Basin flood simulation optimization method based on physical information neural network

Abstract

The invention relates to a basin flood simulation optimization method based on a physical information neural network, and aims to construct a basin flood acceleration solution mode based on PINNs, and ensure the continuity and the physical characteristics of mass conservation during model operation, and the method comprises the following steps: simulating basin flood by using an urban flood space-time simulation model; obtaining a data set required for constructing the physical neural network; physical rules are integrated and simplified into limiting conditions, so that integration of a neural network structure is facilitated; establishing a partial differential equation (PDE) used for describing river flood routing, and taking the partial differential equation as a loss function of the physical information neural network model; constructing and training a PINNs drainage basin flood model constructed on the basis of a CNN (Convolutional Neural Network); and establishing a model evaluation index and performing evaluation. The method has the beneficial effect that the speed and precision of basin flood simulation are improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of urban waterlogging in the field of hydrology and water resources, and particularly relates to a basin flood simulation optimization method based on a physical information neural network. Background Art

[0002] River basin flooding, due to its wide coverage, long duration, and destructive power, poses a threat to the safety of people's lives and property. It also has a significant impact on urban infrastructure such as transportation, electricity, and communications, disrupting normal production and life. Currently, researchers are studying river basin flood models in two ways: physics-based model simulation and numerical simulation based on machine learning (ML).

[0003] Physics-based model simulations focus on the fundamental characteristics of river floods, validating and applying extensive prior knowledge. While these simulations offer high accuracy, they also suffer from computational complexity and time-consuming computations. ML-based numerical simulations, however, require a large number of free parameters to accurately capture the underlying complexity of the data. Furthermore, they are prone to extrapolation and generalization issues, often failing to explain the reasoning and underlying mechanisms behind specific predictions.

[0004] Physically informed neural networks (PINNs) introduce physics-based regularization to neural networks. They restrict the parameter space of learnable models by modifying the loss function to include terms that encode the underlying physical knowledge. A common approach is to incorporate the residuals of partial differential equations (PDEs) into the loss function, aiming to create more physically consistent models. By using the loss function to increase prediction errors that violate the underlying physical principles, the training process produces models that minimize the data fitting error while being consistent with the underlying physical principles. This physics-informed machine learning approach has been successfully applied to various modeling tasks, such as the forward-looking problem, which is to infer the potential solutions of a system governed by known equations.

[0005] In this regard, this application extends the application of PINNs to complex real-world problems in fluid dynamics, and constructs a PINNs-based accelerated solution method for the numerical hydrodynamic simulator in the flood model, ensuring physical properties such as mass conservation during model operation. Summary of the Invention

[0006] The purpose of the present invention is to provide a basin flood simulation optimization method based on physical information neural network to solve the problems raised in the above background technology.

[0007] To achieve the above object, the present invention provides the following technical solutions:

[0008] A basin flood simulation optimization method based on physical information neural network includes the following steps:

[0009] S1: Use the Spatio-temporal flood simulation model for urban (STFS-Urban) to simulate river basin floods and obtain the data set required for building a physical neural network;

[0010] S2: Integrate the physical laws and simplify them into constraints to facilitate the integration of neural network structures;

[0011] S3: Establish a partial differential equation (PDE) to describe the evolution of river floods and use it as the loss function of the physical information neural network model;

[0012] S4: Construct and train the PINNs watershed flood model based on the CNN neural network to obtain the optimized parameters;

[0013] S5: Establish model evaluation indicators and conduct evaluation.

[0014] Furthermore, the S1 includes the following steps:

[0015] S11: Based on topographic maps and underlying surface conditions, detailed modeling of the river channels in the basin was performed. Remote sensing images and digital elevation models (DEMs) were used to determine river direction, channel width, and confluence sequence. The roughness of the channel was determined based on elevation differences. Initial river depths were designed using measured data of channel depths to assist with the design of the initial river depths. In the surface modeling of the urban pipe network, the topology of the rainwater pipe network within the study area was checked and generalized, basic pipe segment parameters (such as pipe roughness) were set, and an underground pipe network model was constructed. DEM data was input for surface runoff calculations, and surface roughness and infiltration parameters were set based on land use data. Consideration was given to the fact that when a river passes through a town, some rainwater enters the river channel through residential outfalls, adding additional flow. To more accurately simulate the hydrological conditions of the watershed, the impact of urban drainage on river flow must be considered. During the modeling process, overflows and outfalls along the river, calculated by coupling the pipe network with the surface, were used to supplement river flows. Urban rainwater discharge was then added to the river flows to complete the overall modeling of the watershed. Following these modeling steps, the Spatio-temporal Flood Simulation Model for Urban (STFS-Urban) was used to simulate flooding in the watershed and construct the dataset required for the physical neural network.

[0016] S12: Based on the results of simulated basin flooding, a training data set is constructed on the variables t (time), Y (water depth), (i, j) (pixel position), s (discharge), riverbed elevation (h), and rainfall (P).

[0017] Furthermore, the step S2 includes the following steps:

[0018] S21: The shallow water equations (SWE) are a simplified form of the Navier-Stokes equations used to describe the motion of fluids at shallow depths (such as rivers, lakes, and estuaries) that are uniform along the depth axis. The partial differential equations for flood evolution described in this paper use the shallow water equations:

[0019]

[0020] In the above formula, u is the velocity vector, t is the time, ν is the kinematic viscosity coefficient, p is the fluid pressure, ρ0 is the fluid density, and g is the acceleration due to gravity; the above formulas are the continuity equation representing the conservation of mass and the momentum equation representing the conservation of momentum, respectively. is a vector derivative (or Hami operator) that satisfies:

[0021]

[0022] in, are the time rates of change of the three coordinate axes (x, y, z) representing the spatial position, i.e., the components of the flow velocity on the three coordinate axes. The optimization simulation method used in the present invention will calculate the interaction of the fluids in the flow domain according to the above equations;

[0023] S22: For the above equations, the present invention expresses them as:

[0024] Δ(storage) = Δ(source - sink)

[0025] That is, the storage capacity in the pixel is equal to the flow difference between the source and the sink. Based on this, the fluid depth at the pixel position (i, j) predicted by the PINNs model under the optimization method at time t is and true fluid depth It can be expressed as:

[0026]

[0027] and Refers to the inflow and outflow of pixel (i, j) at time t, respectively. Δx and Δy refer to the pixel width in the x and y directions. The above formula shows that the total flow volume within the predicted time t minus the actual volume at time t-1 is equal to the total inflow minus the total outflow. Therefore, the formula can be re-expressed as:

[0028]

[0029] because represents the total outflow, It always holds true, so we can deduce that:

[0030]

[0031] This is equivalent to limiting the total amount predicted at time t so that it cannot exceed the sum of the amount of water at time t-1 and the net inflow from time t-1 to time t;

[0032] S23: Continue to integrate the continuity equation and obtain the following constraints:

[0033]

[0034] It refers to the inflow of pixel (i, j) at time t+1. The complete continuity equation is as follows:

[0035]

[0036] By integrating the physical laws and simplifying them into constraints, it is easier to integrate the neural network structure and limit the neural network gradient;

[0037] Furthermore, the step S3 includes the following steps:

[0038] S31: The PDE used in the linearized wave equation model calculation method is expressed as:

[0039]

[0040] Where c is the wave velocity, u(x, t) represents the displacement of the actual wave, is the Laplace operator,

[0041] S32: Using neural network estimation Then back propagate to get Repeat this process to obtain the n-order derivative, add it to the loss function, and optimize the basin flood simulation method based on CNN:

[0042]

[0043] The first term is the data fitting error term, and the second term is the PDE residual regularization term;

[0044] S33: After integrating the physical information of S2, the physical information loss function is defined as:

[0045]

[0046] Among them, the first item is the actual output water depth z and the predicted output water depth The mean square error between , that is, the data fitting term, is the true volume at time t-1, is the actual volume at time t+1, is the predicted volume at time t, Refers to the inflow of pixel (i, j) at time t and t-1, ReLu(x) = max(x, 0), which refers to the ramp function in mathematics and is responsible for penalizing violations of physical laws; the above formula shows that if the shallow water equations are violated, the loss function will include additional values;

[0047] S34: To ensure the effectiveness of the above physical information loss function, the loss function is scaled and regularized so that the expected MSE is less than 10 -1 m 2 :

[0048]

[0049] Among them, n x With n y Represents the total number of pixels in the modeling area in the x and y directions, ΔxΔy×n x ×n y represents the total area of the modeling region;

[0050] Furthermore, the S4 includes the following steps:

[0051] S41: The obtained basin flood evolution corresponding to each rainfall scenario is used as a training sample. Based on the CNN model framework, a neural network architecture is constructed and hyperparameters and weights are initialized. The parameters include: number of iterations (epoch), learning rate (learn_rate), batch size (batch), convolution kernel size (filter), pooling size (pooling), etc.

[0052] S43: Divide the data set into training set and test set;

[0053] S42: The loss function uses the result calculated in S3; the optimizer uses the Adam optimizer;

[0054] S43: In each iterative calculation, the training set is traversed, the loss is calculated, and the parameters are updated; whether to continue the loop is determined based on whether the loss function L < ε or the preset total number of iterations is met, where ε is a constant. When the above conditions are met, the loop is stopped;

[0055] Furthermore, the S5 includes the following steps:

[0056] S5: To evaluate the model prediction performance, this application uses two indicators:

[0057] S51: The first indicator is the root mean square error between the actual depth and the predicted depth:

[0058]

[0059] S52: Use mRMSE to get a more realistic estimate of the true error:

[0060]

[0061] Among them, Ω refers to the pixel set, Refers to the set of pixels whose actual pixel fluid depth and predicted pixel fluid depth are not 0. and Refers to the measured and predicted values of fluid depth within the Ω pixel set.

[0062] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0063] 1. Based on artificial intelligence technology, it has wide applicability and cutting-edge significance in the context of big data and cloud computing;

[0064] 2. By embedding physical knowledge into the modeling ideas of deep learning models, physically consistent simulation prediction results are obtained, thereby more accurately simulating the river flood process with high credibility;

[0065] 3. Compared with hydrological and hydrodynamic models, it can output forecast results more quickly, and the calculation speed after training can be increased by more than 300 times;

[0066] 4. Use physical constraint deep learning parameter optimization method to reduce model uncertainty. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a framework diagram of the present invention;

[0068] Figure 2 Schematic diagram of the network structure of PINNs. DETAILED DESCRIPTION

[0069] The present invention will be further described in detail below with reference to the accompanying drawings.

[0070] Example: A basin flood simulation optimization method based on physical neural network, the process is as follows Figure 1 As shown, the following steps are included:

[0071] S1: Use the Spatio-temporal flood simulation model for urban (STFS-Urban) to simulate river basin floods and construct the data set required for the physical neural network;

[0072] S2: Integrate the physical laws, simplify them into constraints, and integrate them into the physical neural network structure;

[0073] S3: Establish a partial differential equation (PDE) to describe the evolution of river floods and use it as the loss function of the physical information neural network model;

[0074] S4: Construct and train the PINNs watershed flood model based on the CNN neural network to obtain the optimized parameters;

[0075] S5: Establish model evaluation indicators and conduct evaluation;

[0076] Furthermore, the S1 includes the following steps:

[0077] S111: Based on topographic maps and underlying surface conditions, detailed modeling of the river basin was performed. Remote sensing images and digital elevation models (DEMs) were used to determine river direction, channel width, and confluence sequence. The roughness of the river channel was determined based on elevation differences. Initial river depths were designed using measured data of channel depths to assist with the design of river depths. In the surface modeling of the urban pipe network, the topology of the rainwater pipe network within the study area was examined and generalized. Basic pipe segment parameters (such as pipe roughness) were set, and an underground pipe network model was constructed. DEM data was input for surface runoff calculations, and surface roughness and infiltration parameters were set based on land use data. Consideration was given to the fact that when a river passes through a town, some rainwater enters the river channel through residential outfalls, adding additional flow. To more accurately simulate the hydrological conditions of the watershed, the impact of urban drainage on river flow must be considered. During the modeling process, the overflow and outfall flows along the river channel, calculated by coupling the pipe network with the surface, were used to supplement the river flow. Urban rainwater discharge was then added to the river flow to complete the overall modeling of the watershed.

[0078] S112: Design different flood scenarios. Design rainfall patterns (Chicago rain patterns) based on different rainfall recurrence periods (1 year, 5 years, 10 years, 20 years, 50 years, and 100 years). The peak coefficients are 0.3, 0.5, and 0.7. Each rainfall event lasts for 6 hours. Design the river source flow based on measured data, output every half hour, and generate 12 flood depth maps for each rainfall event.

[0079] S113: Use the Spatio-temporal Flood Simulation Model for Urban (STFS-Urban) to simulate flooding in the watershed. Inputs include: elevation (DEM), rainfall, land use data, headwater flow (QFIX), and infiltration coefficient. Input data requirements are as follows:

[0080] Table 1: Data requirements

[0081] Data Name Data format Data Description Digital elevation data (DEM) TIFF DEM data of the experimental area Land use type TIFF DEM data of the experimental area water depth txt Historical measured water depth data of the experimental area rainfall txt Measured water depth data of rainfall in the experimental area

[0082] S113: Flood simulation for multiple rainfall scenarios after parameter calibration using historical water depth and precipitation datasets;

[0083] S12: Construct the variables t (time), Z according to the simulated basin flood results t-1，...，t-n (water depth), (i, j) (pixel spatiotemporal position), s (discharge), riverbed elevation (h), rainfall (P 1，2，...，m ), Z t (water depth) training dataset;

[0084] Furthermore, the step S2 includes the following steps:

[0085] S21: The shallow water equations (SWE) are a simplified form of the Navier-Stokes equations used to describe the motion of fluids at shallow depths (such as rivers, lakes, and estuaries) that are uniform along the depth axis. The partial differential equations for flood evolution described in this paper use the shallow water equations:

[0086]

[0087] In the above formula, u is the velocity vector, t is the time, ν is the kinematic viscosity coefficient, p is the fluid pressure, ρ0 is the fluid density, and g is the acceleration due to gravity; the above formulas are the continuity equation representing the conservation of mass and the momentum equation representing the conservation of momentum, respectively. is a vector derivative (or Hami operator) that satisfies:

[0088]

[0089] in, are the time rates of change of the three coordinate axes (x, y, z) representing the spatial position, i.e., the components of the flow velocity on the three coordinate axes;

[0090] S22: For the above shallow water equations, the present invention expresses them as:

[0091] Δ(storage) = Δ(source - sink)

[0092] That is, the storage capacity in the pixel is equal to the flow difference between the source and the sink. Based on this, the fluid depth at the pixel position (i, j) predicted by the PINNs model under the optimization method at time t is and true fluid depth It can be expressed as:

[0093]

[0094] and Refers to the inflow and outflow of pixel (i, j) at time t, respectively. Δx and Δy refer to the pixel width in the x and y directions. The above formula shows that the total flow volume within the predicted time t minus the actual volume at time t-1 is equal to the total inflow minus the total outflow. Therefore, the formula can be re-expressed as:

[0095]

[0096] because represents the total outflow, It always holds true, so we can deduce that:

[0097]

[0098] This is equivalent to limiting the total amount predicted at time t so that it cannot exceed the sum of the water volume at time t-1 and the net inflow from t-1 to time t.

[0099] S23: Similarly, the continuity equation is integrated to obtain the following constraints:

[0100]

[0101] It refers to the inflow of pixel (i, j) at time t+1. The complete continuity equation is as follows:

[0102]

[0103] Furthermore, the step S3 includes the following steps:

[0104] S31: The PDE used in the linearized wave equation model calculation method is expressed as:

[0105]

[0106] Where c is the wave velocity, u(x, t) represents the displacement of the actual wave, is the Laplace operator,

[0107] S32: Using neural network estimation Then back propagate to get Repeat this process to obtain the n-order derivative, add it to the loss function, and optimize the basin flood simulation method based on CNN:

[0108]

[0109] The first term is the data fitting error term, and the second term is the PDE residual regularization term. The network structure diagram is as follows Figure 2 shown.

[0110] S33: After integrating the physical information in S2, the physical information loss function is defined as:

[0111]

[0112] Among them, the first item is the actual output water depth z and the predicted output water depth The mean square error between , that is, the data fitting term, is the true volume at time t-1, is the actual volume at time t+1, is the predicted volume at time t, Refers to the inflow of pixel (i, j) at time t and t-1, ReLu(x) = max(x, 0), which refers to the ramp function in mathematics and is responsible for punishing violations of physical laws; the above formula shows that if the shallow water equations are violated, the loss function will include additional values.

[0113] S34: To ensure the effectiveness of the above physical information loss function, the loss function is scaled and regularized so that the expected MSE is less than 10 -1 m 2 :

[0114]

[0115] Among them, n x With n y Represents the total number of pixels in the modeling area in the x and y directions, ΔxΔy×n x ×n y represents the total area of the modeling region,

[0116] Furthermore, the S4 includes the following steps:

[0117] S41: The obtained basin flood evolution corresponding to each rainfall scenario is used as a training sample. Based on the CNN model framework, a neural network architecture is constructed and hyperparameters and weights are initialized. The parameters include: number of iterations (epoch), learning rate (learn_rate), batch size (batch), convolution kernel size (filter), pooling size (pooling), etc.

[0118] S43: Divide the data set into training set and test set;

[0119] S42: The loss function uses the result calculated in S3; the optimizer uses the Adam optimizer;

[0120] S43: In each iterative calculation, the training set is traversed, the loss is calculated, and the parameters are updated; whether to continue the loop is determined based on whether the loss function L < ε or the preset total number of iterations is met, where ε is a constant. When the above conditions are met, the loop is stopped;

[0121] Furthermore, the S5 includes the following steps:

[0122] S5: To evaluate the model prediction performance, this application uses two indicators:

[0123] S51: The first indicator is the root mean square error between the actual depth and the predicted depth:

[0124]

[0125] S52: Use mRMSE to get a more realistic estimate of the true error:

[0126]

[0127] Among them, Ω refers to the pixel set, Refers to the set of pixels whose actual pixel fluid depth and predicted pixel fluid depth are not 0. and Refers to the measured and predicted values of fluid depth within the Ω pixel set.

[0128] The above description is intended only to help understand the method and core concepts of the present invention. At the same time, according to the ideas of the present invention in specific embodiments and scope of application, ordinary technicians may make appropriate modifications. Therefore, the contents of this specification should not be regarded as limiting the present invention.

Claims

1. A basin flood simulation optimization method based on physical information neural network, characterized in that: The method comprises the following steps: S1: Use the urban flood spatiotemporal simulation model to simulate basin flooding and obtain the data set required for constructing the physical neural network; S2: Integrate the physical laws, simplify them into constraints, and integrate the neural network structure; S3: Establish a partial differential equation to describe the evolution of river floods and use it as the loss function of the physical information neural network model; S4: Construct and train the PINNs watershed flood model based on the CNN neural network to obtain the optimized parameters; S5: Establish model evaluation indicators and conduct evaluation.

2. The basin flood simulation optimization method based on physical information neural network according to claim 1 is characterized by: S11: Use the spatiotemporal urban flood simulation model to simulate river basin flooding, taking into account the additional flow caused by urban drainage when the river basin flows through the city; S12: Construct a training data set of variables including time t, water depth z, pixel position (i, j), flow s, riverbed elevation h, and rainfall P based on the results of simulated basin flooding.

3. The basin flood simulation optimization method based on physical information neural network according to claim 2 is characterized in that: The S2 comprises the following steps: S21: Shallow Water Equations (SWE) are a simplified form of the Navier-Stokes equations used to describe the flow of fluids at shallow depths that are uniform along the depth axis. The partial differential equations for flood evolution use the shallow water equations: In the above formula, u is the velocity vector, t is the time, ν is the kinematic viscosity coefficient, p is the fluid pressure, ρ0 is the fluid density, and g is the acceleration due to gravity; the above formulas are the continuity equation representing the conservation of mass and the momentum equation representing the conservation of momentum, respectively. is a vector derivative or Hami operator, satisfying: in, are the time rates of change of the three coordinate axes (x, y, z) representing the spatial position, that is, the components of the flow velocity on the three coordinate axes, S22: For the above shallow water equations, it can be expressed as: Δ(storage) = Δ(source - sink) That is, the storage capacity in the pixel is equal to the flow difference between the source and the sink. Based on this, the fluid depth at the pixel position (i, j) predicted by the PINNs model under the optimization method at time t is and true fluid depth Expressed as: and Refers to the inflow and outflow of pixel (i, j) at time t, respectively. Δx and Δy refer to the pixel width in the x and y directions. The above formula shows that the total flow volume within the predicted time t minus the actual volume at time t-1 is equal to the total inflow minus the total outflow. Therefore, the formula can be re-expressed as: because represents the total outflow, It always holds true, so we can deduce that: This is equivalent to limiting the total amount predicted at time t so that it cannot exceed the sum of the amount of water at time t-1 and the net inflow from time t-1 to time t; S23: Continue to integrate the continuity equation and obtain the following constraints: It refers to the inflow of pixel (i, j) at time t+1. The complete continuity equation is as follows:

4. The basin flood simulation optimization method based on physical information neural network according to claim 3 is characterized in that: The S3 includes the following steps: S31: The PDE used in the linearized wave equation model calculation method is expressed as: Where c is the wave velocity, u(x, t) represents the displacement of the actual wave, is the Laplace operator, S32: Using neural network estimation Then back propagate to get Repeat this process to obtain the n-order derivative, add it to the loss function, and optimize the basin flood simulation method based on CNN: The first term is the data fitting error term, and the second term is the PDE residual regularization term. S33: After integrating the physical information of S1, the physical information loss function is defined as: Among them, the first item is the actual output water depth z and the predicted output water depth The mean square error between , that is, the data fitting term, is the true volume at time t-1, is the actual volume at time t+1, is the predicted volume at time t, Refers to the inflow of pixel (i, j) at time t and t-1, ReLu(x) = max(x, 0), which refers to the ramp function in mathematics and is responsible for the penalty for violating the laws of physics. S34: To ensure the effectiveness of the above physical information loss function, the loss function is scaled and regularized so that the expected MSE is less than 10 -1 m 2 : Among them, n x With n y Represents the total number of pixels in the modeling area in the x and y directions, ΔxΔy×n x ×n y Represents the total area of the modeling region.

5. The basin flood simulation optimization method based on physical information neural network according to claim 4 is characterized in that: The S4 comprises the following steps: S41: The obtained basin flood evolution corresponding to each rainfall scenario is used as a training sample, and a neural network architecture is constructed based on the CNN model framework and hyperparameters and weights are initialized. The parameters include: epoch, learning rate, batch size, convolution kernel size, and pooling size. S43: Divide the data set into training set and test set; S42: The loss function uses the result calculated in S3; the optimizer uses the Adam optimizer; S43: In each iterative calculation, the training set is traversed, the loss is calculated, and the parameters are updated; whether to continue the loop is determined based on whether the loss function L<ε or the preset total number of iterations is met, where ε is a constant. When the above conditions are met, the loop is stopped.

6. The basin flood simulation optimization method based on physical information neural network according to claim 5 is characterized in that: The S5 comprises the following steps: S5: To evaluate the model prediction performance, two indicators are used: S51: The first indicator is the root mean square error between the actual depth and the predicted depth: S52: Use mRMSE to get a more realistic estimate of the true error: Among them, Ω refers to the pixel set, Refers to the set of pixels whose actual pixel fluid depth and predicted pixel fluid depth are not 0. and Refers to the measured and predicted values of fluid depth within the Ω pixel set.

7. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the program, the method for optimizing watershed flood simulation based on a physical information neural network as described in any one of claims 1 to 6 is implemented.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed by the processor, a watershed flood simulation optimization method based on physical information neural network as described in any one of claims 1 to 6 is implemented.

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