Causal Deep Operator Networks for Data-Driven Modeling of Dynamical Systems

Truong X. Nghiem, Thang Nguyen, Binh T. Nguyen, Linh Nguyen

Research output: Chapter in Book/Report/Conference proceedingConference contribution


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.

Original languageEnglish (US)
Title of host publication2023 IEEE International Conference on Systems, Man, and Cybernetics
Subtitle of host publicationImproving the Quality of Life, SMC 2023 - Proceedings
PublisherInstitute of Electrical and Electronics Engineers Inc.
Number of pages6
ISBN (Electronic)9798350337020
StatePublished - 2023
Event2023 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2023 - Hybrid, Honolulu, United States
Duration: Oct 1 2023Oct 4 2023

Publication series

NameConference Proceedings - IEEE International Conference on Systems, Man and Cybernetics
ISSN (Print)1062-922X


Conference2023 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2023
Country/TerritoryUnited States
CityHybrid, Honolulu

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Control and Systems Engineering
  • Human-Computer Interaction


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