Dynamic Image Reconstruction With Physics-Informed Masked Convolution
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Solution Overview
Problem
Current spatial mapping methods using sparse point measurements, such as Kriging and convolutional neural networks, produce unreliable results due to missing pixels or outliers, and fail to incorporate physical laws like conservation of mass and energy, especially in complex real-world phenomena.
Innovation Solution
A physics-informed neural network (PINN) performs a three-dimensional partial convolution process using masked convolutional layers to reconstruct a continuous spatial map of a geographical domain, incorporating wind field velocity and air pollutant concentration measurements, ensuring adherence to physical laws like the Advection-Diffusion Equation.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Reliability
If Kriging or traditional convolutional neural networks are used for spatial mapping from sparse point measurements, then the method is simple to implement, but the results are unreliable due to missing pixels or outliers and fail to incorporate physical laws
Solution Approach 1:
The patent merges traditional spatial interpolation methods with physics-based constraints by integrating the Advection-Diffusion Equation into the neural network framework. This combination allows the model to incorporate physical laws while maintaining the spatial mapping functionality, thereby improving reliability without completely abandoning simple interpolation approaches.
Solution Approach 2:
The patent creates a composite modeling approach by combining data-driven neural network components with physics-based mathematical models. The hybrid architecture integrates the flexibility of machine learning with the reliability of physical laws, producing a composite system that leverages the strengths of both approaches to achieve reliable spatial mapping from sparse data.
2Quantity of substance
If sparse sensor network measurements are used to reconstruct continuous spatial maps, then data acquisition cost is reduced, but the quality and completeness of the spatial map deteriorates due to missing pixels
Solution Approach 1:
The patent transforms the problem by changing the parameters used for reconstruction. Instead of directly interpolating from sparse point measurements, the model uses physics-based parameters from the Advection-Diffusion Equation (advection velocity, diffusion coefficient) to guide the reconstruction process, enabling high-quality spatial maps to be generated from limited data.
Solution Approach 2:
The patent introduces physics-based mathematical models as an intermediary between sparse measurements and the final spatial map. The Advection-Diffusion Equation acts as a mediator that fills in the gaps between sparse data points, using physical laws to infer missing information and produce complete, high-quality spatial reconstructions.
3Adaptability or versatility
If purely data-driven approaches are used for spatial reconstruction, then the model can adapt to complex real-world phenomena, but the model fails to satisfy certain physical principles such as conservation of mass and energy
Solution Approach 1:
The patent applies preliminary anti-action by pre-constraining the neural network to satisfy physical laws before the model is deployed for prediction. The architecture is designed with built-in constraints that prevent the model from producing physically impossible results, countering the tendency of purely data-driven models to violate conservation principles.
Solution Approach 2:
The patent creates a universal model that serves multiple functions: it adapts to complex real-world phenomena through neural network flexibility while simultaneously satisfying physical principles through embedded constraints. The multi-functional architecture handles both data-driven pattern recognition and physics-based validation in a single unified framework.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The PINN effectively fills in missing areas of the spatial map while preserving data fidelity to physical simulations, identifying pollutant sources and emission magnitudes, solving both forward and inverse problems.
Implementation Method 1
A physics-informed neural network (PINN) performs a three-dimensional partial convolution process using masked convolutional layers to reconstruct a continuous spatial map of a geographical domain, incorporating wind field velocity and air pollutant concentration measurements, ensuring adherence to physical laws like the Advection-Diffusion Equation
Implementation Method 2
A physics-informed neural network (PINN) performs a three-dimensional partial convolution process using masked convolutional layers to reconstruct a continuous spatial map of a geographical domain, incorporating wind field velocity and air pollutant concentration measurements, ensuring adherence to physical laws like the Advection-Diffusion Equation
Data Source
AI summary
According to one embodiment, a method, computer system, and computer program product for dynamic image reconstruction is provided. The present invention may include training a physics-informed neural network (PINN) using received training data; receiving wind field velocity measurements in a geographical domain from one or more weather information sources and air pollutant concentration measurements of one or more air pollutants from the geographical domain using a sparse sensor network to produce a plurality of input data; processing the plurality of input data through multiple physics-informed masked convolutional layers in the trained PINN to perform a three-dimensional partial convolution process; and performing the dynamic image reconstruction on the processed plurality of input data using the trained PINN to generate a reconstructed continuous spatial map of the geographical domain.