Physics-based Deep Learning

Thuerey, Nils; Holl, Philipp; Mueller, Maximilian; Schnell, Patrick; Trost, Felix; Um, Kiwon

doi:10.48550/arxiv.2109.05237

Cited by 25 publications

(26 citation statements)

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“…These works are often purely data-driven, seldom leveraging the underlying physics for physics-informed DL. Outside the SciVis community, researchers in CFD and fluid simulation have extensively investigated physics-informed DL [80], [141]. For instance, Raissi et al [119] introduced a physicsinformed neural network for solving supervised learning tasks involving nonlinear partial differential equations.…”

Section: Research Opportunitiesmentioning

confidence: 99%

DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization

Wang¹,

Han²

2022

Preprint

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Since 2016, we have witnessed the tremendous growth of artificial intelligence+visualization (AI+VIS) research. However, existing survey papers on AI+VIS focus on visual analytics and information visualization, not scientific visualization (SciVis). In this paper, we survey related deep learning (DL) works in SciVis, specifically in the direction of DL4SciVis: designing DL solutions for solving SciVis problems. To stay focused, we primarily consider works that handle scalar and vector field data but exclude mesh data. We classify and discuss these works along six dimensions: domain setting, research task, learning type, network architecture, loss function, and evaluation metric. The paper concludes with a discussion of the remaining gaps to fill along the discussed dimensions and the grand challenges we need to tackle as a community. This state-of-the-art survey guides SciVis researchers in gaining an overview of this emerging topic and points out future directions to grow this research.

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Section: Research Opportunitiesmentioning

confidence: 99%

DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization

Wang¹,

Han²

2022

Preprint

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“…The inversion process in NIDN is inspired by recent research related to physics-based deep learning 23 and in directly optimizing physical properties using differentiable simulations 32 . The main advantage of these approaches is that gradients in training neural networks are propagated directly through a numerical simulation (also referred to as forward model in the context of inverse problems).…”

Section: Model Inversion Approachmentioning

confidence: 99%

“…In comparison to previous similar efforts such as those by Jiang et al 22 we utilize a fundamentally different technique relying on directly encoding the material inside a neural network. Building on advances in physics-based deep learning 23 , in NIDN, we directly optimize the nanostructure described by the neural network to achieve one specific spectrum. In this approach, no prior knowledge or training datasets are required as gradients are backpropagated through a (differentiable) numerical solver.…”

Section: Introductionmentioning

confidence: 99%

NIDN: Neural Inverse Design of Nanostructures

Gómez¹,

Toftevaag²,

Bogen-Støro³

et al. 2022

Preprint

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In the recent decade, computational tools have become central in material design, allowing rapid development cycles at reduced costs. Machine learning tools are especially on the rise in photonics. However, the inversion of the Maxwell equations needed for the design is particularly challenging from an optimization standpoint, requiring sophisticated software. We present an innovative, open-source software tool called Neural Inverse Design of Nanostructures (NIDN) that allows designing complex, stacked material nanostructures using a physics-based deep learning approach. Instead of a derivative-free or data-driven optimization or learning method, we perform a gradient-based neural network training where we directly optimize the material and its structure based on its spectral characteristics. NIDN supports two different solvers, rigorous coupled-wave analysis and a finite-difference time-domain method. The utility and validity of NIDN are demonstrated on several synthetic examples as well as the design of a 1550 nm filter and anti-reflection coating. Results match experimental baselines, other simulation tools, and the desired spectral characteristics. Given its full modularity in regard to network architectures and Maxwell solvers as well as open-source, permissive availability, NIDN will be able to support computational material design processes in a broad range of applications.

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“…The new branch of Machine Learning techniques that try to merge physical knowledge into RNN modeling takes various names, such as Theory-Guided Data Science [23], eXplainable Artificial Intelligence [85], or merely Physics-Based Modeling [84,86]. A common denominator of these approaches is the attempt to overcome the limitations of black-box modeling, and to shape the adopted machine learning technique according to a grey-box modeling criterion driven by the available physical knowledge of the system.…”

Section: Interpretability Of Rnn Modelsmentioning

confidence: 99%

On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments

Bonassi,

Farina,

Xie

et al. 2021

Preprint

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This paper aims to discuss and analyze the potentialities of Recurrent Neural Networks (RNN) in control design applications. The main families of RNN are considered, namely Neural Nonlinear AutoRegressive eXogenous, (NNARX), Echo State Networks (ESN), Long Short Term Memory (LSTM), and Gated Recurrent Units (GRU). The goal is twofold. Firstly, to survey recent results concerning the training of RNN that enjoy Input-to-State Stability (ISS) and Incremental Input-to-State Stability (δISS) guarantees. Secondly, to discuss the issues that still hinder the widespread use of RNN for control, namely their robustness, verifiability, and interpretability. The former properties are related to the so-called generalization capabilities of the networks, i.e. their consistency with the underlying real plants, even in presence of unseen or perturbed input trajectories. The latter is instead related to the possibility of providing a clear formal connection between the RNN model and the plant. In this context, we illustrate how ISS and δISS represent a significant step towards the robustness and verifiability of the RNN models, while the requirement of interpretability paves the way to the use of physics-based networks. The design of model predictive controllers with RNN as plant's model is also briefly discussed. Lastly, some of the main topics of the paper are illustrated on a simulated chemical system.

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Physics-based Deep Learning

Cited by 25 publications

References 0 publications

DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization

DL4SciVis: A State-of-the-Art Survey on Deep Learning for Scientific Visualization

NIDN: Neural Inverse Design of Nanostructures

On Recurrent Neural Networks for learning-based control: recent results and ideas for future developments

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