Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations

• URL: http://arxiv.org/abs/2205.01222v1
• Date: Mon, 2 May 2022 21:34:52 GMT
• Title: Leveraging Stochastic Predictions of Bayesian Neural Networks for Fluid Simulations
• Authors: Maximilian Mueller, Robin Greif, Frank Jenko and Nils Thuerey
• Abstract summary: We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. We show that BNNs, when used as surrogate models for steady-state fluid flow predictions, provide accurate physical predictions together with sensible estimates of uncertainty. We experiment with perturbed temporal sequences from Navier-Stokes simulations and evaluate the capabilities of BNNs to capture multimodal evolutions.
• Score: 19.961746770975534
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We investigate uncertainty estimation and multimodality via the non-deterministic predictions of Bayesian neural networks (BNNs) in fluid simulations. To this end, we deploy BNNs in three challenging experimental test-cases of increasing complexity: We show that BNNs, when used as surrogate models for steady-state fluid flow predictions, provide accurate physical predictions together with sensible estimates of uncertainty. Further, we experiment with perturbed temporal sequences from Navier-Stokes simulations and evaluate the capabilities of BNNs to capture multimodal evolutions. While our findings indicate that this is problematic for large perturbations, our results show that the networks learn to correctly predict high uncertainties in such situations. Finally, we study BNNs in the context of solver interactions with turbulent plasma flows. We find that BNN-based corrector networks can stabilize coarse-grained simulations and successfully create multimodal trajectories.

Related papers

• Bayesian Entropy Neural Networks for Physics-Aware Prediction [14.705526856205454]
  We introduce BENN, a framework designed to impose constraints on Bayesian Neural Network (BNN) predictions. Benn is capable of constraining not only the predicted values but also their derivatives and variances, ensuring a more robust and reliable model output. Results highlight significant improvements over traditional BNNs and showcase competitive performance relative to contemporary constrained deep learning methods.
  arXiv  Detail & Related papers  (2024-07-01T07:00:44Z)
• Uncertainty in Graph Neural Networks: A Survey [50.63474656037679]
  Graph Neural Networks (GNNs) have been extensively used in various real-world applications. However, the predictive uncertainty of GNNs stemming from diverse sources can lead to unstable and erroneous predictions. This survey aims to provide a comprehensive overview of the GNNs from the perspective of uncertainty.
  arXiv  Detail & Related papers  (2024-03-11T21:54:52Z)
• Uncertainty Quantification in Multivariable Regression for Material Property Prediction with Bayesian Neural Networks [37.69303106863453]
  We introduce an approach for uncertainty quantification (UQ) within physics-informed BNNs. We present case studies for predicting the creep rupture life of steel alloys. The most promising framework for creep life prediction is BNNs based on Markov Chain Monte Carlo approximation of the posterior distribution of network parameters.
  arXiv  Detail & Related papers  (2023-11-04T19:40:16Z)
• Deep Neural Networks Tend To Extrapolate Predictably [51.303814412294514]
  neural network predictions tend to be unpredictable and overconfident when faced with out-of-distribution (OOD) inputs. We observe that neural network predictions often tend towards a constant value as input data becomes increasingly OOD. We show how one can leverage our insights in practice to enable risk-sensitive decision-making in the presence of OOD inputs.
  arXiv  Detail & Related papers  (2023-10-02T03:25:32Z)
• Constraining cosmological parameters from N-body simulations with Variational Bayesian Neural Networks [0.0]
  Multiplicative normalizing flows (MNFs) are a family of approximate posteriors for the parameters of BNNs. We have compared MNFs with respect to the standard BNNs, and the flipout estimator. MNFs provide more realistic predictive distribution closer to the true posterior mitigating the bias introduced by the variational approximation.
  arXiv  Detail & Related papers  (2023-01-09T16:07:48Z)
• Prediction and Uncertainty Quantification of SAFARI-1 Axial Neutron Flux Profiles with Neural Networks [1.4528756508275622]
  Deep Neural Networks (DNNs) are used to predict the assembly axial neutron flux profiles in the SAFARI-1 research reactor. Uncertainty Quantification of the regular DNN models' predictions is performed using Monte Carlo Dropout (MCD) and Bayesian Neural Networks solved by Variational Inference (BNN VI)
  arXiv  Detail & Related papers  (2022-11-16T04:14:13Z)
• Variational Neural Networks [88.24021148516319]
  We propose a method for uncertainty estimation in neural networks called Variational Neural Network (VNN) VNN generates parameters for the output distribution of a layer by transforming its inputs with learnable sub-layers. In uncertainty quality estimation experiments, we show that VNNs achieve better uncertainty quality than Monte Carlo Dropout or Bayes By Backpropagation methods.
  arXiv  Detail & Related papers  (2022-07-04T15:41:02Z)
• Comparative Analysis of Interval Reachability for Robust Implicit and Feedforward Neural Networks [64.23331120621118]
  We use interval reachability analysis to obtain robustness guarantees for implicit neural networks (INNs) INNs are a class of implicit learning models that use implicit equations as layers. We show that our approach performs at least as well as, and generally better than, applying state-of-the-art interval bound propagation methods to INNs.
  arXiv  Detail & Related papers  (2022-04-01T03:31:27Z)
• Spatial-Temporal-Fusion BNN: Variational Bayesian Feature Layer [77.78479877473899]
  We design a spatial-temporal-fusion BNN for efficiently scaling BNNs to large models. Compared to vanilla BNNs, our approach can greatly reduce the training time and the number of parameters, which contributes to scale BNNs efficiently.
  arXiv  Detail & Related papers  (2021-12-12T17:13:14Z)
• Robustness of Bayesian Neural Networks to White-Box Adversarial Attacks [55.531896312724555]
  Bayesian Networks (BNNs) are robust and adept at handling adversarial attacks by incorporating randomness. We create our BNN model, called BNN-DenseNet, by fusing Bayesian inference (i.e., variational Bayes) to the DenseNet architecture. An adversarially-trained BNN outperforms its non-Bayesian, adversarially-trained counterpart in most experiments.
  arXiv  Detail & Related papers  (2021-11-16T16:14:44Z)
• Meaningful uncertainties from deep neural network surrogates of large-scale numerical simulations [34.03414786863526]
  Deep neural networks (DNNs) can serve as highly-accurate surrogate models. Prediction uncertainty estimates are crucial for making such comparisons meaningful.
  arXiv  Detail & Related papers  (2020-10-26T17:39:05Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.