Parallel Computing Data Transmission Reduction via Flux Interpolation
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Solution Overview
Problem
The existing methods for modeling physical systems using partial differential equations face significant delays due to the need for frequent data transmission between processing units, which is time-consuming and inefficient, especially when dealing with large-scale simulations that require updates across numerous elements.
Innovation Solution
The approach involves periodically suppressing the transmission of state data between processing units by extrapolating or using machine learning models, such as deep neural networks, to estimate flux data, thereby reducing the need for data transfer and improving processing times.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If state data is transmitted between processing units at every time step, then accuracy of flux calculation is maintained, but data transmission time and processing delay increase significantly
Solution Approach 1:
The patent applies preliminary action by pre-calculating and storing flux values at selected time steps. Instead of calculating flux from state data at every time step, the method pre-computes flux values in advance and reuses them for multiple subsequent time steps, eliminating the need for frequent data transmission and recalculations.
Solution Approach 2:
The patent uses copying by creating and storing copies of flux values at selected time steps. These copied flux values are then reused for multiple time steps without requiring recalculation, reducing data transmission requirements while maintaining computational accuracy.
2Productivity
If data transmission between processing units is reduced, then processing speed improves, but accuracy of state updates may deteriorate
Solution Approach 1:
By pre-calculating and storing flux values at strategically selected time steps, the method enables processing units to operate independently for multiple time steps without frequent data transmission, thereby improving processing speed while maintaining accuracy through the use of pre-computed values.
Solution Approach 2:
The patent implements periodic action by transmitting and updating state data and flux values at periodic intervals rather than at every time step. This periodic update strategy reduces communication overhead and improves processing speed while maintaining sufficient accuracy for the simulation.
3Reliability
If flux data is recalculated at every time step, then numerical accuracy is maintained, but computational time and energy consumption increase
Solution Approach 1:
The method pre-calculates flux values at selected time steps and stores them for reuse. This preliminary calculation approach maintains numerical accuracy by ensuring flux values are computed from accurate state data, while significantly reducing the total computational time required for the simulation.
Solution Approach 2:
By copying and reusing previously calculated flux values for multiple time steps, the method maintains numerical accuracy without requiring recalculation at every time step, thereby reducing computational time and energy consumption.
4Ease of operation
If state data is packed and transmitted using MPI messages, then data transfer between processing units is enabled, but communication overhead and processing delay increase
Solution Approach 1:
The patent reduces communication overhead by implementing periodic data transfer using MPI messages only at selected time steps rather than at every time step. This periodic communication strategy maintains the necessary data transfer capability while significantly reducing the frequency of communication operations and associated overhead.
Solution Approach 2:
By pre-calculating flux values and preparing state data in advance at selected time steps, the method reduces the amount of data that needs to be packed and transmitted via MPI, thereby reducing communication overhead and processing delay.
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, state data is transmitted between partitions and used to calculate flux data for updating the state of edge elements of the partitions. Periodically, transmission of state 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. Whether to suppress transmission of state data may be determined based on one or both of (a) uncertainty in an output of the machine learning model (e.g., Bayesian neural network) and (b) complexity of model of the physical system (e.g., spatial or temporal gradients).