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Time-evolution of partial differential equations is the key to model several dynamical processes, events forecasting but the operators associated with such problems are non-linear. We propose a Padé approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and activities at a later time. The multiwavelets bases are used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce real-world datasets. The Padé exponential operator uses a to model the non-linearity compared to recent neural operators that rely on using multiple linear operator layers in succession. We show theoretically that the gradients associated with the recurrent Padé network are bounded across the recurrent horizon. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto–Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like Epidemic forecasting (for example, COVID-19) can be formulated as a 2D time-varying operator problem. The proposed Padé exponential operators yield better prediction results ( better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models.
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Rank Position Forecasting in Car Racing
Rank position forecasting in car racing is a challenging problem when using a Deep Learning-based model over timeseries data. It is featured with highly complex global dependency among the racing cars, with uncertainty resulted from existing and external factors; and it is also a problem with data scarcity. Existing methods, including statistical models, machine learning regression models, and several state-of-the-art deep forecasting models all perform not well on this problem. By an elaborate analysis of pit stop events, we find it critical to decompose the cause-and-effect relationship and model the rank position and pit stop events separately. In choosing a sub-model from different neural network models, we find the model with weak assumptions on the global dependency structure performs the best. Based on these observations, we propose RankNet, a combination of the encoder-decoder network and a separate Multilayer Perception network that is capable of delivering probabilistic forecasting to model the pit stop events and rank position in car racing. Further with the help of feature optimizations, RankNet demonstrates a significant performance improvement, where MAE improves 19% in two laps forecasting task and 7% in the stint forecasting task over the best baseline and is also more stable when adapting to unseen new data. Details of the model optimizations and performance profiling are presented. It is promising to provide useful interactions of neural networks in forecasting racing cars and shine a light on solutions to similar challenging issues in general forecasting problems.
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- Award ID(s):
- 2151597
- PAR ID:
- 10320706
- Date Published:
- Journal Name:
- 2021 IEEE International Parallel and Distributed Processing Symposium (IPDPS)
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Time-evolution of partial differential equations is the key to model several dynamical processes, events forecasting but the operators associated with such problems are non-linear. We propose a Padé approximation based exponential neural operator scheme for efficiently learning the map between a given initial condition and activities at a later time. The multiwavelets bases are used for space discretization. By explicitly embedding the exponential operators in the model, we reduce the training parameters and make it more data-efficient which is essential in dealing with scarce real-world datasets. The Padé exponential operator uses a to model the non-linearity compared to recent neural operators that rely on using multiple linear operator layers in succession. We show theoretically that the gradients associated with the recurrent Padé network are bounded across the recurrent horizon. We perform experiments on non-linear systems such as Korteweg-de Vries (KdV) and Kuramoto–Sivashinsky (KS) equations to show that the proposed approach achieves the best performance and at the same time is data-efficient. We also show that urgent real-world problems like Epidemic forecasting (for example, COVID-19) can be formulated as a 2D time-varying operator problem. The proposed Padé exponential operators yield better prediction results ( better MAE than best neural operator (non-neural operator deep learning model)) compared to state-of-the-art forecasting models.more » « less
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/IPDPS49936.2021.00082
