Integral input-to-state-K L∗-stability for hybrid dynamical systems

Liu, Bin; Liu, Dongnan; Wang, Zhong

doi:10.1109/ccdc.2016.7531128

“…Nonetheless, their evaluation of the proposed architecture was limited to a small set of regular PDEs and did not consider the case where the initial condition changes. In [11], Causality-DeepONet was proposed to capture the temporal causality of a dynamical system. However, the approach is limited to linear systems and, instead of designing a new architecture, it replaces the input signals of the branch network by a zero-padding signals with a shifting window to express the causality.…”

Section: Introductionmentioning

confidence: 99%

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

Nghiem¹,

Nguyen²,

Nguyen³

et al. 2023

Preprint

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0

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<p>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 contro</p>

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“…Os principais tratamentos são: remoção cirúrgica do tumor, ligação da artéria hepática ou da veia portal, embolisação terapêutica da artéria hepática ou da veia portal, quimioterapia e transplante de fígado. Embora importantes progressos no tratamento de câncer de fígado tenham sido realizados, existe a necessidade do desenvolvimento Introdução __________________________________________________________ de novas modalidades terapêuticas mais eficientes, entre as quais se estuda a possibilidade da aplicação da PDT [28].…”

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"Análise da necrose em tecidos normais fotossensibilizados pós terapia fotodinâmica - estudo in vivo"

Ferreira¹

View full text Add to dashboard Cite

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

Nghiem¹,

Nguyen²,

Nguyen³

et al. 2023

Preprint

0

View full text Add to dashboard Cite

<p>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 contro</p>

show abstract

Integral input-to-state-K L∗-stability for hybrid dynamical systems

Cited by 3 publications

References 22 publications

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

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

"Análise da necrose em tecidos normais fotossensibilizados pós terapia fotodinâmica - estudo in vivo"

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

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