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The deep operator network (DeepONet) architecture is a promising approach for learning functional operators, that can represent dynamical systems described by ordinary or partial differential equations. However, it has two major limitations, namely its failures to account for initial conditions and to guarantee the temporal causality – a fundamental property of dynamical systems. This paper proposes a novel causal deep operator network (Causal-DeepONet) architecture for incorporating both the initial condition and the temporal causality into data-driven learning of dynamical systems, overcoming the limitations of the original DeepONet approach. This is achieved by adding an independent root network for the initial condition and independent branch networks conditioned, or switched on/off, by time-shifted step functions or sigmoid functions for expressing the temporal causality. The proposed architecture was evaluated and compared with two baseline deep neural network methods and the original DeepONet method on learning the thermal dynamics of a room in a building using real data. It was shown to not only achieve the best overall prediction accuracy but also enhance substantially the accuracy consistency in multistep predictions, which is crucial for predictive control.
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Explorations of Temporal Causality Using Partial Coherence
In this paper we explore partial coherence as a tool for evaluating the causal, anti-causal, or mixed-causal dependence of one time series on another. The key idea is to establish a connection between questions of causality and partial coherence. Once this connection is established, then a scale-invariant partial coherence statistic is used to resolve the question of temporal causality. This coherence statistic is shown to be a likelihood ratio. It may be computed from a composite covariance matrix or from its inverse, the information matrix. Numerical experiments demonstrate the application of partial coherence to the resolution of temporal causality.
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- Award ID(s):
- 1712788
- PAR ID:
- 10096813
- Date Published:
- Journal Name:
- 2018 52nd Asilomar Conference on Signals, Systems, and Computers
- Page Range / eLocation ID:
- 1767 to 1771
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1109/ACSSC.2018.8645359
