Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applications

• URL: http://arxiv.org/abs/2409.05234v1
• Date: Sun, 8 Sep 2024 22:27:50 GMT
• Title: Empowering Bayesian Neural Networks with Functional Priors through Anchored Ensembling for Mechanics Surrogate Modeling Applications
• Authors: Javad Ghorbanian, Nicholas Casaprima, Audrey Olivier,
• Abstract summary: We present a novel BNN training scheme based on anchored ensembling that can integrate a priori information available in the function space. The anchoring scheme makes use of low-rank correlations between NN parameters, learnt from pre-training to realizations of the functional prior. We also perform a study to demonstrate how correlations between NN weights, which are often neglected in existing BNN implementations, is critical to appropriately transfer knowledge between the function-space and parameter-space priors.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, neural networks (NNs) have become increasingly popular for surrogate modeling tasks in mechanics and materials modeling applications. While traditional NNs are deterministic functions that rely solely on data to learn the input--output mapping, casting NN training within a Bayesian framework allows to quantify uncertainties, in particular epistemic uncertainties that arise from lack of training data, and to integrate a priori knowledge via the Bayesian prior. However, the high dimensionality and non-physicality of the NN parameter space, and the complex relationship between parameters (NN weights) and predicted outputs, renders both prior design and posterior inference challenging. In this work we present a novel BNN training scheme based on anchored ensembling that can integrate a priori information available in the function space, from e.g. low-fidelity models. The anchoring scheme makes use of low-rank correlations between NN parameters, learnt from pre-training to realizations of the functional prior. We also perform a study to demonstrate how correlations between NN weights, which are often neglected in existing BNN implementations, is critical to appropriately transfer knowledge between the function-space and parameter-space priors. Performance of our novel BNN algorithm is first studied on a small 1D example to illustrate the algorithm's behavior in both interpolation and extrapolation settings. Then, a thorough assessment is performed on a multi--input--output materials surrogate modeling example, where we demonstrate the algorithm's capabilities both in terms of accuracy and quality of the uncertainty estimation, for both in-distribution and out-of-distribution data.

Related papers

• Active Learning with Fully Bayesian Neural Networks for Discontinuous and Nonstationary Data [0.0]
  We introduce fully Bayesian Neural Networks (FBNNs) for active learning tasks in the'small data' regime. FBNNs provide reliable predictive distributions, crucial for making informed decisions under uncertainty in the active learning setting. Here, we assess the suitability and performance of FBNNs with the No-U-Turn Sampler for active learning tasks in the'small data' regime.
  arXiv  Detail & Related papers  (2024-05-16T05:20:47Z)
• Bayesian Neural Networks with Domain Knowledge Priors [52.80929437592308]
  We propose a framework for integrating general forms of domain knowledge into a BNN prior. We show that BNNs using our proposed domain knowledge priors outperform those with standard priors.
  arXiv  Detail & Related papers  (2024-02-20T22:34:53Z)
• 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)
• Amortised Inference in Bayesian Neural Networks [0.0]
  We introduce the Amortised Pseudo-Observation Variational Inference Bayesian Neural Network (APOVI-BNN) We show that the amortised inference is of similar or better quality to those obtained through traditional variational inference. We then discuss how the APOVI-BNN may be viewed as a new member of the neural process family.
  arXiv  Detail & Related papers  (2023-09-06T14:02:33Z)
• 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)
• Learning Low Dimensional State Spaces with Overparameterized Recurrent Neural Nets [57.06026574261203]
  We provide theoretical evidence for learning low-dimensional state spaces, which can also model long-term memory. Experiments corroborate our theory, demonstrating extrapolation via learning low-dimensional state spaces with both linear and non-linear RNNs.
  arXiv  Detail & Related papers  (2022-10-25T14:45:15Z)
• 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)
• Neural Networks Enhancement with Logical Knowledge [83.9217787335878]
  We propose an extension of KENN for relational data. The results show that KENN is capable of increasing the performances of the underlying neural network even in the presence relational data.
  arXiv  Detail & Related papers  (2020-09-13T21:12:20Z)
• Modeling from Features: a Mean-field Framework for Over-parameterized Deep Neural Networks [54.27962244835622]
  This paper proposes a new mean-field framework for over- parameterized deep neural networks (DNNs) In this framework, a DNN is represented by probability measures and functions over its features in the continuous limit. We illustrate the framework via the standard DNN and the Residual Network (Res-Net) architectures.
  arXiv  Detail & Related papers  (2020-07-03T01:37:16Z)
• Provably Efficient Neural Estimation of Structural Equation Model: An Adversarial Approach [144.21892195917758]
  We study estimation in a class of generalized Structural equation models (SEMs) We formulate the linear operator equation as a min-max game, where both players are parameterized by neural networks (NNs), and learn the parameters of these neural networks using a gradient descent. For the first time we provide a tractable estimation procedure for SEMs based on NNs with provable convergence and without the need for sample splitting.
  arXiv  Detail & Related papers  (2020-07-02T17:55:47Z)
• Hierarchical Gaussian Process Priors for Bayesian Neural Network Weights [16.538973310830414]
  A desirable class of priors would represent weights compactly, capture correlations between weights, and allow inclusion of prior knowledge. This paper introduces two innovations: (i) a process-based hierarchical model for network weights based on unit embeddings that can flexibly encode correlated weight structures, and (ii) input-dependent versions of these weight priors that can provide convenient ways to regularize the function space. We show these models provide desirable test-time uncertainty estimates on out-of-distribution data, demonstrate cases of modeling inductive biases for neural networks with kernels, and demonstrate competitive predictive performance on an active learning benchmark
  arXiv  Detail & Related papers  (2020-02-10T07:19:52Z)

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.