Liquid neural network-based cdom absorption coefficient inversion method and system

Abstract

The application discloses a CDOM absorption coefficient inversion method and system based on a liquid neural network, and relates to the technical field of water ecological environment remote sensing monitoring. The method comprises the following steps: performing spectral transformation on in-situ hyperspectral observation data based on the matching relationship between remote sensing data and hyperspectral data, and performing feature reconstruction on equivalent multi-spectral reflectivity by using the mapping relationship between remote sensing reflectivity spectrum and CDOM optical characteristics; constructing an LNN network with continuous time dynamics characteristics, and performing multi-round iterative training on the LNN network based on remote sensing spectrum variation process by using training samples; and performing inversion on the remote sensing observation data to be predicted by using the trained LNN network, so as to obtain the CDOM absorption coefficient inversion result corresponding to the time step. The application uses the LNN with continuous time dynamic modeling capability to simulate the nonlinear relationship between remote sensing spectrum information and the CDOM absorption coefficient, and constructs a CDOM remote sensing inversion model with accuracy and reliability.

Description

Technical Field

[0001] This invention relates to the field of remote sensing monitoring technology for aquatic ecological environment, and in particular to a method and system for inverting CDOM absorption coefficients based on liquid neural networks. Background Technology

[0002] The statements in this section are merely background information related to the present invention and do not necessarily constitute prior art.

[0003] Colored Dissolved Organic Matter (CDOM), one of the important optically active substances in water, is a significant component of dissolved organic carbon (DOC), and its absorption characteristics are particularly pronounced in the ultraviolet to visible light range. However, current technology cannot directly measure CDOM concentration; therefore, the CDOM absorption coefficient is typically used to characterize the concentration of dissolved organic matter in water. Large-scale and continuous estimation of the CDOM absorption coefficient has significant application value for water environment monitoring, water quality assessment, and carbon cycle process analysis.

[0004] Currently, CDOM absorption coefficients are mainly obtained through on-site sampling combined with laboratory spectroscopic measurements. While this method offers high accuracy, it suffers from drawbacks such as long sampling periods, limited spatial coverage, and high costs, making it difficult to meet the practical needs of large-scale, continuous water environment monitoring. With the development of remote sensing technology, using remote sensing data to retrieve CDOM absorption coefficients from water bodies has become an important means of achieving regional and even global-scale water quality monitoring.

[0005] Liquid Neural Networks (LNNs) are neural network models based on continuous-time dynamics. They feature a small number of parameters and strong dynamic modeling capabilities, enabling them to adaptively characterize state changes in complex nonlinear systems. They are suitable for describing continuous variations in remote sensing spectral data. In the remote sensing inversion of CDOM absorption coefficients, this type of model can theoretically effectively characterize the nonlinear relationship between spectral information and absorption characteristics, maintaining good stability even with small samples and high-noise backgrounds. This has significant scientific and application value for improving the identification of organic pollution in water bodies, supporting the source analysis of black and odorous water bodies, and serving integrated land-sea governance.

[0006] However, the complexity of the aquatic environment makes it difficult to accurately model the CDOM absorption coefficient remote sensing inversion process using liquid neural networks. Typically, it is assumed that the optical properties of water bodies are relatively stable in space and time, making it difficult to effectively characterize the nonlinear and dynamic features of the CDOM absorption coefficient under complex aquatic conditions, which vary with spectral and environmental factors. Under multi-source remote sensing observation conditions, the combined effects of differences in water body optical background, changes in observation conditions, and noise interference result in significant uncertainties in the CDOM absorption coefficient remote sensing inversion process. Traditional methods struggle to simultaneously guarantee inversion accuracy and stability across different water bodies and observation scenarios. Furthermore, in Class II water bodies, the CDOM optical signal is easily affected by multiple factors such as suspended sediment, chlorophyll a, and changes in water structure, exhibiting significant nonlinear and time-varying characteristics between remote sensing reflectance and CDOM concentration. Existing CDOM remote sensing inversion models have fixed parameters, making it difficult to adapt to different water body types, multi-temporal remote sensing observations, and changes in environmental conditions, resulting in insufficient model generalization ability and robustness. Summary of the Invention

[0007] To address the shortcomings of existing technologies, the present invention aims to provide a CDOM absorption coefficient inversion method and system based on liquid neural networks. By utilizing LNNs, which have continuous-time dynamic modeling capabilities, the nonlinear relationship between remote sensing spectral information and CDOM absorption coefficients is simulated, thereby constructing a CDOM remote sensing inversion model that combines accuracy and reliability.

[0008] To achieve the above objectives, the present invention is implemented through the following technical solution:

[0009] The first aspect of this invention provides a method for inverting the CDOM absorption coefficient based on a liquid neural network, comprising the following steps:

[0010] We acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the aquatic environment. Based on the matching relationship between remote sensing data and hyperspectral data, we perform spectral transformation on the in-situ hyperspectral observation data to obtain the equivalent multispectral reflectance. We then use the mapping relationship between the remote sensing reflectance spectrum and the optical properties of CDOM to reconstruct the features of the equivalent multispectral reflectance, resulting in training samples composed of CDOM sensitive feature vectors and remote sensing feature matrices.

[0011] Construct an LNN network with continuous-time dynamics and perform multiple rounds of iterative training on the LNN network using training samples;

[0012] The trained LNN network is used to invert the remote sensing observation data to be predicted, and the inversion results of the CDOM absorption coefficient at the corresponding time step are obtained.

[0013] A second aspect of the present invention provides a CDOM absorption coefficient inversion system based on a liquid neural network, comprising:

[0014] The data acquisition module is configured to acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient and water environment auxiliary parameters. Based on the matching relationship between remote sensing data and hyperspectral data, the in-situ hyperspectral observation data is spectrally transformed to obtain equivalent multispectral reflectance. The equivalent multispectral reflectance is reconstructed using the mapping relationship between remote sensing reflectance spectrum and CDOM optical properties to obtain training samples composed of CDOM sensitive feature vector and remote sensing feature matrix.

[0015] The network construction and training module is configured to construct an LNN network with continuous-time dynamics and perform multiple rounds of iterative training on the LNN network using training samples.

[0016] The inversion module is configured to use a trained LNN network to invert the remote sensing observation data to be predicted, and obtain the CDOM absorption coefficient inversion results for the corresponding time step.

[0017] A third aspect of the present invention provides a computer-readable storage medium storing a computer program adapted to be loaded by a processor and executed the steps of the CDOM absorption coefficient inversion method based on a liquid neural network as described in the first aspect of the present invention.

[0018] A fourth aspect of the present invention provides a computer device comprising:

[0019] A processor, adapted to execute computer programs;

[0020] A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the CDOM absorption coefficient inversion method based on a liquid neural network as described in the first aspect of the present invention.

[0021] A fifth aspect of the present invention provides a computer program product or computer program comprising computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the CDOM absorption coefficient inversion method based on a liquid neural network as described in the first aspect of the present invention.

[0022] The above one or more technical solutions have the following beneficial effects:

[0023] This invention discloses a method and system for CDOM absorption coefficient inversion based on a liquid neural network. By introducing a liquid neural network (LNN) with continuous-time dynamic modeling capabilities, the nonlinear mapping relationship between remote sensing spectral information and the CDOM absorption coefficient is simulated, improving the accuracy and reliability of CDOM remote sensing inversion under complex aquatic environments and multi-source remote sensing conditions. The LNN of this invention can fully mine the dynamic evolution process information of CDOM in multi-temporal remote sensing data and construct a model with adaptive parameter adjustment capabilities. This model can maintain high inversion accuracy and robustness under complex water bodies and long-term monitoring conditions, improving the applicability and promotion value of the CDOM absorption coefficient remote sensing inversion method.

[0024] This invention employs the LNN algorithm to perform continuous-time modeling of remote sensing spectral features, effectively characterizing the dynamic response of CDOM absorption characteristics to changes in time and environment. It is suitable for remote sensing inversion applications where water environments change frequently and temporal characteristics are significant. This characteristic is beneficial for depicting the formation and evolution of polluted water bodies such as black and odorous water bodies, providing key technical support for the identification and source tracing analysis of organic pollution.

[0025] This invention enhances key spectral information that significantly responds to CDOM absorption characteristics through remote sensing spectral matching and sensitive feature mapping, reduces the influence of non-target optical background elements such as suspended matter and chlorophyll on the inversion results, and improves the ability to distinguish different levels of CDOM absorption, thereby improving the accuracy and stability of the inversion results.

[0026] This invention applies non-negative constraints and reasonable value range restrictions to the CDOM absorption coefficient in the inversion output stage, so that the inversion results conform to the physical meaning of water body optical parameters, effectively avoiding unreasonable CDOM prediction results caused by abnormal input or noise conditions, and improving the reliability and engineering usability of the LNN method in practical applications.

[0027] This invention, by constraining temporal continuity and dynamic consistency, suppresses non-physical fluctuations in inversion results in multi-temporal remote sensing data, enabling CDOM absorption coefficient inversion results to maintain good smoothness and consistency over time series, making it suitable for long-term, continuous water environment monitoring tasks.

[0028] The method of this invention is adaptable to multi-source remote sensing data and different types of aquatic environments, and has good applicability in complex aquatic environments such as lakes, reservoirs, rivers, estuaries, and nearshore sea areas. Through continuous monitoring and inversion of the CDOM absorption coefficient, it can provide basic data support for the supervision of urban and rural black and odorous water bodies, the analysis of organic matter transport processes in land-sea integrated areas, and the assessment of carbon sinks in aquatic ecosystems, demonstrating good versatility.

[0029] Advantages of additional aspects of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0030] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0031] Figure 1 This is a flowchart of the CDOM absorption coefficient inversion method based on liquid neural network in Embodiment 1 of the present invention. Detailed Implementation

[0032] It should be noted that the following detailed descriptions are exemplary and intended to provide further illustration of the invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains.

[0033] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the scope of exemplary embodiments according to the invention. As used herein, unless the context clearly indicates otherwise, the singular form is also intended to include the plural form. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0034] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of this application.

[0035] Example 1:

[0036] Embodiment 1 of this invention provides a method for inverting the CDOM absorption coefficient based on a liquid neural network, such as... Figure 1 As shown, it includes the following steps:

[0037] S1: Acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the water environment. Based on the matching relationship between remote sensing data and hyperspectral data, perform spectral transformation on the in-situ hyperspectral observation data to obtain equivalent multispectral reflectance. Utilize the mapping relationship between remote sensing reflectance spectrum and CDOM optical properties to reconstruct the features of the equivalent multispectral reflectance, obtaining training samples composed of CDOM sensitive feature vector and remote sensing feature matrix.

[0038] S1.1: Acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the aquatic environment.

[0039] In one specific implementation, multi-source remote sensing image data is obtained by downloading high-quality Sentinel-2 MSI images with minimal cloud cover. In-situ hyperspectral observation data time-matched to the remote sensing images are collected. Water quality samples from typical water bodies such as lakes, reservoirs, estuaries, and nearshore waters are collected along with satellite-ground synchronous observation data through synchronous or quasi-synchronous field observations. The corresponding CDOM absorption coefficients are measured, and auxiliary water environment parameters such as suspended particulate matter concentration, chlorophyll a concentration, transparency, water temperature, salinity, and meteorological conditions are recorded to construct a CDOM measured dataset covering different hydrological and environmental conditions.

[0040] S1.2: Based on the matching relationship between remote sensing data and hyperspectral data, perform spectral transformation on in-situ hyperspectral observation data to obtain equivalent multispectral reflectance.

[0041] S1.2.1: The data preprocessing and standardization module is used to preprocess and standardize multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient and auxiliary parameters of water environment.

[0042] Specifically, radiometric calibration, geometric correction, and atmospheric correction are performed on multi-source remote sensing image data to obtain remote sensing reflectance data. In-situ hyperspectral observation data undergoes quality control and normalization to construct a remote sensing reflectance spectral library and establish a correspondence with measured CDOM absorption coefficients, providing fundamental data support for subsequent model training and validation. This also includes quality control and preprocessing of all data, removing missing and outlier values ​​to ensure data integrity, and performing temporal matching and spatial registration of data from different sources to guarantee consistency between remote sensing observations and measured samples. All data are also standardized.

[0043] S1.2.2: Perform spectral transformation processing on in-situ hyperspectral observation data.

[0044] In one specific implementation, since hyperspectral data acquired in the laboratory or field has the characteristics of continuous bands and high spectral resolution, while multispectral satellite data is often used for water body monitoring and inversion in actual remote sensing applications, in order to improve the applicability and generalization ability of the model in real remote sensing scenarios, the in-situ hyperspectral observation data is subjected to spectral transformation processing before model construction. Specifically, using the band settings of the target multispectral sensor and the corresponding spectral response function (SRF), the continuous hyperspectral bands are weighted, integrated, and resampled to convert the in-situ hyperspectral observation data into equivalent multispectral reflectance data. This process can be expressed as:

[0045] .

[0046] Where R(λ) represents hyperspectral reflectance, SRFi(λ) is the spectral response function of the i-th multispectral band, and Ri is the corresponding equivalent multispectral reflectance value; λ represents wavelength, λ1 represents the band start wavelength, and λ2 represents the band cutoff wavelength. This spectral transformation process does not involve model training parameters and is a deterministic spectral preprocessing step. It can reduce spectral redundancy while preserving key spectral information, providing a unified data input format for the stable training of the subsequent CDOM remote sensing inversion model.

[0047] In practical remote sensing applications, the Sentinel-2 satellite, with its high spatial resolution and visible-near-infrared band sensitivity to water color, is widely used for the inversion of optical parameters of water bodies. Therefore, using the Sentinel-2 multispectral sensor as the target sensor, spectral resampling processing is performed on the hyperspectral data to ensure that the model input is consistent with the actual satellite observation data in terms of spectral structure.

[0048] After completing the spectral transformation from hyperspectral data to equivalent multispectral data, the resulting equivalent multispectral reflectance is used as the input feature of the LNN.

[0049] S1.3: The equivalent multispectral reflectance is reconstructed using the mapping relationship between the remote sensing reflectance spectrum and the optical properties of CDOM, resulting in training samples composed of CDOM sensitive feature vectors and remote sensing feature matrices.

[0050] In one specific implementation, the remote sensing spectral analysis module is a key link in realizing the high-precision conversion of remote sensing observation information into water body optical parameters. Its core objective is to establish a stable and reliable mapping relationship between the remote sensing reflectance spectrum and the CDOM absorption coefficient.

[0051] To address the spectral inconsistencies caused by differences in water body types, observation conditions, and sensor responses, this module systematically processes and reconstructs the remote sensing spectra through steps such as constructing a water body optical parameter database, remote sensing spectral matching and feature optimization, and CDOM sensitive spectral feature screening. This gradually reduces the interference of non-target optical information and changes in observation conditions on the inversion results, highlighting the effective spectral information of CDOM absorption characteristics. Through this multi-level processing, this module provides highly consistent and discriminative input features and constraint information for subsequent LNN models, laying a stable data foundation for remote sensing inversion of CDOM absorption coefficients.

[0052] Ultimately, the CDOM sensitive spectral feature vector, as the main input feature of the LNN algorithm, together with the corresponding CDOM absorption coefficient and aquatic environment auxiliary parameters in the CDOM optical parameter database, constitutes the training sample, realizing the efficient mapping of remote sensing spectral information to CDOM absorption coefficient, and providing direct support for the stable training and accurate inversion of the subsequent LNN model.

[0053] Among them, spectral feature extraction and sensitive band screening are performed to extract multi-band water reflectance information from multi-source remote sensing image data of Sentinel-2, and continuous wavelet transform is used to decompose the spectral information into multiple scales to obtain spectral features at different scales.

[0054] The specific steps are as follows:

[0055] S1.3.1: Perform continuous wavelet transform on the equivalent multispectral reflectance.

[0056] In one specific implementation, multi-scale analysis of equivalent multispectral reflectance is performed using wavelet basis functions, enabling signal decomposition at different frequencies and time scales. This method is particularly suitable for analyzing non-stationary signals such as spectra. The specific formula is as follows:

[0057] .

[0058] in, ψ(t) is the wavelet function at scale a and position b; f(t) is the wavelet basis function; a is the absorption coefficient, which is the scale parameter and controls the frequency resolution; b is the position parameter and controls the signal position. It is the conjugate wavelet function after scaling and translation.

[0059] S1.3.2: Feature band selection based on inversion stability and sensitivity requirements.

[0060] In one specific implementation, based on the requirements of inversion stability and sensitivity, bands with a signal-to-noise ratio (SNR) greater than 5dB, a mean square error (MSE) less than 0.1, and a correlation test p-value with the CDOM absorption coefficient less than 0.05 are selected.

[0061] S1.3.3: Correlation analysis was performed on the equivalent multispectral reflectance and the CDOM absorption coefficient to obtain the CDOM sensitive feature vector and remote sensing feature matrix.

[0062] In one specific implementation, the Pearson correlation coefficient between the equivalent multispectral reflectance and its transformation characteristics and the CDOM absorption coefficient is calculated. Sensitive bands with an absolute correlation coefficient greater than 0.6 are selected to enhance the model's response to changes in the CDOM absorption coefficient and improve the accuracy and stability of remote sensing inversion. The equivalent multispectral reflectance transformation characteristics include band ratios and the Floating Algae Index (FAI).

[0063] Simultaneously, the correlation between each band and its wavelet coefficients and the CDOM absorption coefficient was calculated to screen out key bands and features that showed significant and stable responses to changes in the CDOM absorption coefficient, thereby characterizing the optical absorption properties of the CDOM in water. Specifically, this embodiment uses Pearson correlation analysis to calculate the correlation between each original spectral band and wavelet coefficients at different scales and the CDOM absorption coefficient.

[0064] This embodiment utilizes continuous wavelet transform (CWT) to extract multi-scale spectral features of remote sensing reflectance data in the 400-900nm band, which are used to characterize the intrinsic and apparent optical absorption properties of the CDOM absorption coefficient at different spectral scales.

[0065] S2: Construct an LNN network with continuous-time dynamics and use training samples to perform multiple rounds of iterative training on the LNN network.

[0066] In one specific implementation, based on the constructed training samples, multi-band remote sensing reflectance data (equivalent multispectral reflectance) of the same water body acquired at different times are used to construct an input feature vector X. t And construct a time series input X in chronological order. in =[X1,…,X T The liquid neural network (LNN) inputs time-series features, and models the changes in remote sensing spectra by continuously updating the state of liquid neurons over time. It then outputs the CDOM absorption coefficient inversion results for the corresponding time step, achieving time-phase remote sensing inversion of the CDOM absorption coefficient.

[0067] In one specific implementation, this embodiment also applies post-processing constraints to the CDOM absorption coefficient results output by the LNN: First, a non-negative constraint is applied to the inversion results, and the range of values ​​is limited to a reasonable range obtained based on the statistical analysis of measured samples; Second, a temporal continuity constraint is applied to the CDOM inversion results of the same pixel at adjacent time steps. When the difference between adjacent time phases exceeds a preset threshold, abnormal results are corrected or smoothed to reduce the impact of remote sensing observation noise and instantaneous environmental disturbances on the inversion results.

[0068] S2.1: Construct an LNN network with continuous-time dynamics.

[0069] In one specific implementation, considering the continuous evolution of the CDOM absorption coefficient across time and space under complex water conditions, this embodiment does not treat the CDOM absorption coefficient as an independent, static inversion object. Instead, it models it as a dynamic state variable driven by both historical optical conditions and current remote sensing observations. Based on this, a continuous-time dynamics neural network (LNN) is introduced to construct a continuous-time state modeling framework for CDOM absorption coefficient remote sensing inversion. The inversion prediction module is used to invert the initial parameters to characterize the dynamic response process of CDOM absorption characteristics as environmental conditions change.

[0070] Unlike traditional static neural networks that rely solely on the input features at the current moment to establish a mapping relationship, LNNs achieve adaptive memory and decay of historical information through the continuous evolution of internal states in the time dimension. This allows them to simultaneously characterize the instantaneous response features and long-term cumulative effects of the CDOM absorption coefficient within a unified state space, thereby improving the stability and physical consistency of the model in multi-temporal remote sensing inversion tasks.

[0071] S2.1.1: Design an input-state coupling structure for state transition of input parameters.

[0072] In one specific implementation, the input data includes, but is not limited to, the following types: remote sensing reflectance Rrs (covering the 400-900nm band), spectral indices (NDCI, FAI), surface water temperature (SST), suspended particulate matter concentration (SPM), and other auxiliary parameters of the water environment that can reflect the optical and environmental state of the water body. In the time dimension, the input can be either a multi-temporal remote sensing observation sequence or a single-temporal remote sensing image; when it is a single-temporal image, the time dimension T is 1. At each time step, the above multi-source input features are concatenated along the channel dimension to form an input tensor, which is represented as follows:

[0073] .

[0074] Among them, X in The tensor representing the input data of the model. B indicates that the data belongs to the real number field, C indicates the number of batch samples, and T indicates the length of the time series.

[0075] To eliminate the impact of differences in feature dimensions under different sensors and water conditions on model stability, this embodiment performs linear projection and normalization operations on the input features. Specifically, a 1×1 convolution operator is used to achieve linear mapping between channels, mapping the input features to a unified latent space dimension Dmodel. Combined with layer normalization, the state-driven input E is obtained.

[0076] .

[0077] in, The normalization results are standardized by calculating the mean and variance of the sample features, and then adjusted using learnable parameters. This represents a set of convolution operators used for local weighted mapping and feature extraction of input sequence features.

[0078] This embodiment preserves the physical meaning of the original spectrum and environmental features through the above steps, and converts them into external excitation signals suitable for continuous state updates of LNN, providing stable and controllable input boundary conditions for subsequent state evolution processes.

[0079] S2.1.2: Construct a continuous-time state update mechanism to adaptively adjust the weight ratio of historical states and current input features in state updates based on the time interval and the rate of state change.

[0080] In one specific implementation, at each moment, the internal state of the previous moment is... With the input feature vector at the current time The parts are then assembled. Among them, Dynamic memory information characterizing the optical state of CDOM at historical moments; The input features are based on the current observation conditions, specifically including multi-band remote sensing reflectance features, multi-scale spectral features extracted through continuous wavelet transform, and hydrological and environmental driving factors closely related to the CDOM absorption process. .

[0081] Then, the concatenated state-feature vector is transformed using a linear mapping to construct an intermediate driving term, the expression of which is:

[0082] .

[0083] in, It is the gating (or intermediate drive) vector at time t, reflecting the result of information adjustment; This is the hidden state (historical information) from the previous moment. The input features at the current time; To concatenate historical states with the current input to form a joint feature vector; It is a learnable weight matrix used to perform linear mapping on joint features; This is the bias term, used to shift the translation mapping result.

[0084] This driving term is used to comprehensively characterize the coupling relationship between historical state and current spectral-water quality characteristics. Its physical meaning corresponds to the response gain or suppression effect of CDOM absorption signal under different water body backgrounds.

[0085] Adaptive modulation mechanism of time constant: To simulate the memory effect and attenuation behavior in water optical processes, this invention introduces an adaptive time constant τ for each state dimension, the calculation formula of which is as follows:

[0086] .

[0087] in, The weight matrix is ​​f, which consists of trainable parameters. t The input feature vector representing time t; This is a bias term used to adjust the overall activation level; This is the Sigmoid activation function, used to constrain the time constant within a reasonable range; is the adjustment coefficient at time t, used to control information retention.

[0088] A closed-form solution for continuous-time state updates is established. Under the combined effect of the aforementioned driving term and the time constant, the state update of the liquid neuron adopts an exponential decay form:

[0089] .

[0090] in, This represents the internal state of the liquid neuron at time t, used to characterize the dynamic memory features of the CDOM absorption coefficient; The historical state of the previous moment is represented by the driving term, which is determined by the spectral input characteristics of the current moment and the historical state, and is used to characterize the instantaneous response of CDOM to environmental disturbances (such as changes in hydrological conditions and changes in material input). The exponential decay term reflects the natural decay process of historical information over time, thereby achieving a unified modeling of long-term cumulative effects and current spectral response in state updates.

[0091] and, t represents the time step between adjacent observations; when it is a single-phase image, t is taken as a fixed constant. Through this continuous-time state update mechanism, the model can adaptively adjust the weight ratio of historical states and current input features in the state update according to the time interval and the rate of state change, thereby stably expressing the continuous evolution process of the CDOM absorption coefficient with environmental changes within a unified state space.

[0092] Through the aforementioned continuous-time state update mechanism, the model can adaptively balance the contribution ratio of historical information and current input features in the state evolution according to the observation time interval and the state change rate, and stably describe the continuous change process of the CDOM absorption coefficient over time within a unified state space.

[0093] S2.1.3: Model the multi-temporal input sequence and extract state features.

[0094] In one specific implementation, the process includes a time-recursive optical-assisted information modeling state and a time-step-based dynamic update step for weight coefficients. Let the internal state vector at time t be h. t This state vector is used to characterize the potential dynamic state of CDOM absorption properties, focusing on the comprehensive evolution of CDOM absorption intensity, spectral morphology, and source structure over time and space. This state vector serves as the memory unit of the LNN liquid neuron, used to retain the cumulative effect of CDOM optical processes under historical observation conditions.

[0095] The inversion input time series for CDOM absorption coefficients is not a single-time remote sensing spectral observation data, but rather a time series input consisting of remote sensing features acquired at multiple observation times for the same water body spatial unit. Specifically, for the same water body pixel or spatial unit, the input data at different times t1, t2…t… n Next, the corresponding remote sensing observation feature vectors are obtained, forming the following input sequence:

[0096] X in ={X1,X2,…,X T}

[0097] Wherein, the input feature vector X at each time step t It consists of one of the following two forms: a multi-band remote sensing reflectance vector, which contains several visible and near-ultraviolet reflectance values ​​related to the absorption characteristics of CDOM; and a CDOM sensitive feature vector obtained after the aforementioned remote sensing spectral matching and feature mapping steps, which is used to characterize the comprehensive feature information that is highly correlated with the changes in CDOM absorption coefficient in remote sensing observations. The above input sequence maintains sequential consistency in the time dimension, which is used to describe the process of spectral characteristics of the same water body changing with time at different observation times, and provides the basic input for the subsequent dynamic inversion of CDOM absorption coefficient.

[0098] LNNs dynamically model the time series through continuous recursion of internal states. After completing the state update along the time dimension, the final stable state or time-weighted average state is extracted as the global state feature representation, which takes the following form:

[0099] .

[0100] Among them, H out This is the hidden state representation for the final output. B indicates that the data belongs to the real number field, B represents the batch sample size, and D represents the number of samples in the batch. model This is the hidden space dimension.

[0101] The state feature vector comprehensively reflects the overall evolution characteristics of the CDOM absorption coefficient under multi-temporal observation conditions, providing a highly stable and discriminative state input for subsequent quantitative inversion.

[0102] By constructing a continuous-time dynamics-based LNN structure, this embodiment achieves a unified modeling of the dynamic relationship between remote sensing spectral information and the CDOM absorption coefficient. This structure can not only finely characterize the instantaneous spectral response of CDOM absorption characteristics, but also preserve the cumulative effect of historical optical processes through the continuous evolution of internal states, providing core model support for subsequent high-precision and robust remote sensing inversion of the CDOM absorption coefficient.

[0103] S2.1.4: The mapping output is obtained by the multi-band scale dynamic inversion process based on temporal fusion.

[0104] In one specific implementation, after extracting multi-temporal state features, the LNN utilizes a multi-band scale dynamic inversion module based on temporal fusion to map the accumulated continuous-time state vector to the target output space, thereby predicting the CDOM absorption coefficient or other water body optical parameters. This module effectively converts the dynamic features and historical accumulated information in the high-dimensional state vector into interpretable physical quantities, allowing the state space and output space to connect naturally. Simultaneously, the module can incorporate physical consistency constraints during the mapping process, such as non-negativity constraints or spectral attenuation laws, to ensure that the prediction results conform to the optical characteristics of the water body and avoid unreasonable values. By integrating historical states with current observational dynamic information, this module can smooth short-term fluctuations, enhance the stability and reliability of the output, and adapt to CDOM inversion tasks in complex water environments. Furthermore, this module provides a standardized output interface for subsequent analysis, visualization, or remote sensing applications, achieving an effective bridge from network state representation to actual water body optical parameters, ensuring the logical integrity and functional interpretability of the overall network structure.

[0105] S2.2: Use training samples to perform multiple rounds of iterative training on the LNN network.

[0106] In one specific implementation, after completing the LNN structure construction and continuous-time state modeling, this embodiment further performs end-to-end dynamic inversion and model training of the CDOM absorption coefficients based on the constructed LNN network. Unlike traditional static inversion methods that treat each observation time as independent, this embodiment focuses on the continuous evolution of the internal state of the LNN, modeling the inversion process of the CDOM absorption coefficients as a dynamic mapping problem that changes continuously with time, thereby improving the stability and physical rationality of the inversion results under multi-temporal remote sensing observation conditions.

[0107] S2.2.1: Design an inversion mapping learning from state features to CDOM absorption coefficients.

[0108] In one specific implementation, after receiving multi-temporal remote sensing feature input, the LNN uses its internal state vector h t The dynamic evolution of CDOM absorption properties is encoded. This state vector not only contains current remote sensing observation information, but also implicitly retains the cumulative influence of historical spectral states on current absorption properties.

[0109] Quantitative inversion mapping relationship construction: Through multi-level linear transformation and nonlinear activation function, the internal state vector h is transformed... t The state vector is mapped to the CDOM absorption coefficient output space to achieve quantitative inversion. Based on this, a mapping relationship between the state vector and the CDOM absorption coefficient is established through multi-level linear transformation and nonlinear activation function, realizing continuous and stable inversion of the CDOM absorption coefficient while ensuring the physical rationality of the inversion results.

[0110] A mapping relationship is established between the state vector of the liquid neural network, which contains the cumulative response of the liquid neural network to spectral features, environmental parameters, and other input features, and the CDOM absorption coefficient. The state vector comprehensively encodes the nonlinear response of multi-band spectral reflectance features, the modulation effect of environmental parameters on the spectral-absorption relationship, and the continuous evolution information of CDOM absorption characteristics between adjacent observation times, serving as the core intermediate variable for subsequent CDOM absorption coefficient inversion. During the continuous evolution of the LNN network state over time, this embodiment generates the corresponding CDOM absorption coefficient inversion result for each observation time. Specifically, for any time t, the network internal state h corresponding to that time is used to generate the inversion result. t Mapping to the output space, we obtain the inverted CDOM absorption coefficient values ​​at that moment, and their relationship can be expressed as:

[0111] .

[0112] in, The CDOM absorption coefficient inversion result at time t. and The output mapping parameters are defined by g(), which is a constraint function used to ensure the physical rationality of the output.

[0113] Therefore, this embodiment realizes a time-by-time mapping relationship from multi-temporal remote sensing feature inputs to the time series output of CDOM absorption coefficients, rather than a single time point or a single comprehensive result, thus fully depicting the change process of CDOM absorption coefficients in the time dimension. Under multi-temporal remote sensing observation conditions, the CDOM absorption coefficient inversion results obtained at different times are comprehensively analyzed and fused to form a stable comprehensive inversion result of CDOM absorption coefficients, which serves as the final output of the system for subsequent CDOM source analysis, aquatic organic matter cycle research, and aquatic environment change assessment.

[0114] S2.2.2: Construct training data and train based on a continuous-time state-driven training mechanism.

[0115] In one specific implementation, to ensure that the LNN can effectively learn the dynamic changes in the CDOM absorption coefficient, the remote sensing feature data and the measured CDOM absorption coefficient are preprocessed uniformly, including denoising, outlier removal, and standardization. The input features are constructed into a three-dimensional tensor according to temporal order and spatial correspondence, and divided into training, validation, and test sets. The model is then iteratively trained multiple times using the remote sensing feature matrix and measured CDOM data to continuously optimize the model parameters.

[0116] During training, LNN solves the continuous-time state equation using numerical integration. Training data is input into the model for forward propagation to calculate predicted values. Errors are calculated using a loss function, and model parameters are updated using a backpropagation algorithm until the model converges or reaches the set number of iterations.

[0117] Forward propagation formula: LNN uses a continuous-time state equation to propagate the internal state vector h t An integral solution is performed to progressively map the multi-temporal remote sensing feature input sequence to the predicted CDOM absorption coefficient output. At each time step, the model combines the current input X... t Compared with the previous state h t 1. The evolution of the internal state is calculated using a nonlinear activation function f() to form a new state vector h. t Furthermore, the predicted CDOM absorption coefficients for the corresponding time point are generated through output mapping.

[0118] Using the remote sensing spectral feature vector obtained through feature mapping as the external input signal, the internal state of the LNN network continuously evolves over time. Its state update process can be represented as:

[0119]

[0120] Among them, X t h represents the input feature vector at time t. t Let τ be the state vector inside the LNN network, and τ be the adaptive time constant. and Let b be the input weight matrix and the state weight matrix, respectively, b be the bias term, and f() be the nonlinear activation function.

[0121] The forward propagation formula is not only used for forward computation in LNN model training, but also provides a basic support for the physical rationality of the inversion results: through continuous state evolution, LNN can automatically accumulate historical spectral information and generate stable, continuous and physically consistent CDOM absorption coefficient predictions at each time step.

[0122] Model Evaluation: To comprehensively evaluate the robustness and generalization ability of the LNN remote sensing inversion model, K-Fold Cross-Validation was employed. Specifically, the dataset was divided into K subsets, with one subset selected sequentially as the validation set, and the remaining subsets used for training. This process was repeated K times, and the average performance index of each validation iteration was calculated. This method reduces the impact of randomness caused by data partitioning, ensuring the reliability of the evaluation results. Based on the validation results, the model structure and hyperparameters can be further adjusted to improve the accuracy and stability of CDOM inversion. Furthermore, model performance was quantitatively evaluated using multiple regression metrics, including:

[0123] Root Mean Square Error (RMSE):

[0124] .

[0125] Mean Absolute Error (MAE):

[0126] .

[0127] R² coefficient of determination (R²):

[0128] .

[0129] Relative Squared Error (RSE):

[0130] .

[0131] In the formula, This represents the CDOM value predicted by the model. This represents the corresponding observed value. is the average of the observations, N is the number of samples, and i represents the sample index.

[0132] By numerically solving the above continuous-time state equation, the steady-state representation of the LNN at each time step is obtained, and after transformation by the output mapping layer, the inversion result of the CDOM absorption coefficient at the corresponding time step is obtained.

[0133] S2.2.3: Optimize the model using the joint loss function.

[0134] In one specific implementation, to avoid the model generating predictions that violate physical laws, a joint loss function is defined when constructing the LNN network training objective. First, the mean squared error (MSE) is used as the basic loss function to measure the difference between the predicted and measured CDOM values. Second, considering the exponential decay of CDOM with increasing wavelength, a final optimization objective function is introduced, defined as follows:

[0135] .

[0136] Among them, L total For the weighted comprehensive loss function, L MSE For mean square error, L CE For cross-entropy loss, L phys Penalty for physical consistency As the weight of the data-driven error, The weights of the distribution error, The weights are the physical rule constraints.

[0137] The loss function measures the difference between the CDOM predicted value and the measured value through mean square error (MSE); by performing differential calculation on the output of adjacent time steps, the predicted sequence is smoothly transitioned, reflecting the natural evolution of the CDOM absorption coefficient over time; based on the law that the CDOM absorption spectrum decays exponentially with wavelength in the visible to near-infrared band, the output spectrum deviation is constrained to ensure that the CDOM inversion results conform to optical physical characteristics.

[0138] Thanks to the continuous-time state memory capability of LNNs, the model can integrate historical spectral information, allowing temporal continuity and spectral physical constraints to play a full role. The joint loss function ensures the stability, physical rationality, and reliability of the CDOM remote sensing inversion model under different water body types and multi-temporal observation conditions.

[0139] During model training, a gradient descent-based optimization algorithm is used to update the LNN network parameters, and the training process is dynamically monitored using a validation set to prevent overfitting or underfitting. To further improve the model's predictive performance in CDOM absorption coefficient remote sensing inversion, this embodiment introduces a hyperparameter optimization mechanism to jointly tune key parameters such as the number of liquid neurons, the range of time constants, the learning rate, and the time step. Through multiple rounds of iterative training and parameter updates, the LNN gradually converges to a stable solution in the continuous time state space, achieving adaptive matching for different water body types and multi-temporal remote sensing observation conditions.

[0140] Building upon this, this embodiment employs Bayesian optimization to systematically optimize the hyperparameters, thereby further improving the prediction accuracy and stability of the CDOM remote sensing model based on liquid neural networks. The specific steps are as follows:

[0141] 1) Design common hyperparameters (including number of liquid neurons, time constant τ, learning rate, time step Δt, Dropout, batch size, and gradient clipping).

[0142] 2) Based on the preliminary experimental results, a Gaussian process surrogate model was constructed to learn the mapping relationship between different hyperparameter configurations and the performance of the validation set.

[0143] 3) Use Gaussian process models to predict the performance distribution and uncertainty of candidate hyperparameter combinations on the validation set.

[0144] 4) Based on the expected improvement or probabilistic improvement criteria, select the optimal next set of hyperparameter combinations for model training, and evaluate its inversion performance on the validation set.

[0145] 5) Add the newly obtained hyperparameter combinations and the corresponding validation set performance results to the training samples to update the Gaussian process model.

[0146] 6) Repeat steps 3-5 to continuously iterate and search the hyperparameter space until the preset maximum number of iterations is reached or the model performance converges. Finally, determine the optimal hyperparameter configuration for CDOM inversion model construction.

[0147] Through the above strategies, this embodiment not only ensures the convergence and robustness of the model during gradient descent training, but also combines Bayesian optimization to finely tune key hyperparameters, enabling LNN to have higher accuracy, stability and generalization ability in predicting CDOM absorption coefficients under multi-temporal remote sensing conditions.

[0148] S2.3: Further optimize model parameters using a post-processing mechanism based on prior knowledge.

[0149] In one specific implementation, to avoid LNN relying solely on statistical correlation during the remote sensing inversion of CDOM absorption coefficients and thus producing prediction results that violate the optical and physical laws of water bodies, this embodiment introduces a post-processing mechanism based on prior knowledge.

[0150] It should be noted that post-processing is not the traditional method of numerically pruning or smoothing the inversion results after model inference. Instead, it directly integrates the physical prior knowledge of the CDOM absorption coefficients and the temporal continuity constraints into the model training process. These constraints are used as knowledge to participate in the learning and optimization of LNN network parameters, enabling the model to learn and internalize physical laws such as "non-negativity" and "continuity" during the training phase. As a result, the model naturally outputs CDOM inversion results that satisfy the physical constraints during the inference phase.

[0151] By moving post-processing constraints to the model training stage, this embodiment achieves a consistency mechanism between constraint learning in the training stage and automatic execution of constraints in the inference stage, avoiding the discontinuity and physical distortion problems that may be introduced by traditional post-correction methods.

[0152] S2.3.1: Modeling based on prior physical knowledge of CDOM absorption coefficient.

[0153] In one specific implementation, the CDOM absorption coefficient, as an inherent optical parameter of water, is subject to explicit physical constraints in terms of its magnitude and variation. Therefore, this embodiment first systematically models the prior physical knowledge of the CDOM absorption coefficient to characterize the fundamental physical laws that the inversion results should satisfy in terms of numerical range, continuity of variation, and spectral morphology, thus providing a theoretical basis for the subsequent introduction of constraint mechanisms during the model training phase.

[0154] From a physical perspective, the CDOM absorption coefficient should be non-negative under any natural water body conditions; it cannot be negative. Furthermore, the composition of CDOM sources, hydrological conditions, and biogeochemical backgrounds vary significantly among different water body types, such as lakes, reservoirs, and nearshore estuaries. Consequently, the corresponding CDOM absorption coefficients typically fall within a statistically significant and reasonable range. Therefore, based on historical measured data and statistical analysis results, the reasonable range for the CDOM absorption coefficient can be expressed as follows:

[0155] .

[0156] in, This refers to the absorption coefficient of CDOM.

[0157] This range of values ​​is not used to simply prune the prediction results, but rather serves as a criterion for judging the rationality of the inversion results during the LNN model training phase, guiding the model parameters to tend towards a solution space that conforms to physical meaning during the optimization process.

[0158] Furthermore, the CDOM absorption process is controlled by the molecular composition and optical absorption properties of the dissolved organic matter, and its changes typically exhibit a continuous evolution over time. Abrupt abrupt changes or oscillations without physical basis should not occur between adjacent observation times. Therefore, in the time dimension, the CDOM absorption coefficient inversion results should satisfy the continuity constraint, and its basic form can be expressed as:

[0159] .

[0160] This represents the common-mode output voltage at time t. The larger of 0 and 0. In other words, it performs a "lower limit clamping" on the common-mode output voltage to ensure that the value will not be negative.

[0161] The aforementioned continuity description is used to characterize the gradual evolution of the optical features of CDOM in natural water bodies, providing a priori basis for introducing a time continuity penalty term in the subsequent model training phase.

[0162] Furthermore, from the perspective of spectral mechanism, the absorption spectrum of CDOM typically exhibits an approximately exponential decay characteristic with increasing wavelength in the visible to near-infrared range. This spectral morphology reflects the strong absorption of short-wavelength light and the weak absorption of long-wavelength light by CDOM, which is a widely accepted fundamental law in water optics.

[0163] The physical prior knowledge modeling of the CDOM absorption coefficient described in this embodiment does not directly participate in the numerical prediction process of the CDOM absorption coefficient. Instead, it is used to define the physical rationality constraints that the inversion results must satisfy during the model training phase. These prior rules will be explicitly introduced into the model training objective function in the subsequent construction of nonnegativity constraints, temporal continuity constraints, and physical consistency penalty terms, enabling the LNN to gradually learn and internalize the physical evolution law of the CDOM absorption coefficient during the parameter optimization process.

[0164] S2.3.2: Setting an embedded implementation mechanism for non-negativity constraints.

[0165] In one specific implementation, in view of the fundamental constraint that the CDOM absorption coefficient cannot be negative in a physical sense, this embodiment directly integrates nonnegative prior knowledge into the training process of the LNN model, rather than simply pruning the prediction results during the inference stage.

[0166] Specifically, in an LNN, the internal state vector h t During the mapping to the CDOM absorption coefficient output space, the output layer uses a mapping function that includes nonlinear transformation, so that the network is constrained to only output non-negative results during the training phase.

[0167] Based on this physical understanding, a reasonable prior description of the CDOM absorption spectrum can be made, and its expression is as follows:

[0168] .

[0169] Among them, H out Let W1 represent the input features, b1 be the first-layer weight matrix, b1 be the first-layer bias vector, ReLU(...) be the vector after non-linearization, W2 be the second-layer weight matrix, and b2 be the output bias vector. This is the final output vector.

[0170] It describes a two-layer neural network transformation process for generating nonnegative neighborhood representations: it first processes the input features... Perform a linear transformation Then, the ReLU activation function is used to filter out negative values ​​to introduce nonlinearity, followed by a second linear transformation on the activated result. Finally, the exponential function exp(·) is used to ensure the final output's neighborhood representation. It is a non-negative value and is often used in feature representation or similarity calculation scenarios that require non-negativity constraints.

[0171] in, It is X t The latent space representation after mapping via a network (such as a temporal modeling or coding layer). The relationship between the two is: ,Right now It is X t The feature transformation results.

[0172] The aforementioned spectral morphology constraints provide a theoretical basis for the subsequent construction of a physical consistency penalty term, which is used to suppress inversion results that violate the optical mechanism of water bodies, such as abnormal enhancement with wavelength, during the training process of the LNN model.

[0173] Through the above output mapping design, the nonnegativity constraint continues to act on the LNN network parameter update during backpropagation, enabling the model to gradually learn parameter combinations that conform to physical meaning during the training phase. Thus, the CDOM absorption coefficient inversion result can always be greater than zero without additional numerical correction during the inference phase.

[0174] This mechanism avoids the gradient discontinuity problem that may be introduced by traditional post-processing pruning methods, and improves the stability of model training and the physical consistency of inversion results.

[0175] S2.3.3: Set continuity constraints and physical consistency penalties.

[0176] In one specific implementation, given that the CDOM absorption coefficient in natural water bodies typically exhibits a continuous and gradual evolution over time and space, relying solely on traditional data-driven network models for inversion can easily lead to non-physical abrupt changes between adjacent time points or adjacent pixels under conditions of noise interference or sample imbalance. Therefore, this embodiment does not employ the traditional post-processing method of prediction followed by pruning. Instead, it directly integrates the constraints of continuity and physical consistency into the LNN model training process, participating in parameter optimization in the form of knowledge constraints.

[0177] Specifically, during the model training phase, for adjacent time steps t Predicted CDOM absorption coefficients for 1 and t (t-1) and (t), construct the time continuity penalty term It is used to measure the magnitude of change between inversion results at adjacent time points, and its mathematical expression is defined as:

[0178] .

[0179] in, (t) represents the action or output predicted by the model at time t; (t 1) For the model at the t-th The predicted action or output at time 1; To calculate the squared L2 norm of a vector.

[0180] This continuity penalty term generates additional loss when the model's prediction results fluctuate drastically, thereby guiding the model to learn the evolution law of the CDOM absorption coefficient changing smoothly over time during the training process. This ensures that the inversion results maintain physically reasonable continuity in the time dimension and are consistent with the continuous evolution characteristics of the internal state vector of the LNN.

[0181] Based on this, and taking into account the objective physical law that the absorption spectrum of CDOM exhibits exponential decay with increasing wavelength in the visible to near-infrared range, a physical consistency penalty term L is further constructed. phys The CDOM absorption coefficient used to constrain model predictions satisfies the exponential decay characteristic in the spectral dimension.

[0182] Correspondingly, physical consistency penalty Defined as:

[0183] .

[0184] in, The average of all N samples is taken to make the loss more stable overall. It iterates through all time steps or event sequences. The CDOM absorption coefficient predicted by the model. This is the predicted absorption coefficient at the previous wavelength. For the i-th wavelength, is the (i-1)th wavelength, and k is the spectral attenuation slope parameter.

[0185] S2.3.4: Construct the training objective function for the LNN network.

[0186] The model's training objective function consists of a data fitting error term and a continuity penalty term. and physical consistency penalty items Together, through multi-constraint joint optimization, the LNN can output CDOM absorption coefficient inversion results that meet the requirements of non-negativity, continuity and physical consistency while ensuring fitting accuracy.

[0187] It should be noted that the time continuity constraint is defined separately as a special step in S2.3.3. It is essentially an extension of the physical rationality constraint. Therefore, the continuity penalty term is not repeated in the formula of the objective function, but it has participated in parameter optimization in the actual training process.

[0188] S3: Use the trained LNN network to invert the remote sensing observation data to be predicted, and obtain the CDOM absorption coefficient inversion results for the corresponding time step.

[0189] In one specific implementation, the constrained CDOM absorption coefficient inversion results are spatially mapped according to the pixel positions of remote sensing images to generate two-dimensional spatial distribution data within the study area; and according to the time series of remote sensing images, a temporal spatial distribution dataset of CDOM absorption coefficients is formed to characterize the spatial differentiation features of CDOM and its changes over time.

[0190] Example 2:

[0191] Embodiment 2 of the present invention provides a CDOM absorption coefficient inversion system based on a liquid neural network, comprising:

[0192] The data acquisition module is configured to acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the water environment. Based on the matching relationship between remote sensing data and hyperspectral data, the in-situ hyperspectral observation data is spectrally transformed to obtain equivalent multispectral reflectance. The equivalent multispectral reflectance is reconstructed using the mapping relationship between remote sensing reflectance spectrum and CDOM absorption characteristics to obtain training samples composed of CDOM sensitive feature vector and remote sensing feature matrix.

[0193] The network construction and training module is configured to construct an LNN network with continuous-time dynamics and perform multiple rounds of iterative training on the LNN network using training samples.

[0194] The inversion module is configured to use a trained LNN network to invert the remote sensing observation data to be predicted, and obtain the CDOM absorption coefficient inversion results for the corresponding time step.

[0195] Example 3:

[0196] Embodiment 3 of the present invention provides a computer-readable storage medium storing a computer program adapted for loading by a processor and executing the steps in the CDOM absorption coefficient inversion method based on a liquid neural network as described in Embodiment 1 of the present invention.

[0197] Example 4:

[0198] Embodiment 4 of the present invention provides a computer device, the device comprising:

[0199] A processor, adapted to execute computer programs;

[0200] A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the steps in the CDOM absorption coefficient inversion method based on a liquid neural network as described in Embodiment 1 of the present invention.

[0201] Example 5:

[0202] Embodiment 5 of the present invention provides a computer program product or computer program, which includes computer instructions stored in a computer-readable storage medium. A processor of a computer device reads the computer instructions from the computer-readable storage medium and executes the computer instructions, causing the computer device to perform the steps in the CDOM absorption coefficient inversion method based on a liquid neural network as described in Embodiment 1 of the present invention.

[0203] The steps and methods involved in Examples 2, 3, 4 and 5 above correspond to those in Example 1. For specific implementation methods, please refer to the relevant description section of Example 1.

[0204] Those skilled in the art will recognize that the units and algorithm steps of the various examples described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0205] In the above embodiments, implementation can be achieved, in whole or in part, through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented, in whole or in part, as a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the flow or function according to the embodiments of this application is generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in or transmitted through a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The computer-readable storage medium can be any available medium that a computer can access or a data processing device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, an optical medium, or a semiconductor medium, etc.

[0206] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for inverting the CDOM absorption coefficient based on a liquid neural network, characterized in that, Includes the following steps: Multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the water environment are acquired. Based on the matching relationship between remote sensing data and hyperspectral data, spectral transformation is performed on the in-situ hyperspectral observation data to obtain equivalent multispectral reflectance. Continuous wavelet transform is performed on the equivalent multispectral reflectance, and feature bands are screened based on inversion stability and sensitivity requirements. The mapping relationship between remote sensing reflectance spectrum and CDOM optical properties is used to reconstruct the features of the equivalent multispectral reflectance to obtain training samples composed of CDOM sensitive feature vectors and remote sensing feature matrices. Construct an LNN network with continuous-time dynamics and perform multiple rounds of iterative training using training samples. The specific steps for constructing an LNN network with continuous-time dynamics are as follows: Design an input-state coupling structure for state transition of input parameters; construct a continuous-time state update mechanism to adaptively adjust the weight ratio of historical states and current input features in state update according to the time interval and state change rate; model multi-temporal input sequences and extract state features; The mapping output is obtained through a multi-band scale dynamic inversion process based on temporal fusion; The trained LNN network is used to invert the remote sensing observation data to be predicted, and the CDOM absorption coefficient inversion results for the corresponding time step are obtained. Post-processing constraints are applied to the CDOM absorption coefficient results output by LNN: First, non-negativity constraints are applied to the inversion results, and the range of values ​​is limited to a reasonable range obtained based on the statistical analysis of measured samples; Second, temporal continuity constraints are applied to the CDOM inversion results of the same pixel at adjacent time steps. When the difference between adjacent time phases exceeds a preset threshold, abnormal results are corrected or smoothed.

2. The CDOM absorption coefficient inversion method based on liquid neural networks as described in claim 1, characterized in that, The specific steps for performing spectral transformation on in-situ hyperspectral observation data to obtain equivalent multispectral reflectance based on the matching relationship between remote sensing data and hyperspectral data are as follows: Preprocessing and standardization operations were performed on multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient, and auxiliary parameters of the aquatic environment. Spectral transformation processing was performed on the in-situ hyperspectral observation data.

3. The CDOM absorption coefficient inversion method based on liquid neural networks as described in claim 2, characterized in that, The specific steps for spectral transformation processing of in-situ hyperspectral observation data are as follows: By utilizing the band settings and corresponding spectral response functions of the target multispectral sensor, weighted integration and resampling are performed on the hyperspectral continuous bands to convert the in-situ hyperspectral observation data into equivalent multispectral reflectance data.

4. The CDOM absorption coefficient inversion method based on liquid neural networks as described in claim 1, characterized in that, The specific steps for performing multiple rounds of iterative training on an LNN network using training samples are as follows: The design incorporates an inverse mapping learning process from state features to CDOM absorption coefficients. Construct training data and train based on a continuous-time state-driven training mechanism; The model is optimized using a joint loss function.

5. A CDOM absorption coefficient inversion system based on a liquid neural network, employing the CDOM absorption coefficient inversion method based on a liquid neural network as described in any one of claims 1-4, characterized in that, include: The data acquisition module is configured to acquire multi-source remote sensing image data, in-situ hyperspectral observation data, CDOM absorption coefficient and water environment auxiliary parameters. Based on the matching relationship between remote sensing data and hyperspectral data, the in-situ hyperspectral observation data is spectrally transformed to obtain equivalent multispectral reflectance. The equivalent multispectral reflectance is reconstructed using the mapping relationship between remote sensing reflectance spectrum and CDOM optical properties to obtain training samples composed of CDOM sensitive feature vector and remote sensing feature matrix. The network construction and training module is configured to construct an LNN network with continuous-time dynamics and perform multiple rounds of iterative training on the LNN network using training samples. The inversion module is configured to use a trained LNN network to invert the remote sensing observation data to be predicted, and obtain the CDOM absorption coefficient inversion results for the corresponding time step.

6. A computer program product, characterized in that, The computer program product includes a computer program that, when executed by a processor, implements the CDOM absorption coefficient inversion method based on a liquid neural network as described in any one of claims 1-4.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program adapted to be loaded by a processor and executed as described in any one of claims 1-4: the CDOM absorption coefficient inversion method based on a liquid neural network.

8. A computer device, characterized in that, include: A processor, adapted to execute computer programs; A computer-readable storage medium storing a computer program, which, when executed by the processor, implements the CDOM absorption coefficient inversion method based on a liquid neural network as described in any one of claims 1-4.

Images