Parallel PDE Simulation Flux Data Suppression
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Solution Overview
Problem
The existing methods for modeling physical systems using partial differential equations face significant challenges due to the high computational requirements and data transmission delays when updating elements in a mesh or grid, especially when processed across multiple partitions by separate processing units.
Innovation Solution
The solution involves periodically suppressing the transmission of flux data between processing units by extrapolating flux values from past data points, and using machine learning models, such as deep neural networks, to estimate flux data, thereby reducing data transmission and processing times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If flux data is transmitted between processing units at every time step, then accuracy of numerical simulation is maintained, but data transmission time and processing delay increase significantly
Solution Approach 1:
The patent implements periodic suppression of flux data transmission between processing units, where transmission occurs only at selected time steps rather than every time step. This periodic action reduces data transmission frequency and associated delays while maintaining simulation accuracy through extrapolation of flux values during non-transmission time steps.
Solution Approach 2:
The patent performs preliminary extrapolation of flux values using past flux data before transmission occurs. By predicting future flux values based on historical data, the system prepares accurate estimates in advance, allowing transmission to be suppressed at certain time steps without compromising simulation accuracy.
2Productivity
If flux data transmission is suppressed to reduce data transmission time, then processing speed improves, but accuracy of numerical simulation deteriorates
Solution Approach 1:
The patent implements a feedback mechanism where the system monitors simulation accuracy and adjusts the frequency of flux data transmission accordingly. By evaluating whether suppressed transmissions maintain acceptable accuracy thresholds, the system dynamically optimizes the balance between processing speed and simulation accuracy.
Solution Approach 2:
The patent changes the transmission parameter from fixed-frequency (every time step) to variable-frequency (based on accuracy requirements and extrapolation quality). This parameter change allows the system to adapt transmission frequency to maintain accuracy while maximizing processing speed improvements.
3Manufacturing precision
If flux data is transmitted frequently between processing units, then accuracy of boundary element updates is maintained, but communication overhead and energy consumption increase
Solution Approach 1:
The patent applies periodic suppression to boundary element flux transmissions, reducing communication frequency between processing units while maintaining boundary update accuracy through extrapolation. This periodic approach significantly reduces communication overhead and associated energy consumption.
Solution Approach 2:
The patent creates copies of past flux data and uses extrapolation to generate predicted flux values for boundary elements during non-transmission time steps. This copying approach eliminates the need for frequent actual data transmissions while maintaining accuracy, thereby reducing communication energy overhead.
Data Source
AI summary
A physical system is simulated using a model including a plurality of elements in a mesh or grid. The elements are divided into partitions processed by different processing units. For some time steps, flux data is transmitted between partitions for updating the state of edge elements of the partitions. Periodically, transmission of flux data is suppressed and flux data is obtained by linear interpolation based on past flux data. Alternatively, flux data is obtained by processing state variables of an edge element and past flux data using a machine learning model, such as a DNN.