Multi-objective decision method and system for physical information inversion of water environment

Abstract

The application discloses a kind of physical information inversion multi-objective decision-making method and system of water environment, it is related to the data processing technical field for water quality management and prediction purposes, method includes obtaining reservoir multivariate high-frequency monitoring sequence;Decomposition-interaction Mamba world model is constructed, sequence decomposition front end, double-path selective state encoder and cross-variable gate state injection module are internally set;Physical information constraint layer is constructed based on Streeter-Phelps equation, physical consistency loss and dynamic safety boundary are defined;From historical passive observation, detect natural recovery event, train generation model to build feasible ecological restoration manifold;With prediction loss as main, in combination with physical consistency loss and safety constraint, world model is trained using gradual strategy;Natural baseline is deduced using frozen model, potential variables are extracted from manifold to generate recovery trajectory, and pareto solution set and physical intervention flux are output by EPO multi-objective search and sorting.The application improves water quality prediction accuracy and multi-objective decision-making real-time and interpretability.

Description

Technical Field

[0001] This invention relates to the field of data processing technology for water quality management and prediction purposes, and specifically to a multi-objective decision-making method and system for physical information inversion of the water environment. Background Technology

[0002] Traditional reservoir water quality management requires meeting basic requirements such as continuous monitoring, accurate forecasting, and real-time decision-making. However, these three objectives are fundamentally contradictory, forcing decision-makers to explore the optimal path between achieving environmental standards and ensuring operational costs. Dissolved oxygen (DO) and permanganate index (COD) are also key factors to consider. Mn Water quality is a core indicator reflecting the self-purification capacity of water bodies and the load of organic pollution. Most existing intelligent water quality management solutions adopt a two-stage system of first making time-series predictions and then carrying out multi-objective decision-making. However, there are still many problems in decision-making regarding the improvement of the basic prediction architecture and the integration of physical mechanisms.

[0003] Recently, the Mamba architecture based on a selective state-space mechanism has achieved performance comparable to the Transformer with linear complexity and is gradually being applied to multivariate time series forecasting. However, existing Mamba applications almost universally employ an independent channel strategy, confining each water quality variable in an isolated encoding pipeline, completely ignoring DO and COD. Mn The impact between them. This disconnect directly leads to serious inaccuracies in prediction accuracy under dynamic environments and highly sensitive conditions such as extreme algal blooms and hypoxia stress, which are precisely the critical moments for management intervention.

[0004] Furthermore, and more importantly, most purely data-driven models lack constraints from basic physical principles. While they can provide reasonable predictions within their training distribution, they may produce absurd results that violate fundamental laws of oxygen consumption and reoxygenation when faced with operating conditions outside that distribution. Such physically untenable predictions, if applied to downstream decision-making, can lead the entire management system astray. Currently, most existing water quality management systems merely use physical equations as post-hoc verification tools, failing to truly integrate them into the integrated training process, thus limiting their effectiveness. Moreover, water quality safety assessments have long relied on fixed concentration thresholds, neglecting the dynamic impact of water temperature fluctuations and organic load changes on the self-purification boundary of water bodies. This leads to overly conservative or overly lenient safety judgments, hindering accurate decision-making.

[0005] Decision-making also faces several challenges. Water quality management requires a balance between environmental and cost considerations, but the single-step optimization of traditional multi-objective evolutionary algorithms is extremely time-consuming. While weighted model predictive control improves efficiency, it is constrained by the one-time setting of prior weights, severely lacking insight into the Pareto global picture. Fortunately, in recent years, gradient-based multi-objective methods such as multigradient descent and Exact Pareto Optimization (EPO) have been able to efficiently search for the Pareto front in continuous space, offering hope for real-time decision-making. However, the historical databases of reservoirs are almost entirely composed of uninterrupted natural observation sequences, making it impossible to find fixed causal relationships. The logic of closed-loop control is highly dependent on such relationships; without this foundation, extracting searchable and physically interpretable decision-making logic from purely passive observations becomes a significant obstacle.

[0006] In summary, existing systems suffer from multiple problems. They cannot simultaneously balance linear computational complexity and cross-variable linkage modeling in prediction networks; physical constraints are not embedded in data-driven gradient training of the model; and safety assessments adhere to rigid thresholds instead of dynamically adjusting to system states. Furthermore, at the most critical decision-making level, lacking real control labels, there is no fast system capable of automatically constructing feasible paths from passively observed data and performing multi-objective optimization. Summary of the Invention

[0007] To address the aforementioned technical problems, the present invention aims to provide a multi-objective decision-making method and system for physical information inversion of the water environment. This method achieves cross-variable dynamic linkage prediction of water quality by constructing a decomposed-interactive Mamba world model while maintaining linear computational complexity; it embeds physical mechanisms into model training and achieves adaptive safety assessment by constructing physical consistency loss and dynamic safety boundaries; and it achieves multi-objective decision-making under uninterventional labeling conditions by constructing a feasible ecological restoration manifold and employing precise Pareto optimization search.

[0008] This invention is achieved through the following technical solution:

[0009] A multi-objective decision-making method for physical information inversion of the water environment includes the following steps:

[0010] S1: Obtain the raw multivariate high-frequency monitoring sequence of the reservoir, and output a clean and usable multivariate sequence after preprocessing;

[0011] S2: Construct a decomposed-interactive Mamba world model. The world model includes a sequence decomposition front-end, a dual-path selective state space encoder, and a cross-variable gated state injection module. The multivariate sequence is input into the world model. The sequence decomposition front-end decomposes the multivariate sequence into trend components and seasonal-residual components. The trend components and seasonal-residual components are respectively sent to the two encoding paths of the dual-path selective state space encoder for feature extraction. The encoding path contains multiple Mamba encoding layers. After each layer of Mamba encoding is completed, the cross-variable gated state injection module is triggered to interactively inject the hidden states of each variable channel under the encoding path. The interactively enhanced state is sent to the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion is finally progressively deduced to predict the future multi-step water quality trajectory.

[0012] S3: Construct a physical information coupling constraint layer. Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized. The physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change of the equation. The dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the derivative of the equation is zero. It is then constructed as a differentiable safety distance function in the form of exponential penalty.

[0013] S4: Construct a feasible ecological restoration manifold by detecting natural restoration or disturbance events from historical passive observation sequences, extracting the imprints of state changes before and after the events to form a restoration sample set; use the restoration sample set to train a generative model, and the low-dimensional latent space spanned by the model after training convergence is the feasible ecological restoration manifold.

[0014] S5: World model training and freezing. Taking prediction bias loss as the core, combined with the physical consistency loss and the safe distance function, a progressive constraint enhancement strategy is used to jointly optimize and train the world model. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model.

[0015] S6: Online multi-objective decision-making inputs the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; extracts latent variables from the feasible ecological restoration manifold, transforms them into variables, and superimposes them onto the natural baseline trajectory to generate restoration trajectories for numerous objectives; performs multi-objective search in the continuous latent space using precise Pareto optimization, sorts the obtained solution set by non-dominated order, selects the Pareto non-dominated solution set for the current water quality conditions, and outputs the corresponding objective restoration trajectory and physical intervention flux.

[0016] In S1, the preprocessing includes time-domain filtering, missing value imputation, and reversible normalization.

[0017] In step S2, the multivariate sequence is divided according to a preset backtracking window length to obtain a fixed-length observation window sequence, and the observation window sequence is input to the sequence decomposition front end of the world model.

[0018] The built-in sequence decomposition front end uses a learnable moving average kernel, and the kernel width is weighted in the candidate set using softmax to achieve differentiability selection, so as to adaptively track the trend fluctuation of the sequence; the dual-path selective state space encoder consists of two Mamba encoding paths with the same structure, independent parameters, and mirror images of each other, and selectively processes information flow using input-driven step size parameters; the cross-variable gated state injection module concatenates the hidden states of each variable channel output by the current Mamba encoding layer into a matrix, and determines the strength of each channel accepting information from other channels through a learnable weight matrix and a gate vector;

[0019] The implicit representation after dual-path fusion is used to progressively deduce the future multi-step water quality trajectory, including: adding the final outputs of the two paths element by element after linear projection to obtain the fused global implicit representation; using the global implicit representation as the initial state, using an autoregressive method to progressively deduce and generate the future multi-step water quality trajectory step by step.

[0020] In S3, the Streeter-Phelps oxygen consumption-reoxygenation equation is used to describe DO and COD. Mn The oxygen consumption-reoxygenation kinetic relationship between them is determined, and the reoxygenation coefficient, oxygen consumption coefficient, and self-purification coefficient are all learnable positive parameters; the physical consistency loss is the DO and COD predicted by the world model. Mn The one-step change and the DO and COD calculated by the equation Mn The mean square error between expected changes.

[0021] In S4, training the generative model using the recovery sample set includes: training a conditional variational autoencoder using the recovery sample set; the encoder maps the recovery signal and the current state conditions to a low-dimensional latent space; the decoder reconstructs the change in the target recovery trajectory based on the latent variables and the current state conditions; after training converges, only the decoder is retained and frozen, and the low-dimensional latent space spanned by it is the desired feasible ecological restoration manifold.

[0022] In S4, the natural recovery or disturbance event includes influent dilution events, temperature jump events, and / or sudden changes in water quality events.

[0023] In S5, during the training of the world model, a progressive constraint enhancement strategy is adopted, including: optimizing only the data prediction loss in the first 30% of iterations, linearly increasing the physical consistency weight from zero in 30% to 60% of iterations, and waking up the safety penalty weight after 60% of iterations.

[0024] In S6, a multi-objective search is carried out in the continuous latent space using exact Pareto optimization, including: starting from multiple preference rays uniformly distributed on the preference simplex, the latent variables are initialized in parallel, and then the exact Pareto optimization gradient update is iteratively performed so that each solution point approaches the Pareto front along its respective preference direction.

[0025] In S6, the current water quality conditions include at least the dissolved oxygen concentration, permanganate index, and water temperature at the current moment; the physical intervention flux includes at least the external aeration rate and the organic matter reduction rate; the external aeration rate is calculated by calculating the positive portion of the difference between the natural baseline DO change rate and the target recovery DO change rate step by step, and accumulating them to obtain the minimum oxygen flux; the organic matter reduction rate is calculated by calculating the natural baseline COD step by step. Mn Rate of change and target recovery COD Mn The positive portions of the difference in rates of change are accumulated to obtain the organic matter reduction flux; the aeration cost is obtained by multiplying the aeration unit cost coefficient by the minimum oxygen flux, and the reduction cost is obtained by multiplying the chemical reduction unit cost coefficient by the organic matter reduction flux. Finally, the trajectory smoothing constraint is superimposed to obtain the engineering intervention cost.

[0026] A multi-objective decision-making system for physical information inversion of the water environment, comprising:

[0027] Multivariate Sequence Acquisition Unit: Used to acquire raw multivariate high-frequency monitoring sequences of reservoirs, and outputs clean and usable multivariate sequences after preprocessing;

[0028] World Model Construction Unit: Used to construct a decomposed-interactive Mamba world model. The world model includes a sequence decomposition front-end, a dual-path selective state space encoder, and a cross-variable gated state injection module. The multivariate sequence is input into the world model. The sequence decomposition front-end decomposes the multivariate sequence into trend components and seasonal-residual components. The trend components and seasonal-residual components are respectively sent to the two encoding paths of the dual-path selective state space encoder for feature extraction. The encoding path contains multiple Mamba encoding layers. After each layer of Mamba encoding is completed, the cross-variable gated state injection module is triggered to interactively inject the hidden states of each variable channel under the encoding path. The interactively enhanced state is sent to the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion is finally progressively deduced to predict the future multi-step water quality trajectory.

[0029] Physical information coupling constraint layer building unit: Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized, the physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change of the equation, the dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the derivative of the equation is zero, and it is constructed as a differentiable safety distance function in the form of exponential penalty.

[0030] Feasible ecological restoration manifold building unit: used to detect natural restoration or disturbance events from historical passive observation sequences, extract the imprints of state changes before and after the event to form a restoration sample set; use the restoration sample set to train the generation model, and the low-dimensional latent space spanned by it after training convergence is the feasible ecological restoration manifold;

[0031] World model training and freezing unit: It is used to jointly optimize and train the model with prediction bias loss as the core, combined with the physical consistency loss and the safe distance function, and adopts a progressive constraint enhancement strategy. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model.

[0032] Online multi-objective decision unit: It is used to input the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; extract latent variables from the feasible ecological restoration manifold, convert them into variables, and superimpose them onto the natural baseline trajectory to generate restoration trajectories for numerous objectives; conduct multi-objective search in the continuous latent space using exact Pareto optimization, sort the obtained solution set by non-dominated sorting, select the Pareto non-dominated solution set for the current water quality conditions, and output the corresponding objective restoration trajectory and physical intervention flux.

[0033] The multi-objective decision-making method and system for physical information inversion of the water environment according to the present invention have the following advantages and beneficial effects compared with the prior art:

[0034] (1) The DC-Mamba world model of this invention combines sequence decomposition with cross-variable gated injection, taking into account both the linear complexity O(L) of the selective state-space model and the dense modeling of the unidirectional driving and asymmetric coupling relationship between multiple water quality indicators. Compared with the current channel-independent Mamba and Transformer paradigms, it can simultaneously ensure efficiency and high-fidelity inference in long-window high-frequency data streams, and its prediction accuracy under extreme conditions is particularly advantageous.

[0035] (2) The Streeter-Phelps equation is deeply embedded in the training network in the form of learnable parameters, and a dynamic safety boundary that adapts to the system state is introduced, which completely breaks the long-standing problem of the disconnect between prediction and physics. The safety margin drifts with real-time water temperature and organic load, eliminating the root cause of the stubborn problems of fixed thresholds, conservatism, or missed judgments, and enabling the safety assessment to have dynamic response capabilities.

[0036] (3) Constructing feasible ecological restoration manifolds from natural disturbance events, this invention can lay out healthy paths for water body restoration on continuous low-dimensional manifolds without relying on historical artificial intervention labels. Then, by inverting exogenous physical fluxes through the calibrated physical equations as the intervention cost, it innovatively connects an end-to-end closed loop of "from passive observation to physically interpretable multi-objective decision-making".

[0037] (4) The precise Pareto optimization search performed on the continuous potential space is fully differentiable and highly parallel. The time for a single online decision is reduced to the sub-second level. It can provide managers with a complete Pareto front and a well-organized physical feasible recommendation in an instant, pushing the automation and scientific level of high-frequency water quality management to a new level. Attached Figure Description

[0038] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0039] Figure 1 This is a flowchart of a multi-objective decision-making method for physical information inversion of the water environment according to Embodiment 1 of the present invention;

[0040] Figure 2 This is a comparison chart of data preprocessing before and after according to Embodiment 1 of the present invention;

[0041] Figure 3 This is a convergence curve of the learnable physical parameters according to Embodiment 1 of the present invention;

[0042] Figure 4 This is a comparison diagram of the Pareto front according to Embodiment 1 of the present invention;

[0043] Figure 5 This is a 14-day continuously rolling simulated panoramic visualization diagram according to Embodiment 1 of the present invention;

[0044] Figure 6 This is a block diagram of the logical structure of a multi-objective decision-making system for physical information inversion of the water environment according to Embodiment 2 of the present invention. Detailed Implementation

[0045] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0046] Definitions:

[0047] The Mamba world model is a sequence prediction and decision-making framework based on a state-space model (SSM) for learning world models in reinforcement learning. Its task is not simply to generate text or images, but rather for an agent to learn the dynamics of the environment based on past actions and observations, and to "imagine" or "predict" future states and rewards.

[0048] The Streeter-Phelps equation is a classic water quality model describing the degradation of organic pollutants and changes in dissolved oxygen (DO) in rivers. It was proposed by Streeter and Phelps in 1925 and is the first coupled oxygen balance model in water environmental science.

[0049] Example 1

[0050] like Figure 1 As shown in the figure, the multi-objective decision-making method for physical information inversion of the water environment proposed in this embodiment is applicable to watershed or reservoir water environment management scenarios. It constructs a multi-objective decision-making model by integrating physical hydrological and water quality process data with multi-source observation inversion information.

[0051] The multi-objective decision-making method for inverting physical information of the water environment in this embodiment may include the following steps:

[0052] S1: Obtain the original high-frequency monitoring sequence of the reservoir multivariate data, and output a clean and usable multivariate sequence after preprocessing, laying the foundation for subsequent multidimensional modeling.

[0053] Preprocessing may include temporal filtering, missing value imputation, and reversible normalization.

[0054] The standard sampling interval can be 4 hours, meaning that data on multiple water quality variables are collected every 4 hours using various sensors. These variables include nine physicochemical variables: water temperature, pH, dissolved oxygen, conductivity, turbidity, permanganate index, ammonia nitrogen, total phosphorus, and total nitrogen. The multivariate high-frequency monitoring raw sequence includes the original time series of the nine physicochemical variables, and the time series of each of the nine physicochemical variables over time. Each variable has a sequence of the same length and is aligned by time.

[0055] S2: Constructing a decomposed-interactive Mamba world model. The world model incorporates a sequence decomposition front-end, a dual-path selective state-space encoder, and a cross-variable gated state injection (CV-GSI) module. Multivariate sequences are input into the world model. The sequence decomposition front-end decomposes the multivariate sequences into trend components and seasonal-residual components. These trend and seasonal-residual components are then fed into two encoding paths of the dual-path selective state-space encoder for feature extraction. Each encoding path contains multiple Mamba encoding layers. After each Mamba encoding layer is completed, the cross-variable gated state injection module is triggered to interactively inject the hidden states of each variable channel within the encoding path, repairing the information flow between variables that was fragmented by independent encoding. The enhanced interactive states are then fed into the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion ultimately progressively infers the future multi-step water quality trajectory. Model training is driven by a hybrid loss mechanism, with prediction bias loss as the core. Parameters are frozen upon convergence, resulting in a deterministic, globally differentiable state transition world model.

[0056] The decomposition-interaction structure can capture the characteristics of long-term trend evolution and short-term fluctuations in water quality sequences. The design of dual-path independent encoding and layer-by-layer cross-variable interaction not only preserves the characteristic independence of different components, but also effectively explores the dynamic correlation between multiple variables. At the same time, the Mamba structure can efficiently process long-term monitoring sequences, realize accurate prediction of future multi-step water quality changes, and provide a reliable environmental dynamic prediction basis for subsequent decision-making.

[0057] Before being input into the world model, the multivariate sequences are segmented according to a preset backtracking window length to obtain fixed-length observation window sequences. These observation window sequences are then input into the sequence decomposition front end of the world model. This fixed backtracking window segmentation ensures uniformity in the scale of the input data, adapts to the model's fixed-dimensional input requirements, preserves the temporal dependencies of the sequences, avoids computational redundancy caused by long sequence inputs, and aligns with the practical application needs of water quality prediction, which relies on recent observations to extrapolate future trends.

[0058] The built-in sequence decomposition front-end is integrated into the decomposition-interaction Mamba world model as its first component. This front-end employs a learnable moving average kernel, with the kernel width selected via a weighted softmax function across a candidate set to adaptively track the trend fluctuations of the sequence. Softmax is a continuously differentiable normalization function. For a predefined set of candidate kernel widths, the model learns a normalized weight distribution and weights and fuses moving average kernels of different widths. This soft selection method ensures that the kernel width selection process participates in gradient backpropagation, enabling the model to adaptively combine multi-scale operators and effectively capture the trend changes of the time series at different scales. The decomposed trend component and seasonal-residual component are fed into two mirror-image Mamba encoding paths, achieving tight-coupled end-to-end learning of decomposition and encoding.

[0059] The dual-path selective state-space encoder consists of two identical, parameter-independent, mirror-image Mamba encoding paths. It selectively processes information using an input-driven step size parameter. While the two processing paths are completely identical, each has its own independent parameters, and they are designed as mirror images of each other. A step size parameter is dynamically adjusted based on the input data; this parameter determines how information is selectively retained, transmitted, or filtered in the two paths, thus achieving intelligent control of the information flow. The two encoding paths process the trend component and the seasonal-residual component respectively. These parallel paths, processing different decomposed components, introduce a cross-variable gated state injection module to interactively inject the latent states of each variable channel after each encoding layer.

[0060] The cross-variable gating state injection module concatenates the hidden states of each variable channel output by the current Mamba coding layer into a matrix. Using a learnable weight matrix and a gating vector, it determines the strength at which each channel receives information from other channels. The gating vector, primarily located in the CV-GSI module, is used to precisely control the information transmission strength between different water quality variables, selecting effective correlations and filtering redundant noise—a core learnable parameter. Its basic gating mechanism formula is as follows: and Among them, G t This represents the global channel gating at time t; This represents the Sigmoid activation function; This represents the learnable weight matrix of the gated layer; This represents the learnable bias term of the gating layer; The mean represents the output feature tensor of the l-th layer network. time Perform mean pooling along the time dimension; This represents the final eigenvalue of the i-th channel and j-th cell at time t after gating calibration; This represents the original feature value of the i-th channel and j-th unit at time t before the gating operation; This represents the global channel gating corresponding to the i-th channel at time t; The weights are learnable linear transformation parameters that can be used to improve feature representation capabilities. This represents the feature vector of the l-th layer network at time t. This represents the data from channel i after one round of feature processing. It is primarily used to perform linear weighted fusion of the global feature tensor at time t, forming a residual structure to enhance features and filter out noise. A gating mechanism is applied to the hidden states of each variable channel to achieve cross-variable information interaction and injection. Through a learnable weight matrix and gating vector, the strength at which each channel receives information from other channels is controlled. The alternating progressive design of encoding → interaction → encoding → interaction ensures that information between variables is fully fused at each layer. This achieves information interaction and complementary fusion between different water quality variables. Simultaneously, the gating mechanism filters out redundant noise in cross-variable transmission, resulting in highly targeted feature transmission that better adapts to the varying correlation strengths among different variables in multi-index water quality monitoring sequences.

[0061] The final outputs of the trend path and the seasonal-residual path are linearly projected and then summed element-wise to obtain a complete prediction. Finally, the encoded features of the two paths are concatenated and fused to obtain latent state features that contain both global trend information and local fluctuation information, providing a more comprehensive feature foundation for subsequent prediction outputs.

[0062] The implicit representation after dual-path fusion ultimately evolves into a progressive deduction of future multi-step water quality trajectories. This process includes: linearly projecting the final outputs of the two paths and then adding them element-wise to obtain the fused global implicit representation; using this global implicit representation as the initial state, an autoregressive approach is used to progressively deduce and generate future multi-step water quality trajectories step-by-step. After obtaining the standardized water quality time series in the previous step, a learnable multi-scale decomposition is performed, splitting it into two input paths: a trend path for low-frequency components and a seasonal-residual path for high-frequency components. Each path enters an independent Mamba encoding module, and multiple implicit relationships are established through cross-variable gated state injection (CV-GSI). Finally, linear projection and element-wise addition are used to fuse the features of the two channel paths, achieving a combination of multi-scale features. During this process, the fused global implicit representation serves as the basic core state, and an autoregressive rolling progressive method is used to generate future multi-step water quality trajectories.

[0063] This embodiment's decomposition-interaction Mamba prediction architecture organically combines a sequence decomposition front-end with a cross-variable gated state injection mechanism, achieving asymmetric combined modeling of multivariate time series based on Mamba's linear complexity. Besides water quality prediction, this architecture can be directly extended to fields such as air pollution monitoring and industrial system state forecasting. This embodiment unifies decomposition and cross-variable interaction within the Mamba framework, forming a complete differentiable world model and laying the foundation for downstream physical constraints and gradient decision-making.

[0064] S3: Construct a physical information coupling constraint layer. Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized. The physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change in the equation. A dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the equation's derivative is zero. This boundary is then constructed as a differentiable safety distance function with exponential penalties. By directly constraining the model's prediction direction through physical laws, no additional data labeling costs are required, ensuring that the model's predictions always conform to the fundamental physical laws of water quality evolution. Simultaneously, the differentiable safety distance function can be directly embedded into the end-to-end training process of the entire model, ensuring smooth gradient transfer throughout the training process. This improves the model's prediction stability and reliability under conditions of few samples and abnormal operating conditions.

[0065] The Streeter-Phelps equation is used to describe the relationship between DO (dissolved oxygen) and COD. Mn The oxygen consumption-reoxygenation kinetics between (permanganate index) are established, with the reoxygenation coefficient, oxygen consumption coefficient, and self-purification coefficient all being learnable positive parameters; the physical consistency loss is the DO and COD predicted by the world model. Mn The one-step change and the DO and COD calculated by the equation Mn The mean square error between expected changes.

[0066] This step involves constructing a physical information coupling constraint layer, which will govern DO-COD. Mn The Streeter-Phelps lumped-parameter equation for the oxygen consumption-reoxygenation relationship is discretized, and the reoxygenation coefficient, oxygen consumption coefficient, and self-purification coefficient are made into learnable positive parameters. The dynamic safety boundary is derived from the critical equilibrium surface where the derivative of the Streeter-Phelps oxygen consumption-reoxygenation equation is zero, and it can be adjusted according to water temperature and COD. Mn The concentration changes in real time, continuously, and smoothly, and participates in the gradient optimization training of the world model in the form of a differentiable safe distance function.

[0067] S4: Construct a feasible ecological restoration manifold by detecting natural restoration or disturbance events from historical passive observation sequences and extracting the imprints of state changes before and after the events to form a restoration sample set; use the restoration sample set to train the generative model, and the low-dimensional latent space spanned by the model after training convergence is the feasible ecological restoration manifold.

[0068] Natural recovery or disturbance events may include influent dilution events, temperature jump events, and / or sudden changes in water quality events.

[0069] The generative model is trained using the recovery sample set, including: training a conditional variational autoencoder using the recovery sample set, the encoder mapping the recovery signal and the current state conditions to a low-dimensional latent space, and the decoder reconstructing the change in the target recovery trajectory based on the latent variables and the current state conditions; after training converges, only the decoder is retained and frozen, and the low-dimensional latent space spanned by it is the desired feasible ecological restoration manifold.

[0070] This step extracts feasible ecological restoration manifolds from historical passive observations. It automatically detects natural restoration / disturbance events in historical sequences caused by water dilution, temperature jumps, or sudden changes in water quality, extracting traces of state changes before and after the events to form a restoration sample set. This sample set is used to train a Conditional Variational Autoencoder (CVAE). The encoder maps the restoration signal along with the current state conditions to a low-dimensional latent space, while the decoder reconstructs the changes in the target restoration trajectory from the latent variables and the current state conditions. After training convergence, the encoder is discarded, leaving only the decoder frozen. The low-dimensional latent space spanned by the decoder is the obtained feasible ecological restoration manifold. Relying on passive observation data and learning indirectly by detecting natural restoration events, this method completely avoids human intervention and labels, capturing differentiated restoration patterns under different scenarios. It provides a feasible restoration space that fits the actual system for subsequent decision-making. After training, the encoder is discarded, and only the decoder is retained, making the decoder's input space directly the space of feasible solutions.

[0071] S5: World model training and freezing. With prediction bias loss as the core, combined with physical consistency loss and safe distance function, a progressive constraint enhancement strategy is used to jointly optimize and train the world model. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model.

[0072] In training the world model, a progressive constraint reinforcement strategy is employed: the first 30% of iterations focus solely on optimizing the data prediction loss; from 30% to 60% of iterations, the physical consistency weight linearly increases from zero; and after 60% of iterations, the safety penalty weight is activated. This three-stage progressive activation involves: in the first stage, the model learns the surface patterns of the data to prevent physical constraints from interfering with initial convergence; in the second stage, physical parameters have initially converged, and physical constraints are gradually applied for a smooth transition; in the third stage, physical parameters have stabilized, and the safety boundary has physical meaning, allowing for the application of safety penalties. This ensures that physical information does not become a distraction in the early stages of training, enabling the world model to not only fit the data but also internally adhere to physical laws and inherently possess dynamic safety assessment capabilities.

[0073] In this step, physical information coupling constraints and dynamic safety boundaries are jointly trained. The Streeter-Phelps equations in lumped parameter form are parameterized and deeply embedded into the network training loss function. This is supplemented by a dynamic safety boundary and differentiable penalty term derived from dynamic equilibrium, along with progressive weight scheduling to ensure robust convergence of physical parameters. This joint training chain achieves a deep integration of physical information learning and safety constraints. It can be extended to any environmental process with simplified dynamic equations, such as river BOD decay and atmospheric diffusion. This embodiment focuses on DO-COD. Mn The specific lumped parameter form of the coupling and the dynamic safety boundary derived from the equilibrium surface constitute a unique world model training scheme for water quality prediction and assessment.

[0074] S6: Online multi-objective decision-making inputs the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; extracts latent variables from feasible ecological restoration manifolds, transforms them into variables, and superimposes them onto the natural baseline trajectory to generate restoration trajectories for numerous objectives; conducts multi-objective search in the continuous latent space using precise Pareto optimization, sorts the obtained solution set by non-dominated ordering, selects the Pareto non-dominated solution set for the current water quality conditions, and outputs the corresponding objective restoration trajectory and physical intervention flux.

[0075] Current water quality conditions include at least the dissolved oxygen concentration, permanganate index, and water temperature at the current moment. Physical intervention fluxes include at least external aeration and organic matter reduction. External aeration is calculated by calculating the positive portion of the difference between the natural baseline DO change rate and the target restored DO change rate at each time step, and then summing these values ​​to obtain the minimum oxygen flux. Organic matter reduction is calculated by calculating the natural baseline COD at each time step. Mn Rate of change and target recovery COD MnThe positive parts of the difference in the rate of change are accumulated to obtain the organic matter reduction flux; the calculation method of the engineering intervention cost is as follows: multiply the minimum oxygen flux by the aeration unit cost coefficient to obtain the aeration cost, multiply the organic matter reduction flux by the chemical reduction unit cost coefficient to obtain the reduction cost, and then superimpose the trajectory smoothing constraint to form the engineering intervention cost.

[0076] The calculation method for the cost of engineering intervention is clear and straightforward. The positive part of the difference between the natural baseline DO change rate and the target recovery DO change rate is calculated hourly and accumulated to form the minimum oxygen flux that must be provided by external aeration. Similarly, the additional organic matter reduction flux is calculated. Both are multiplied by the unit cost coefficients of aeration and chemical reduction, respectively, and then the trajectory smoothing constraint is added to form a cost function with clear physical meaning.

[0077] The environmental benefit objective in the multi-objective search consists of both asymmetric penalties under the condition of compliance and dynamic safety penalties, ensuring that the recovery process does not exceed the safety boundary. The asymmetric penalty mainly uses national water quality standards as the basic basis and differentiates penalties based on the risk characteristics of different indicators to eliminate trajectories with significant water quality exceeding the standards, ensuring that all candidate paths meet basic management requirements. At the same time, the dynamic safety penalty incorporates water dynamic rules as a basic verification to intercept some trajectories that, although meeting short-term indicators, may evolve into risky trajectories with hypoxia and biochemical imbalances over time.

[0078] Multi-objective search can be carried out in a continuous latent space using exact Pareto optimization. This can include: starting from multiple preference rays uniformly distributed on the preference simplex, initializing latent variables in parallel, and then iteratively performing exact Pareto optimization gradient updates so that each solution point approaches the Pareto front along its respective preference direction.

[0079] When the natural baseline evolution trajectory deduced by the frozen world model touches or falls below the dynamic safety boundary within a preset future time step, a multi-objective decision is triggered. After each decision cycle, the newly acquired real-time observation status is used as the input for the next round of decision-making, and step S6 is repeated to achieve closed-loop feedback control.

[0080] A multi-objective decision-making system based on physical flux inversion is constructed. In real-time decision-making, the observed state is fed back into the frozen world model to deduce a natural baseline evolution trajectory unaffected by human intervention. Subsequently, latent variables are extracted from the recovered state, converted into changing signals by a decoder, and superimposed on the baseline trajectory to instantly generate recovered trajectories for numerous objectives. Exact Pareto Optimization (EPO) is used to conduct a multi-objective search in a continuous latent space. Starting from multiple preference rays uniformly distributed on the preference simplex, latent variables are initialized in parallel, and then EPO gradient updates are iteratively performed to make each solution point approach the Pareto front along its respective preference direction. The obtained solution set is sorted by non-dominated parameters, and finally, the Pareto non-dominated solution set under the current water quality conditions is selected. Managers can choose a scheme according to their preferences, and the system provides the corresponding objective recovered trajectory and the inverted physical intervention fluxes, such as precise aeration rate and chemical reduction rate.

[0081] This embodiment of label-free multi-objective decision-making based on naturally recovering manifolds and physical flux inversion bypasses the dilemma of missing artificial control labels. First, it detects naturally recovering events from historical passive records and constructs feasible ecological recovery manifolds using CVAE (Continuous Ecological Action Optimization). Then, it uses calibrated physical equations to inversely calculate exogenous physical fluxes as intervention costs. Finally, it combines environmental benefit objectives to perform an EPO (External Physical Flux) search in the potential space. This constitutes a complete process of "manifold construction—physical flux inversion cost—potential space gradient multi-objective optimization." It can be extended to any decision-making framework that generates feasible intervention spaces from passive observations and defines costs using physical inversion, such as similar applications in atmospheric governance based on diffusion models to invert reduction amounts. Other generative models (such as GANs and diffusion models) can replace CVAE, or other optimizers can replace EPO. The overall process and the method of defining the cost of physical flux inversion are innovations of this embodiment.

[0082] This embodiment presents an online deployment closed-loop feedback and parallel real-time search protocol. This protocol includes a decision-making process encompassing safe distance prediction triggering, multi-preference ray parallel EPO gradient search, non-dominated solution screening, and rolling optimization over time steps, enabling sub-second-level high-frequency real-time decision-making. This deployment protocol features parallel computation flow and sub-second decision response time.

[0083] This embodiment addresses the shortcomings of mainstream water quality prediction architectures, which consistently fail to accurately reproduce the dynamic physical relationships between various water quality indicators while preserving linear computational complexity. It resolves the issues of the physical mechanisms of oxygen consumption and reoxygenation in water bodies being isolated from the training process of data-driven models and unable to participate in gradient optimization, and the loss of the ability to adaptively adjust to water conditions due to the rigid adherence to unchanging concentration limits in safety assessments. It also compensates for the lack of a pathway to construct feasible decision-making schemes and conduct efficient multi-objective trade-off searches under the stringent condition that historical data is only passively recorded and lacks any active intervention labels.

[0084] Using high-frequency water quality monitoring data from a control section of a reservoir from June 2021 to January 2025 as the object, the implementation process of this method is described:

[0085] S1: Multivariate Sequence Acquisition

[0086] The data used in this example comes from a publicly released high-frequency monitoring sequence of a reservoir control section from the National Surface Water Quality Automatic Monitoring System, spanning from June 2021 to January 2025. The standard sampling interval ∆T is 4 hours. At each time step, water temperature (Temp, ℃), pH, dissolved oxygen (DO, mg / L), conductivity (EC, µS / cm), turbidity (Turb, NTU), and permanganate index (COD) are recorded simultaneously. Mn Nine physicochemical variables were included: total phosphorus (TP, mg / L), total nitrogen (NH3-N, mg / L), total phosphorus (TP, mg / L), and total nitrogen (TN, mg / L). After processing, 6847 effective time steps were obtained, which were then divided into 23 continuous subsequences based on natural breakpoints.

[0087] For the original time series, a multi-step cleaning process is applied progressively. First, a Savitzky-Golay filter is used to smooth the time domain to remove high-frequency noise introduced by the sensor. Then, for breakpoints with consecutive missing values ​​not exceeding 72 hours, conformal piecewise cubic Hermite interpolation is used for imputation. For segments with missing values ​​exceeding 72 hours, the sequence is truncated to prevent long segments of fictitious data from corrupting statistical properties. Finally, based on the training set statistics, reversible normalization (RevIN) is performed independently for each variable channel to ensure a consistent distribution between training and inference phases, while preventing information leakage. Figure 2 The figures show the dissolved oxygen (DO) and permanganate index (COD) before and after pretreatment. MnThe sequence comparison diagram shows that (a) is the dissolved oxygen sequence of the raw sensor readings (including outliers), (b) is the dissolved oxygen sequence after preprocessing to remove outliers, (c) is the permanganate index sequence of the raw sensor readings (including outliers), and (d) is the permanganate index sequence after preprocessing to remove outliers. It can be clearly seen that the purified sequence, while reducing noise and filling short-term gaps, still retains the nonlinear dynamic characteristics of the water body. After preprocessing, the dataset was divided into three parts according to time sequence: the training set (70%), corresponding to June 2021 to December 2023; the validation set (10%), corresponding to January to June 2024; and the test set (20%), corresponding to July 2024 to January 2025.

[0088] S2: Decomposition-Interaction Mamba World Model Construction.

[0089] In this step, the model selects a backtracking window of L=24 time steps, equivalent to 96 hours; the prediction horizon H examines 6, 12, and 24 steps respectively, corresponding to forecast durations of 24, 48, and 96 hours. Hidden dimension d model Take 64, state dimension d state The Mamba layer number is set to 2, with 16 layers selected. The front-end sequence decomposition module is configured with a set of learnable moving average convolutional kernels, with candidate kernel sizes drawn from the set {3, 7, 13, 25}, and the trend component is adaptively extracted using softmax weighting. Accordingly, the input sequence is decomposed into a trend component and a seasonal-residual component, which are then fed into their respective independent Mamba encoding paths.

[0090] Following each layer of Mamba encoding is a cross-variable gated state injection module (CV-GSI). This module first concatenates the hidden states of each variable channel, and then uses a learnable gating vector to finely control the intensity of information injection, thereby reliably recovering the DO and COD. Mn The asymmetric coupling relationship between variables. The outputs of the two coding paths are linearly projected and then added element by element to form a multi-step prediction result.

[0091] S3: Joint calibration of the physical information coupling constraint layer

[0092] During training, the Streeter-Phelps lumped parametric equation is directly embedded into the loss function, giving it learnable capabilities. The reoxygenation coefficient k... a Oxygen consumption coefficient k d and self-cleaning coefficient k s All parameters are defined as learnable scalar parameters, and their positive values ​​are strictly ensured by the Softplus function. Forward Euler discretization is performed with a step size of ∆t = 4 hours, and the physical consistency loss L... physDefined as DO and COD predicted by the model Mn The root mean square error between the single-step change and the expected change of the equation. Meanwhile, starting from the critical equilibrium surface dDO / dt=0, a dynamic safety boundary DO is derived. min =f(COD) Mn (Water temperature), and this boundary can be dynamically adjusted to follow the real-time water temperature and organic matter concentration. Based on this, a differentiable safety distance function d is constructed. safe =DO pred -DO min DO pred To predict the dissolved oxygen value, and using the exponential penalty L safe Strengthen the rejection of various unsafe conditions. For example... Figure 3 As shown, k is plotted. a k d and k s Convergence curves of the three parameters during training. (a) is the reoxygenation coefficient k. a The convergence curve during the training process, (b) represents the oxygen consumption coefficient k. d The convergence curve during the training process, (c) represents the self-cleaning coefficient k. s In the convergence curves during training, the horizontal axis in all three graphs represents the number of training epochs, and the vertical axis represents the reference value. d -1 As can be seen, after a brief initial oscillation, each parameter eventually settles smoothly within the reasonable range typical for freshwater reservoirs (the gray shaded area in the figure). The learned physical parameters are compared with empirical ranges from literature: reoxygenation coefficient k... a =0.45±0.02d -1 Oxygen consumption coefficient k d =0.18±0.01d -1 Self-cleaning coefficient k s =0.08±0.01d -1 The coupling ratio was 0.40 ± 0.03, all within the reference range of deep-water static lakes and reservoirs. This result strongly supports the reliability and interpretability of the physical constraints of this system.

[0093] Further from DO-COD Mn The perspective of the phase space trajectory verifies the crucial role played by physical constraints. Taking a high-temperature summer scenario as an example, if physical constraints are removed, the DC-Mamba predicted trajectory will directly penetrate the dynamic safety boundary and enter the physical violation risk zone; while the predicted trajectory of the present invention, DC-Mamba+Phys (physical), when approaching the dynamic safety boundary, produces a significant "bounce" effect due to the repulsion penalty of physical loss, and instead evolves safely along the edge of the high-density historical manifold.

[0094] S4: Feasible ecological restoration manifold construction

[0095] Based on the described detection rules, natural recovery and disturbance events are automatically identified from the passive observation sequences in the training set. A total of 47 events were captured, including 18 water dilution events, 16 temperature jump events, and 13 water quality mutation events. For each event, the state sequence s0 of the 48 time steps before the event and the state change Δs of the 96 time steps during the event are extracted and compiled to form the recovery sample set D. rec .

[0096] Subsequently, a conditional variational autoencoder (CVAE) is constructed, whose latent space dimension d z The depth is set to 8, and the hidden layer dimension is 128. The encoder, guided by condition s0, maps ∆s to a set of mean and log-variance; the decoder takes s0 and the latent variable z extracted from the latent space as inputs, attempting to reconstruct the change. The training objective is a weighted sum of the reconstruction loss and the KL divergence, with the KL weights increasing from 0 to 1 over four cyclic annealing cycles. After training, only the decoder is retained. The low-dimensional potential space spanned by this decoder constitutes the so-called feasible ecological restoration manifold.

[0097] S5: Model Training and Freezing

[0098] The AdamW optimizer was used during training, with an initial learning rate of [missing information]. The batch size is 32, the maximum training epochs are 200, and the termination tolerance is set to 15. To ensure smooth injection of physical knowledge, a gradual constraint reinforcement strategy is adopted: in the first 30% of iterations, only the data-driven mean squared error loss is optimized. Physical consistency weights are applied for 30% to 60% of the cycles. The equations are linearly increased from 0 to 0.1, and a physical consistency loss based on the Streeter-Phelps equations is gradually introduced. After 60% of the cycle, the security penalty weight will be activated. Similarly, the penalty increases linearly from 0 to 1, based on the safety distance index constructed using dynamic safety boundaries. Included in training. The resulting total loss function is: Once the validation set termination condition is triggered, all network parameters are frozen to obtain a deterministic world model. .

[0099] S6: Multi-objective physical flux inversion and exact Pareto optimization

[0100] Entering the online decision-making phase, real-time acquisition of observation values. Then the frozen world model was invoked. Projecting the natural baseline trajectory over the next 24 hours (H=24 hours) This depicts the evolutionary trend without human intervention. Simultaneously, a decoder is used in manifold restoration. Generate a recovery signal and superimpose it onto the baseline trajectory to obtain the target recovery trajectory. S target .

[0101] To find the optimal trade-off between environmental benefits and engineering costs, this embodiment defines two differentiable objective functions. Environmental benefit objective Asymmetric penalties and dynamic safety penalties under compliance conditions Together they form a whole. The cost of engineering intervention. The mass balance is then inverted using calibrated physical parameters: the positive difference between the natural baseline DO change rate and the target recovery DO change rate is calculated step-by-step, and the sum is used to obtain the minimum oxygen flux that must be supplied from an external source; then the additional organic matter flux that needs to be reduced is calculated in the same way. After that, the cost is multiplied by the unit cost weights of aeration oxygen supply and chemical reduction, and a trajectory smoothness constraint is added, thus forming a cost function with a clear physical meaning.

[0102] M=50 preference rays are uniformly distributed on a normalized two-dimensional preference simplex. Each ray starts at z=0 and performs 60 EPO iterations with a step size of 0.05. All rays are updated in parallel on the GPU. After the search is completed, the solution set is sorted non-dominated to obtain the Pareto front under the current condition.

[0103] like Figure 4 As shown, a visual comparison is presented between the Pareto fronts generated by the Physical Information Inverse Decision Framework (PI-IDF) of this invention and those generated by NSGA-III (Non-dominated Sorting Genetic Algorithm III) and WMPC (Weighted Model Predictive Control). The NSGA-III population size is set to 200. The horizontal axis in the figure represents the normalized intervention cost (%), and the vertical axis represents the average permanganate index (COD). MnThe concentration (mg / L) of PI-IDF is shown in Table 1. The solution set of PI-IDF (blue dots) forms a dense and uniform non-dominated front, which is effectively truncated by the ecological safety boundary (red dashed line), completely eliminating the possibility of entering the risk area (pink area). The red five-pointed star is the optimal inflection point. In contrast, the solutions of NSGA-III (orange circles) are not only scattered, but some points even cross the safety boundary, while WMPC (green triangle) can only provide scattered discrete solutions. The quantitative comparison in Table 1 further demonstrates the advantages of the present invention: the hypervolume (HV) of PI-IDF reaches 0.824, the reverse generation distance (IGD) is as low as 0.019, the single-step decision time is only 0.65 seconds, and zero safety violations are achieved at all test time points.

[0104] Table 1: Comparison of Multi-Objective Optimization Algorithms

[0105] WMPC (11 weights) 0.487 ± 0.018 0.094 ± 0.007 0.18 ± 0.03 4 / 55 independent NSGA-III (Pop=200) 0.706 ± 0.031 0.047 ± 0.009 34.2 ± 3.8 7 / 55 population PI-IDF (This invention) 0.824 ± 0.012 0.019 ± 0.004 0.65 ± 0.08 0 / 55 gradient

[0106] In actual operation, a safe distance prediction trigger mechanism is adopted: once the world model predicts that a certain distance will occur within the next 24 hours... d safe < If the value is 0, a multi-target search is automatically initiated and an intervention plan is provided; otherwise, the "maintain status quo" command is directly output. The decision-making process moves forward with each sampling time step and continuously incorporates the latest observation information to complete closed-loop correction.

[0107] like Figure 5 As shown, a 14-day dynamic preference switching simulation is presented. The black dashed lines in each coordinate panel represent the first phase (days 1-8): economy priority (compressing costs using safety margins), and the black dashed lines represent the second phase (days 8-14): water quality priority (actively restoring and establishing a safety buffer). The "economy priority" preference is used from day 1 to day 8, and a smooth transition to "water quality priority" is achieved from day 8 onwards. Figure 5 The panels sequentially present the changes in preference weights, the rapid increase in intervention intensity ||z|| in the second stage, the strong rebound in actual dissolved oxygen (DO) concentration (mg / L) after closely adhering to the dynamic safety boundary in the second stage, and the permanganate index (COD). Mn The concentration (mg / L) was completely suppressed below the national Class II standard limit in the second stage, and the continuous safety margin (Ф) remained positive. The quantitative results in Table 2 indicate that PI-IDF maintained zero safety violations for 14 days, and the response stabilization time required for preference switching was approximately 6 hours, which is far superior to approximately 24 hours for NSGA-III and approximately 36 hours for WMPC.

[0108] Table 2: Dynamic response performance under preference switching simulation

[0109] 14-day average DO concentration (mg / L) 6.25 6.1 5.95 <![CDATA[14-day average COD Mn Concentration (mg / L)]]> 3.42 3.55 3.68 Number of security violations throughout the entire lifecycle (times) 0 5 8 <![CDATA[Full-cycle minimum safety margin Ф min (mg / L)]]> 0.12 -0.45 -0.72 Preference switching response and settling time (hours) ~ 6 ~ 24 ~ 36

[0110] To clarify the true contribution of each module to performance, comprehensive prediction accuracy comparisons and ablation experiments were conducted on the test set. Under the most challenging long-range prediction condition of H=24 steps, the present invention DC-Mamba+Phys achieved RMSE=0.305 and R²=0.885 on DO, and on COD... Mn The results showed RMSE=0.318 and R²=0.875; compared with the best-performing baseline model PatchTST, the two errors were reduced by 20.8% and 14.1%, respectively.

[0111] Simultaneous physical violation rate (PVR) analysis further revealed that the PVR of the complete model was only 0.3%, while that of the DC-Mamba model without physical constraints was 8.4%, and the remaining baseline models ranged from 12.3% to 18.7%. Table 3 quantitatively revealed the following from the ablation experiments: removing the sequence decomposition front (w / o Decomposition) increased the DO RMSE to 0.385; removing CV-GSI (w / o CV-GSI) increased it to 0.365; and removing physical consistency loss alone (w / o Physics (L phys )) or safety constraints (Safety(L) safety The structured enhancement and dual physical constraints respectively increased the DO RMSE to 0.338 and 0.325; if both were removed simultaneously (degenerating to pure DC-Mamba), the RMSE rebounded to 0.350, and the PVR jumped to 8.4%; while when replaced with standard Mamba, the DO RMSE deteriorated further to 0.498, and the PVR reached 16.5%. These results strongly demonstrate that structured enhancement and dual physical constraints make decisive contributions to the accuracy and physical consistency of long-range extrapolation.

[0112] Table 3: Ablation studies of structural and physical components (assessed at the H=24 level)

[0113] Full Model (DC-Mamba+Phys) 0.305 0.885 0.318 0.875 0.3 18.7 w / o Decomposition 0.385 0.805 0.37 0.825 1.8 16.4 w / o CV-GSI 0.365 0.812 0.355 0.835 2.3 15.9 <![CDATA[w / o Physics (L phys )]]> 0.338 0.852 0.328 0.86 3.2 18.5 <![CDATA[w / o Safety (L safety )]]> 0.325 0.862 0.332 0.858 2.1 18.3 w / o Phys&Safety (ie, DC-Mamba) 0.35 0.842 0.335 0.855 8.4 17.9 Vanilla Mamba 0.498 0.685 0.44 0.748 16.5 11.2

[0114] The above embodiments fully demonstrate that the physical information inversion decision framework proposed in this invention can extract searchable recoverable manifolds from passively observed data, thereby achieving physically interpretable multi-objective online decision-making. It represents a significant leap forward compared to existing technologies in terms of prediction accuracy, physical consistency, and decision-making efficiency.

[0115] Example 2

[0116] like Figure 6 As shown, this embodiment provides a multi-objective decision-making system for physical information inversion of the water environment, which corresponds one-to-one with the multi-objective decision-making system for physical information inversion of the water environment described in Embodiment 1. It is used to implement the method of Embodiment 1 and includes:

[0117] Multivariate Sequence Acquisition Unit: Used to acquire raw multivariate high-frequency monitoring sequences of reservoirs, and outputs clean and usable multivariate sequences after preprocessing;

[0118] World Model Construction Unit: Used to construct a decomposed-interactive Mamba world model. The world model includes a sequence decomposition front-end, a dual-path selective state space encoder, and a transvariable gated state injection module. Multivariable sequences are input into the world model. The sequence decomposition front-end decomposes the multivariable sequences into trend components and seasonal-residual components. The trend components and seasonal-residual components are respectively sent to the two encoding paths of the dual-path selective state space encoder for feature extraction. The encoding path contains multiple Mamba encoding layers. After each layer of Mamba encoding is completed, the transvariable gated state injection module is triggered to interactively inject the hidden states of each variable channel under the encoding path. The interactively enhanced state is sent to the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion is finally progressively deduced to predict the future multi-step water quality trajectory.

[0119] Physical information coupling constraint layer building unit: Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized, the physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change of the equation, the dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the derivative of the equation is zero, and it is constructed as a differentiable safety distance function in the form of exponential penalty.

[0120] Feasible ecological restoration manifold building unit: used to detect natural restoration or disturbance events from historical passive observation sequences, extract the imprints of state changes before and after the event to form a restoration sample set; use the restoration sample set to train the generative model, and the low-dimensional latent space spanned by it after training convergence is the feasible ecological restoration manifold.

[0121] The world model training and freezing unit is used to jointly optimize and train the original decomposed-interactive Mamba world model with prediction bias loss as the core, combined with physical consistency loss and safety distance function, and adopts a progressive constraint enhancement strategy. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model.

[0122] Online multi-objective decision unit: It is used to input the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; extract latent variables from the feasible ecological restoration manifold, transform them into variables, and superimpose them onto the natural baseline trajectory to generate restoration trajectories for many objectives; conduct multi-objective search in the continuous latent space using exact Pareto optimization, and after non-dominated sorting of the obtained solution set, select the Pareto non-dominated solution set for the current water quality conditions, and output the corresponding objective restoration trajectory and physical intervention flux.

[0123] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A multi-objective decision-making method for physical information inversion of the water environment, characterized in that, Includes the following steps: S1: Obtain the original multivariate high-frequency monitoring sequence of the reservoir, and output the multivariate sequence after preprocessing; S2: Construct a decomposed-interactive Mamba world model. The world model includes a sequence decomposition front-end, a dual-path selective state space encoder, and a cross-variable gated state injection module. The multivariate sequence is input into the world model and decomposed into trend components and seasonal-residual components by the sequence decomposition front-end. The trend components and seasonal-residual components are respectively sent to the two encoding paths of the dual-path selective state space encoder for feature extraction. The encoding path contains multiple Mamba encoding layers. After each layer of Mamba encoding is completed, the cross-variable gated state injection module is triggered to interactively inject the hidden states of each variable channel under the encoding path. The interactively enhanced state is sent to the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion is finally progressively deduced to predict the future multi-step water quality trajectory. S3: Construct a physical information coupling constraint layer. Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized. The physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change of the equation. The dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the derivative of the equation is zero. It is then constructed as a differentiable safety distance function in the form of exponential penalty. S4: Construct a feasible ecological restoration manifold by detecting natural restoration or disturbance events from historical passive observation sequences, extracting the imprints of state changes before and after the events to form a restoration sample set; use the restoration sample set to train a generative model, and the low-dimensional latent space spanned by the model after training convergence is the feasible ecological restoration manifold. S5: World model training and freezing. Taking prediction bias loss as the core, combined with the physical consistency loss and the safe distance function, a progressive constraint enhancement strategy is used to jointly optimize and train the world model. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model. S6: Online multi-objective decision-making, inputting the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; Potential variables are extracted from the feasible ecological restoration manifold, transformed into variables, and superimposed on the natural baseline trajectory to generate restoration trajectories for numerous objectives. A multi-objective search is carried out in the continuous potential space using precise Pareto optimization. The resulting solution set is sorted by non-dominated order, and Pareto non-dominated solution set for the current water quality conditions is selected. The corresponding objective restoration trajectory and physical intervention flux are output.

2. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S1, the preprocessing includes time-domain filtering, missing value imputation, and reversible normalization.

3. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In step S2, the multivariate sequence is divided according to a preset backtracking window length to obtain a fixed-length observation window sequence, and the observation window sequence is input to the sequence decomposition front end of the world model. The built-in sequence decomposition front end uses a learnable moving average kernel, and the kernel width is weighted in the candidate set using softmax to achieve differentiability selection, so as to adaptively track the trend fluctuation of the sequence; the dual-path selective state space encoder consists of two Mamba encoding paths with the same structure, independent parameters, and mirror images of each other, and selectively processes information flow using input-driven step size parameters; the cross-variable gated state injection module concatenates the hidden states of each variable channel output by the current Mamba encoding layer into a matrix, and determines the strength of each channel accepting information from other channels through a learnable weight matrix and a gate vector; The implicit representation after dual-path fusion ultimately predicts the future multi-step water quality trajectory in a progressive manner, including: adding the final outputs of the two paths element by element after linear projection to obtain the fused global implicit representation; Using this global implicit representation as the initial state, an autoregressive approach is used to progressively deduce and generate future water quality trajectories step by step.

4. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S3, the Streeter-Phelps oxygen consumption-reoxygenation equation is used to describe DO and COD. Mn The oxygen consumption-reoxygenation kinetic relationship between them is determined, and the reoxygenation coefficient, oxygen consumption coefficient, and self-purification coefficient are all learnable positive parameters; the physical consistency loss is the DO and COD predicted by the world model. Mn The one-step change and the DO and COD calculated by the equation Mn The mean square error between expected changes.

5. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S4, training the generative model using the recovery sample set includes: training a conditional variational autoencoder using the recovery sample set; the encoder maps the recovery signal and the current state conditions to a low-dimensional latent space; the decoder reconstructs the change in the target recovery trajectory based on the latent variables and the current state conditions; after training converges, only the decoder is retained and frozen, and the low-dimensional latent space spanned by it is the desired feasible ecological restoration manifold.

6. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S4, the natural recovery or disturbance event includes influent dilution events, temperature jump events, and / or sudden changes in water quality events.

7. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S5, during the training of the world model, a progressive constraint enhancement strategy is adopted, including: optimizing only the data prediction loss in the first 30% of iterations, linearly increasing the physical consistency weight from zero in 30% to 60% of iterations, and waking up the safety penalty weight after 60% of iterations.

8. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S6, a multi-objective search is carried out in the continuous latent space using exact Pareto optimization, including: starting from multiple preference rays uniformly distributed on the preference simplex, the latent variables are initialized in parallel, and then the exact Pareto optimization gradient update is iteratively performed so that each solution point approaches the Pareto front along its respective preference direction.

9. The multi-objective decision-making method for physical information inversion of the water environment as described in claim 1, characterized in that, In S6, the current water quality conditions include at least the dissolved oxygen concentration, permanganate index, and water temperature at the current moment, and the physical intervention flux includes at least the external aeration rate and the organic matter reduction rate. The calculation method for the exogenous aeration rate is as follows: The positive portion of the difference between the natural baseline DO change rate and the target recovered DO change rate is calculated step-by-step over time, and the sum is used to obtain the minimum oxygen flux; the calculation method for the organic matter reduction rate is as follows: The natural baseline COD is calculated step-by-step over time. Mn Rate of change and target recovery COD Mn The positive portions of the difference in rates of change are accumulated to obtain the organic matter reduction flux; the aeration cost is obtained by multiplying the aeration unit cost coefficient by the minimum oxygen flux, and the reduction cost is obtained by multiplying the chemical reduction unit cost coefficient by the organic matter reduction flux. Finally, the trajectory smoothing constraint is superimposed to obtain the engineering intervention cost.

10. A multi-objective decision-making system for physical information inversion of the water environment, characterized in that, include: Multivariate sequence acquisition unit: used to acquire the raw multivariate high-frequency monitoring sequence of the reservoir, and output the multivariate sequence after preprocessing; World Model Construction Unit: Used to construct a decomposed-interactive Mamba world model. The world model includes a sequence decomposition front-end, a dual-path selective state space encoder, and a cross-variable gated state injection module. The multivariate sequence is input into the world model. The sequence decomposition front-end decomposes the multivariate sequence into trend components and seasonal-residual components. The trend components and seasonal-residual components are respectively sent to the two encoding paths of the dual-path selective state space encoder for feature extraction. The encoding path contains multiple Mamba encoding layers. After each layer of Mamba encoding is completed, the cross-variable gated state injection module is triggered to interactively inject the hidden states of each variable channel under the encoding path. The interactively enhanced state is sent to the next Mamba encoding layer for further processing. The hidden representation after dual-path fusion is finally progressively deduced to predict the future multi-step water quality trajectory. Physical information coupling constraint layer building unit: Based on the Streeter-Phelps oxygen consumption-reoxygenation equation, the equation is discretized, the physical consistency loss is defined as the mean square error between the one-step state change predicted by the world model and the expected change of the equation, the dynamic safety boundary that varies with water temperature and organic matter concentration is derived from the critical equilibrium surface where the derivative of the equation is zero, and it is constructed as a differentiable safety distance function in the form of exponential penalty. Feasible ecological restoration manifold building unit: used to detect natural restoration or disturbance events from historical passive observation sequences, extract the imprints of state changes before and after the event to form a restoration sample set; use the restoration sample set to train the generation model, and the low-dimensional latent space spanned by it after training convergence is the feasible ecological restoration manifold; World model training and freezing unit: It is used to jointly optimize and train the model with prediction bias loss as the core, combined with the physical consistency loss and the safety distance function, and adopts a progressive constraint enhancement strategy. After the parameters converge, the model is frozen to obtain a deterministic, globally differentiable state transition world model. Online multi-objective decision unit: used to input the real-time observed current water quality status into the frozen world model to deduce the evolution trajectory of the natural baseline; Potential variables are extracted from the feasible ecological restoration manifold, transformed into variables, and superimposed on the natural baseline trajectory to generate restoration trajectories for numerous objectives. A multi-objective search is carried out in the continuous potential space using precise Pareto optimization. The resulting solution set is sorted by non-dominated order, and Pareto non-dominated solution set for the current water quality conditions is selected. The corresponding objective restoration trajectory and physical intervention flux are output.

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