising: extracting the current time rainfall input data in the historical meteorological forcing sequence; calculating the surface runoff state component at the current time by using a surface state update function based on the current time rainfall input data and the pre-stored surface runoff state component at the previous time; calculating the interflow state component at the current time by using an interflow state update function based on the current time rainfall input data and the pre-stored interflow state component at the previous time; calculating the baseflow recharge state component at the current time by using a baseflow state update function based on the current time rainfall input data and the pre-stored baseflow recharge state component at the previous time; splicing the surface runoff state component, the interflow state component and the baseflow recharge state component at the current time to obtain the multi-physical mechanism state vector at the current time.

3. The method of claim 1, wherein, generating an extreme runoff prediction component and a normal runoff prediction component, respectively, further comprising adding a representation of an orthogonality loss term L ortho to a preconfigured loss function ortho , implementing a representation of an orthogonality constraint, wherein the representation of the orthogonality loss term is calculated as L ortho =|F far T F near | F ; where F far T denotes the transpose matrix of the extreme representation intermediate feature matrix; | | F denotes the Frobenius norm operation, which characterizes the orthogonal loss term for minimizing the correlation of the extreme features and the normal features in the feature space.

4. The method of claim 1, wherein, It also comprises constructing a dynamic extremeness judgment mechanism, and calculating the soil moisture saturation, the instantaneous extremeness index and the cumulative extremeness index based on the following formula: η t = S re t / S max ; E t = η t · g P t + (1 - η t ) · g ΔS t ; E* t = α · E t + (1 - α) · E* t-1 ; where η t is the soil moisture saturation degree; S re t is the redistributed soil water state extracted from the multi-physical mechanism state vector; S max is the maximum water storage capacity of the watershed; E t is the instantaneous extremeness index; g P t is the rainfall anomaly degree calculated based on the historical meteorological forcing sequence; g ΔS t is the soil water state change anomaly degree calculated based on the time difference of the multi-physical mechanism state vector; E* t is the cumulative extremeness index, used to characterize the time series cumulative effect of consecutive extreme events; a is the time series attenuation coefficient.

5. The method of claim 4, wherein, The physical bootstrapped fusion weights are calculated, including dividing hydrological scenarios based on the cumulative extremeness index and soil moisture saturation, and calculating the physical driven extreme value weight γ according to the following strategy far t : when E t > θ E and η t > θ η，h , an extreme high flow scenario is determined and the calculation formula is: γ far t = σ (β1· (E t - θ E ) + β2· (η t - θ η，h ) ) ; when E t > θ E and η t < θ η，l , the extreme low flow scenario is determined and the calculation formula is: γ far t = σ (β3· (E t - θ E ) + β4· (θ η，l - η t )) ; Otherwise, the normal traffic scenario is determined, and the calculation formula is: far t =σ(β5·E* t ); where θ E , θ η，h , and θ η，l are extremity decision threshold, high saturation threshold, and low saturation threshold, respectively; β1to β5are learnable scaling parameters; σ() is a Sigmoid activation function; and the physically guided fusion weight is generated based on the physically driven extremum weight γ far t .

6. The method of claim 1, wherein, The multi-physical mechanism state model adopts a soil water state equation based on a gating unit to update the state, calculates and outputs a multi-physical mechanism state vector at the current time, including calculating the soil water state S at the current time based on the following formula t : R st = ReLU(W Rp P t + W Rh h t + W Rs S t-1 +b R ); i st = σ(W ip P t + W ih h t + W is S t-1 + b i ); m int = i st ·P t ; S t = m int + R st ·S t-1 -O other ; where S t is the soil water state at the current time; S t-1 is the soil water state at the previous time; P t is the rainfall data at the current time; h t is the high-dimensional dynamic feature vector; R st is the mass redistribution coefficient; i st is the input gate unit; m int is the system mass input; O other represents the outflow component containing the system mass non-closed term and the runoff output term; ReLU() is a column-normalized linear rectified activation function, and σ() is a column-normalized Sigmoid activation function; W Rp , W Rh , W Rs , b R are the weights and biases of the rainfall, dynamic features, and historical state corresponding to the calculation of the mass redistribution coefficient; W ip , W ih , W is , b i are the weights and biases of the rainfall, dynamic features, and historical state corresponding to the calculation of the input gate unit.

7. The method of claim 1, wherein, Both the extreme runoff representation network and the normal runoff representation network adopt a neural network structure based on the Kolmogorov-Arnold representation theorem, wherein the calculation formula of the jth feature of the lth layer is: x l，j =∑ i=1 nl-1 Φ l-1，j，i (x l-1，i ); where Φ l，j，i is a learnable univariate activation function approximated by a B-spline function with the expression Φ(x) = ∑ k=0 K c k B k (x) x l-1，i is the i-th input feature of the l-1 layer; n l-1 is the input feature dimension of the previous layer; B k (x) is the k-th B-spline basis function; c k is the learnable spline coefficient; K is the spline order.

8. The method of claim 1, wherein, receiving a historical meteorological forcing sequence and a historical runoff observation sequence of a river basin, comprising: establishing a unified time index benchmark, extracting the time intersection interval of all original data sources as a public period, and based on the public period, intercepting and aligning the pre-stored original data sequences to obtain aligned original data sequences; For the missing data in the aligned original data sequence, historical year data with similar runoff characteristics are retrieved to fill in the missing data, obtaining the filled original data sequence; In addition to the rainfall factor, all filled original data sequences are standardized to obtain historical meteorological forcing sequences and historical runoff observation sequences.

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