Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to flood modeling

Jacquier, Pierre; Abdedou, Azzedine; Delmas, Vincent; Soulaïmani, Azzeddine

doi:10.1016/j.jcp.2020.109854

Cited by 47 publications

(48 citation statements)

References 27 publications

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“…In this work, we train artificial neural networks (ANNs), developed with the TensorFlow [49] library, to accurately and efficiently estimate the projection coefficients of a reduced basis representation. ANNs are a versatile tool [50] and have recently been applied to solve reduced-order modeling problems across multiple disciplines using a nonintrusive framework [51][52][53][54][55]. The use of ANNs in GW astronomy is increasing [48,[56][57][58][59][60][61][62][63][64][65][66][67][68][69][70][71][72][73].…”

Section: Introductionmentioning

confidence: 99%

Gravitational-wave surrogate models powered by artificial neural networks

Khan

Green

2021

Phys. Rev. D

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Inferring the properties of black holes and neutron stars is a key science goal of gravitational-wave (GW) astronomy. To extract as much information as possible from GW observations, we must develop methods to reduce the cost of Bayesian inference. In this paper, we use artificial neural networks (ANNs) and the parallelization power of graphics processing units (GPUs) to improve the surrogate modeling method, which can produce accelerated versions of existing models. As a first application of our method, the artificial neural networks surrogate model (ANN-Sur), we build a time-domain surrogate model of the spinaligned binary black hole (BBH) waveform model SEOBNRv4. We achieve median mismatches of approximately 2e − 5 and mismatches no worse than approximately 2e − 3. For a typical BBH waveform generated from 12 Hz with a total mass of 60 M ⊙ , the original SEOBNRv4 model takes 1794 ms. Existing custom-made code optimizations (SEOBNRv4opt) reduced this to 83.7 ms, and the interpolation-based, frequency-domain surrogate SEOBNRv4ROM can generate this waveform in 3.5 ms. Our ANN-Sur model when run on a CPU takes 1.2 ms and when run on a graphics processing unit (GPU) takes just 0.5 ms. ANN-Sur can also generate large batches of waveforms simultaneously. We find that batches of up to 10 3 waveforms can be evaluated on a GPU in just 1.57 ms, corresponding to a time per waveform of 0.0016 ms. This method is a promising way to utilize the parallelization power of GPUs to drastically increase the computational efficiency of Bayesian parameter estimation.

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Section: Introductionmentioning

confidence: 99%

Gravitational-wave surrogate models powered by artificial neural networks

Khan

Green

2021

Phys. Rev. D

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“…If, for different parameter sampling, the output is unvaried, then the model has a good confidence on the prediction and vice versa if different parameters give different results. Jacquier et al (2021) used…”

Section: Probabilistic Deep Learningmentioning

confidence: 99%

“…CNNs were initially discarded but are used more in recent years (e.g.,Guo et al, 2021;Löwe et al, 2021;Kabir et al, 2020) Hu et al (2019). andJacquier et al (2021) use a LSTM and a MLP, respectively, in combination with a reduced order modelling framework. In the first case, the DL model is applied on the reduced space, while in the latter DL is used as surrogate for the decomposition method.https://doi.org/10.5194/hess-2022-83 Preprint.…”

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confidence: 99%

Deep Learning Methods for Flood Mapping: A Review of Existing Applications and Future Research Directions

Bentivoglio

Isufi

Jonkman

et al. 2022

Preprint

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Abstract. Deep Learning techniques have been increasingly used in flood management to overcome the limitations of accurate, yet slow, numerical models, and to improve the results of traditional methods for flood mapping. In this paper, we review 58 recent publications to outline the state-of-the-art of the field, identify knowledge gaps, and propose future research directions. The review focuses on the type of deep learning models used for various flood mapping applications, the flood types considered, the spatial scale of the studied events, and the data used for model development. The results show that models based on convolutional layers are usually more accurate as they leverage inductive biases to better process the spatial characteristics of the flooding events. Models based on fully-connected layers, instead, provide accurate results when coupled with other statistical models. Deep learning models showed increased accuracy when compared to traditional approaches and increased speed when compared to numerical methods. While there exist several applications in flood susceptibility, inundation, and hazard mapping, more work is needed to understand how deep learning can assist real-time flood warning during an emergency, and how it can be employed to estimate flood risk. A major challenge lies in developing deep learning models that can generalize to unseen case studies. Furthermore, all reviewed models and their outputs, are deterministic, with limited considerations for uncertainties in outcomes and probabilistic predictions. The authors argue that these identified gaps can be addressed by exploiting recent fundamental advancements in deep learning or by taking inspiration from developments in other applied areas. Models based on graph neural networks and neural operators can work with arbitrarily structured data and thus should be capable of generalizing across different case studies and could account for complex interactions with the natural and built environment. Physics-based deep learning can be used to preserve the underlying physical equations resulting in more reliable speed-up alternatives for numerical models. Similarly, probabilistic models can be built by resorting to Deep Gaussian Processes or Bayesian neural networks.

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“…They refer to this approach as POD‐NN and apply it in the field of fluid dynamics, for example, to the Navier–Stokes equations. This method can be extended by uncertainty quantification with deep ensembles and variational inference‐based Bayesian neural networks 12 . In other papers the temporal sequence of the reduced states or rather coefficients is approximated by radial basis functions, 13 k‐nearest neighbor methods, 14 or neural networks 15 .…”

Section: Introductionmentioning

confidence: 99%

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

Kneifl

Grunert

Fehr

2021

Numerical Meth Engineering

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Model order reduction (MOR) has become one of the most widely used tools to create efficient surrogate models for time-critical applications. For nonlinear models, however, linear MOR approaches are only practicable to a limited extent. Nonlinear approaches, on the contrary, often require intrusive manipulations of the used simulation code. Hence, non-intrusive MOR approaches using classic model order reduction along with machine learning (ML) algorithms can provide remedy. Such approaches have drawn a lot of attention in the recent years. They rely on the idea to learn the dynamics not in a high-dimensional but in a reduced space, i.e., they predict the discrete sequence of reduced system states successively. Open questions are the suitability of such methods in the field of structural dynamics and the best choice of the used ML algorithm. Both are addressed in this paper in addition to the integration of the methodology into a modular and flexible framework that can effortless be adapted to various requirements. By applying the methodology to a dynamic mechanical system, accurate surrogate models are received, which can speed up the simulation time significantly, while still providing high-quality state approximations.

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Non-intrusive reduced-order modeling using uncertainty-aware Deep Neural Networks and Proper Orthogonal Decomposition: Application to flood modeling

Cited by 47 publications

References 27 publications

Gravitational-wave surrogate models powered by artificial neural networks

Gravitational-wave surrogate models powered by artificial neural networks

Deep Learning Methods for Flood Mapping: A Review of Existing Applications and Future Research Directions

A nonintrusive nonlinear model reduction method for structural dynamical problems based on machine learning

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