Crowd Flow Prediction Using Kernel Dynamic Mode Decomposition
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Existing crowd flow estimation methods fail to model the influence of control inputs on dynamical systems, limiting their ability to accurately predict and segment crowd flows in complex environments.
Innovation Solution
The implementation of a system and method using dynamical system analysis with control inputs, specifically employing kernel dynamic mode decomposition (KDMD) operators to learn system dynamics and input-mapping operators from training data, allowing for flow completion in partially observed scenes by estimating coefficients and reconstructing complete flows.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If traditional crowd flow estimation methods are used, then the system is simpler to implement, but the prediction accuracy deteriorates because control inputs are not modeled
Solution Approach 1:
The system performs preliminary learning of the dynamics operator and input-mapping operator from training data before actual flow prediction. This offline training phase prepares the models in advance, allowing them to accurately capture system dynamics and control input relationships, thereby improving prediction accuracy without adding complexity during real-time operation
Solution Approach 2:
The patent introduces a dynamics operator and an input-mapping operator as intermediary mathematical models that bridge the relationship between control inputs, system state, and flow evolution. These operators act as mediators that encode the underlying physical laws and system behavior, enabling accurate prediction by transforming control inputs into meaningful flow predictions
2Measurement precision
If complete scene observations are obtained, then the flow reconstruction is more accurate, but the cost of data collection and processing increases
Solution Approach 1:
The system extracts and utilizes only the essential features and dynamics from training data to build compact operator models. By extracting the core dynamic relationships rather than storing or processing all raw observation data, the system achieves accurate flow reconstruction from limited observations while minimizing data storage and processing requirements
Solution Approach 2:
The patent transforms the problem from directly processing large volumes of observation data to working with parameterized operator models. By changing the representation from raw data to mathematical operators with learned parameters, the system maintains high reconstruction accuracy while significantly reducing the quantity of data needed during operation
3Speed
If real-time prediction is achieved, then the system responsiveness improves, but the computational complexity during operation increases
Solution Approach 1:
The system performs computationally intensive learning and model training in advance during an offline phase. By completing the heavy computational work beforehand to establish the dynamics operator and input-mapping operator, the system enables fast real-time predictions with minimal computational complexity during operational use
Solution Approach 2:
The patent replaces direct numerical simulation or complex real-time computation with pre-trained operator models that can be efficiently evaluated. By substituting heavy computational mechanics with lightweight operator applications, the system achieves real-time prediction speed while keeping operational computational complexity low
Data Source
AI summary
Systems and methods for determining states of flow of objects in a scene. The methods and systems include measuring states of the flow at observed sample points of the scene, wherein the scene contains a set of sample points having subsets of observed and unobserved sample points. Store in a memory an operator specifying time-varying dynamics of training states of flow of the objects in the scene. Estimate, using the operator and the measured states at the subset of observed sample points, the states of the flow of the objects at the subset of unobserved sample points of the scene. Output the states of the flow at the set of unobserved sample points of the scene, so as to assist in a management of managing states of flow of objects in the scene.