Development of method for latent space representation of weather control
The goal of this research project is to prevent heavy rainfall damage on land by generating torrential rain over the sea. To achieve this, we need to redirect weather scenarios from causing heavy rain on land to reducing atmospheric water vapor over the sea, preventing damage. Comprehensive meteorological data, such as temperature, humidity, and wind direction, result in ultra-high-dimensional data, making prediction and control challenging. However, if weather conditions lead to several typical patterns, with one being undesirable, we can effectively describe these abstracted meteorological conditions to improve control efficiency. We aim to extract essential low-dimensional degrees of freedom, that we call as latent space representation, crucial for these branching points. We investigate three approaches to acquire latent space representations beneficial for weather control; reservoir computing, Koopman mode decomposition, and landscape analysis.
Item 3-1Latent space representation of weather control using reservoir computing
Principal investigator: Keita Tokuda
Outline
The goal is to develop a method for accurately evolving chaotic dynamical systems over time by combining dimensionality reduction techniques with reservoir computing. Specifically, we aim to reduce the dimensionality of meteorological data using techniques such as singular value decomposition or machine learning, and then evolve the latent variable in the reduced space over time using reservoir computing. This approach combines dimensionality reduction techniques, which capture spatial features, with reservoir computing, which is well suited for learning temporal dynamics, to develop a new method.
Methods
We perform simulations of high-dimensional nonlinear systems, such as weather models described by partial differential equations, and use the resulting time series as training data to build surrogate models of the system. As the learning model, we use a combination of dimensionality reduction techniques, such as deep learning models that excel in reducing dimensionality, and reservoir computing, which is well-suited for time series prediction.
Importance
In this study, we aim to identify the tipping point between the “organization” and “disorganization” of cumulonimbus clouds, predict which state the system will transition into, and explore the control of weather fields based on these predictions. For example, we may encounter multiple weather fields where a linearly elongated precipitation zone develops and others where it does not. In such cases, it is essential to recognize that weather fields with a linearly elongated precipitation zone may be considered “close” to each other in some sense, while those without it should be regarded as “distant” from the ones with it. However, if we directly treat weather fields with a linearly elongated precipitation zone as vectors and compute naïve inner products or cosine similarity, the results may be misleading. This is because a linearly elongated precipitation zone has an elongated, linear shape, and unless the positions of these systems align perfectly, their representations will almost always be nearly orthogonal. On the other hand, deep learning, which excels in image recognition, can provide robust responses to translational shifts of objects on the screen. This is because the model incorporates translational symmetry into its response, mapping the image to a lower-dimensional latent representation that is independent of the object’s position. Therefore, dimensionality reduction techniques such as deep learning are considered promising for the reduction of weather filed data to lower-dimensional representations. On the other hand, considering the crucial aspect of prediction in this project, it is well-known that reservoir computing exhibits high performance in forecasting nonlinear systems. Reservoir computing also excels at capturing the dynamics of the target system, and by using the internal states or models learned during training, it allows for tasks such as quantifying orbital instability. Therefore, developing a model that integrates both approaches becomes crucial for this project.
Expected problems and solutions
The reservoir computing framework is fundamentally a machine learning approach for learning time series data, and while it excels at capturing temporal dynamics, it is not inherently suited for extracting the gradient components, the Conley-Morse graph or the global bifurcation structures of the dynamical system. Therefore, for tasks such as identifying phenomena to be controlled, we refer to the results of Item 3-3, which focuses on landscape analysis of meteorological data and is proficient in extracting dynamics structures.
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Item 3-2Dimensionality reduction by Koopman mode decomposition
Principal investigator: Yoshihiko Susuki
Outline
This study aims at dimensionality reduction of ensemble data and computation reduction to solve the Model Prediction Control (MPC) in low-dimensional space. Specifically, we develop a mathematical foundation of dimensionality reduction for weather data based on Koopman Mode Decomposition (KMD) and apply control techniques based on Koopman operator to weather control.
Methods
As the methods of dimensionality reduction, Dynamic Mode Decomposition (DMD) has been widely used while being integrated with machine learning techniques, Koopman linearization, and Proper Orthogonal Decomposition (POD). As the control techniques, Koopman MPC, Koopman LQR, and so on are proposed. We consider multiple methods to hedge risks and select the best method(s), with a criterion as to whether or not to they apply to ensemble data or weather control.
Importance
By developing a low-dimensional model that can effectively approximate large-scale data, such as ensemble prediction data, the goal of this project can be demonstrated computationally. This study is essential to the project’s goal of “artificial generation of upstream maritime heavy rains to govern intense-rain-induced disasters over land”. The high-dimensionality of the target control model can be a bottleneck in terms of computational time and amount and optimality of control efforts. Developing effective dimensionality reduction and latent space representation is needed.
Expected problems and solutions
The data obtained with KMD or Koopman linearization can be challenging to interpret because ensemble data involve complex physical processes. Therefore, by using foresight information of physical process, we find a solution to interpretability in dimensionality reduction and estimated result of latent space. For example, it may be possible to extract low-dimensional data approximated in the sense of the energy norm (L2 norm) with POD or to model the inherent non-linearity in the dominant POD mode with the Koopman operator. Not limited to DMD, it may be possible to use more straightforward and less computationally demanding methods will be explored.
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Item 3-3Landscape analysis of meteorological information
Principal investigator: Yusuke Imoto
Outline
This study constructs a method to capture and extract the abstract structure of the boundary between the ‘organization’ and ‘disorganization’ of cumulonimbus clouds within a mathematical framework. Specifically, we develop dimensionality reduction for meteorological data based on landscape analysis to identify the boundary between phenomena. Based on the obtained landscape, we conduct trajectory and time series analysis to identify the weather inputs necessary to guide cumulonimbus clouds towards organization.
Methods
We develop methods to extract landscape structures that represents the essential dynamical change of events based on graph Hodge decomposition, as well as methods to extract the boundary (controllable regions) and its branching structures (factors inducing branching) from these landscape structures. We apply the methods to ensemble weather prediction data real data focused on heavy rainfall, and verify the methods and confirm their validity.
Importance
In order to identify the abstract branching structure that represents the boundary between the ‘organization’ and ‘disorganization’ of cumulonimbus clouds, it is essential to develop dimensionality reduction methods that extracts latent dynamical structures from the high-dimensional data of weather phenomena. Graph Hodge decomposition separates high-dimensional vector fields into a potential flow that describes global flow and a rotational flow that describes cycle structure. By graphing the data, computationally cost reduction, we can avoid the combinatorial explosion of computational costs associated with solving high-dimensional partial differential equations, thereby significantly reducing computational demands. In addition, by combining the landscape structure composed of potential flow with statistical analysis and time series analysis, it is possible to identify the essential routes that lead to each outcome and their boundaries. Thus, graph Hodge decomposition can serve as an effective way for the methods developed in this study to identify the boundary that separates the ‘organization’ and ‘disorganization’ of cumulonimbus clouds in latent space.
Expected problems and solutions
This study is expected to face computational challenges due to the use of a large amount of ensemble weather prediction data for validation. To reduce the computational demands in a single calculation, we hierarchically separate the data resolution. While landscape analysis excels at extracting latent dynamical structures and their branching structures, other methods are needed to predict the phenomena against perturbations, such as changes in trajectories due to interventions. Therefore, we promote the development and validation by complementary use of analysis data based on reservoir computing of item 3-1, which excels in prediction, and Koopman mode decomposition of item 3-2.
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