Computability of Differential Equations

Graça, Daniel S.; Zhong, Ning

doi:10.1007/978-3-030-59234-9_3

Cited by 7 publications

(2 citation statements)

References 72 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The sampling evaluation in every iteration is based on the simulation result. As the principle of the FVCOM mentioned above, the dynamic analysis consists of PDEs and ODEs, which bring in a large computational expense and are highly time-consuming 24,25 . Thus, to guarantee the efficiency of the proposed COSSD method, a parallel technique is necessary.…”

Section: Methodsmentioning

confidence: 99%

Cyber-physical oil spill monitoring and detection for offshore petroleum risk management service

Wang

Chen

Wang

2023

Sci Rep

View full text Add to dashboard Cite

Petroleum industry has started to embrace the advanced petroleum cyber-physical system (CPS) technologies. Offshore petroleum CPS is particularly hard to build, mainly due to the difficulty in detecting and preventing offshore oil leaking. During the oil exploration and transportation process, the remote multi-sensing technology is typically employed for emerging service. It can be utilized for leak detection by enabling the underwater modeling of an offshore petroleum CPS. However, such a technology suffers from insufficient remote sensing resources and expensive computational overhead. In this work, a cross-entropy based leak detection technique is proposed to detect the oil leak, which facilitates the understanding of the oil leak induced marine pollution. Furthermore, a hierarchical parallel approach is proposed on the super computer Tianhe-2 to improve the efficiency of the proposed leak detection technique. Experimental results on Penglai oil spill events demonstrate that the proposed method can effectively identify the sources of oil spilling with accuracy up to $$100\%$$ 100 % .

show abstract

Section: Methodsmentioning

confidence: 99%

Cyber-physical oil spill monitoring and detection for offshore petroleum risk management service

Wang

Chen

Wang

2023

Sci Rep

View full text Add to dashboard Cite

show abstract

“…Otherwise, the obtained output may be, unknowingly to the user of the digital machine, far away from the sought true solution as worst-case error bounds are missing. A specific use case where such problems arise is the numerical solution of differential equations [14], [32], [63], [70].…”

Section: Digital Computations Of Continuous Modelsmentioning

confidence: 99%

Limitations of Deep Learning for Inverse Problems on Digital Hardware

Boche¹,

Fono²,

Kutyniok³

2022

Preprint

View full text Add to dashboard Cite

Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. In fact, our result even holds for Borel-Turing computability., i.e., there does not exist an algorithm which performs the training of a neural network on digital hardware for any given accuracy. This establishes a conceptual barrier on the capabilities of neural networks for finite-dimensional inverse problems given that the computations are performed on digital hardware.

show abstract

Computational Complexity of Classical Solutions of Partial Differential Equations

Selivanova

2022

Revolutions and Revelations in Computability

View full text Add to dashboard Cite

Computability of Differential Equations

Cited by 7 publications

References 72 publications

Cyber-physical oil spill monitoring and detection for offshore petroleum risk management service

Cyber-physical oil spill monitoring and detection for offshore petroleum risk management service

Limitations of Deep Learning for Inverse Problems on Digital Hardware

Computational Complexity of Classical Solutions of Partial Differential Equations

Contact Info

Product

Resources

About