Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems

• URL: http://arxiv.org/abs/2306.15159v1
• Date: Tue, 27 Jun 2023 02:35:25 GMT
• Title: Evaluation of machine learning architectures on the quantification of epistemic and aleatoric uncertainties in complex dynamical systems
• Authors: Stephen Guth, Alireza Mojahed, and Themistoklis P. Sapsis
• Abstract summary: Uncertainty Quantification (UQ) is a self assessed estimate of the model error. We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks. We evaluate UQ accuracy (distinct from model accuracy) using two metrics: the distribution of normalized residuals on validation data, and the distribution of estimated uncertainties.
• Score: 0.0
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Machine learning methods for the construction of data-driven reduced order model models are used in an increasing variety of engineering domains, especially as a supplement to expensive computational fluid dynamics for design problems. An important check on the reliability of surrogate models is Uncertainty Quantification (UQ), a self assessed estimate of the model error. Accurate UQ allows for cost savings by reducing both the required size of training data sets and the required safety factors, while poor UQ prevents users from confidently relying on model predictions. We examine several machine learning techniques, including both Gaussian processes and a family UQ-augmented neural networks: Ensemble neural networks (ENN), Bayesian neural networks (BNN), Dropout neural networks (D-NN), and Gaussian neural networks (G-NN). We evaluate UQ accuracy (distinct from model accuracy) using two metrics: the distribution of normalized residuals on validation data, and the distribution of estimated uncertainties. We apply these metrics to two model data sets, representative of complex dynamical systems: an ocean engineering problem in which a ship traverses irregular wave episodes, and a dispersive wave turbulence system with extreme events, the Majda-McLaughlin-Tabak model. We present conclusions concerning model architecture and hyperparameter tuning.

Related papers

• Quantifying uncertainty for deep learning based forecasting and flow-reconstruction using neural architecture search ensembles [0.8258451067861933]
  We present an automated approach to deep neural network (DNN) discovery and demonstrate how this may also be utilized for ensemble-based uncertainty quantification. We highlight how the proposed method not only discovers high-performing neural network ensembles for our tasks, but also quantifies uncertainty seamlessly. We demonstrate the feasibility of this framework for two tasks - forecasting from historical data and flow reconstruction from sparse sensors for the sea-surface temperature.
  arXiv  Detail & Related papers  (2023-02-20T03:57:06Z)
• IB-UQ: Information bottleneck based uncertainty quantification for neural function regression and neural operator learning [11.5992081385106]
  We propose a novel framework for uncertainty quantification via information bottleneck (IB-UQ) for scientific machine learning tasks. We incorporate the bottleneck by a confidence-aware encoder, which encodes inputs into latent representations according to the confidence of the input data. We also propose a data augmentation based information bottleneck objective which can enhance the quality of the extrapolation uncertainty.
  arXiv  Detail & Related papers  (2023-02-07T05:56:42Z)
• A critical look at deep neural network for dynamic system modeling [0.0]
  This paper questions the capability of (deep) neural networks for the modeling of dynamic systems using input-output data. For the identification of linear time-invariant (LTI) dynamic systems, two representative neural network models are compared. For the LTI system, both LSTM and CFNN fail to deliver consistent models even in noise-free cases.
  arXiv  Detail & Related papers  (2023-01-27T09:03:05Z)
• Learning to Learn with Generative Models of Neural Network Checkpoints [71.06722933442956]
  We construct a dataset of neural network checkpoints and train a generative model on the parameters. We find that our approach successfully generates parameters for a wide range of loss prompts. We apply our method to different neural network architectures and tasks in supervised and reinforcement learning.
  arXiv  Detail & Related papers  (2022-09-26T17:59:58Z)
• An advanced spatio-temporal convolutional recurrent neural network for storm surge predictions [73.4962254843935]
  We study the capability of artificial neural network models to emulate storm surge based on the storm track/size/intensity history. This study presents a neural network model that can predict storm surge, informed by a database of synthetic storm simulations.
  arXiv  Detail & Related papers  (2022-04-18T23:42:18Z)
• EINNs: Epidemiologically-Informed Neural Networks [75.34199997857341]
  We introduce a new class of physics-informed neural networks-EINN-crafted for epidemic forecasting. We investigate how to leverage both the theoretical flexibility provided by mechanistic models as well as the data-driven expressability afforded by AI models.
  arXiv  Detail & Related papers  (2022-02-21T18:59:03Z)
• Investigating the Relationship Between Dropout Regularization and Model Complexity in Neural Networks [0.0]
  Dropout Regularization serves to reduce variance in Deep Learning models. We explore the relationship between the dropout rate and model complexity by training 2,000 neural networks. We build neural networks that predict the optimal dropout rate given the number of hidden units in each dense layer.
  arXiv  Detail & Related papers  (2021-08-14T23:49:33Z)
• A Framework for Machine Learning of Model Error in Dynamical Systems [7.384376731453594]
  We present a unifying framework for blending mechanistic and machine-learning approaches to identify dynamical systems from data. We cast the problem in both continuous- and discrete-time, for problems in which the model error is memoryless and in which it has significant memory. We find that hybrid methods substantially outperform solely data-driven approaches in terms of data hunger, demands for model complexity, and overall predictive performance.
  arXiv  Detail & Related papers  (2021-07-14T12:47:48Z)
• ANNETTE: Accurate Neural Network Execution Time Estimation with Stacked Models [56.21470608621633]
  We propose a time estimation framework to decouple the architectural search from the target hardware. The proposed methodology extracts a set of models from micro- kernel and multi-layer benchmarks and generates a stacked model for mapping and network execution time estimation. We compare estimation accuracy and fidelity of the generated mixed models, statistical models with the roofline model, and a refined roofline model for evaluation.
  arXiv  Detail & Related papers  (2021-05-07T11:39:05Z)
• Using Data Assimilation to Train a Hybrid Forecast System that Combines Machine-Learning and Knowledge-Based Components [52.77024349608834]
  We consider the problem of data-assisted forecasting of chaotic dynamical systems when the available data is noisy partial measurements. We show that by using partial measurements of the state of the dynamical system, we can train a machine learning model to improve predictions made by an imperfect knowledge-based model.
  arXiv  Detail & Related papers  (2021-02-15T19:56:48Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)

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.