Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential

Grubišić, Luka; Hajba, Marko; Lacmanović, Domagoj

doi:10.3390/e23010095

Cited by 10 publications

(7 citation statements)

References 40 publications

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“…In the contribution by Grubišić et al [8], "Deep Neural Network Model for Approximating Eigenmodes Localized by a Confining Potential," a class of physics-informed deep dense neural networks is used to learn the mapping from potential to ground eigenstate for the Schrödinger equation for several confining potentials. The authors present an approach that combines the expressivity of the set of neural network realizations with the standard error indicators.…”

Section: Contributions To Intelligence Augmentationmentioning

confidence: 99%

Human-Centric AI: The Symbiosis of Human and Artificial Intelligence

Horvatić

Lipić

2021

Entropy

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Well-evidenced advances of data-driven complex machine learning approaches emerging within the so-called second wave of artificial intelligence (AI) fostered the exploration of possible AI applications in various domains and aspects of human life, practices, and society. Most of the recent success in AI comes from the utilization of representation learning with end-to-end trained deep neural network models in tasks such as image, text,and speech recognition or strategic board and video games. By enabling automatic feature engineering, deep learning models significantly reduce the reliance on domain-expert knowledge, outperforming traditional methods based on handcrafted feature engineering and achieving performance that equals or even supersedes humans in some respects.

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Section: Contributions To Intelligence Augmentationmentioning

confidence: 99%

Human-Centric AI: The Symbiosis of Human and Artificial Intelligence

Horvatić

Lipić

2021

Entropy

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“…They extend this model to a Bayesian framework to quantify both epistemic and aleatoric uncertainty. Finally, Grubišić et al [54] also used an encoder-decoder fully convolutional neural network.…”

Section: Convolutional Encoder-decoder Networkmentioning

confidence: 99%

Scientific Machine Learning Through Physics–Informed Neural Networks: Where we are and What’s Next

et al. 2022

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Physics-Informed Neural Networks (PINN) are neural networks (NNs) that encode model equations, like Partial Differential Equations (PDE), as a component of the neural network itself. PINNs are nowadays used to solve PDEs, fractional equations, integral-differential equations, and stochastic PDEs. This novel methodology has arisen as a multi-task learning framework in which a NN must fit observed data while reducing a PDE residual. This article provides a comprehensive review of the literature on PINNs: while the primary goal of the study was to characterize these networks and their related advantages and disadvantages. The review also attempts to incorporate publications on a broader range of collocation-based physics informed neural networks, which stars form the vanilla PINN, as well as many other variants, such as physics-constrained neural networks (PCNN), variational hp-VPINN, and conservative PINN (CPINN). The study indicates that most research has focused on customizing the PINN through different activation functions, gradient optimization techniques, neural network structures, and loss function structures. Despite the wide range of applications for which PINNs have been used, by demonstrating their ability to be more feasible in some contexts than classical numerical techniques like Finite Element Method (FEM), advancements are still possible, most notably theoretical issues that remain unresolved.

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“…VPINN Kharazmi et al (2019) is also used to solve Schrödinger Hamiltonians, i.e. an elliptic reaction-diffusion operator (Grubišić et al, 2021).…”

Section: Steady State Pdementioning

confidence: 99%

“…They extend this model to a Bayesian framework to quantify both epistemic and aleatoric uncertainty. Finally, Grubišić et al (2021) also used an encoder-decoder fully convolutional neural network.…”

Section: Convolutional Encoder-decoder Networkmentioning

confidence: 99%