Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties

• URL: http://arxiv.org/abs/2411.13361v2
• Date: Thu, 21 Nov 2024 09:51:22 GMT
• Title: Integration of Active Learning and MCMC Sampling for Efficient Bayesian Calibration of Mechanical Properties
• Authors: Leon Riccius, Iuri B. C. M. Rocha, Joris Bierkens, Hanne Kekkonen, Frans P. van der Meer,
• Abstract summary: We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models. We identify the forward model as the bottleneck in the inference process, not the MCMC algorithm.
• Score: 0.5242869847419834
• License:
• Abstract: Recent advancements in Markov chain Monte Carlo (MCMC) sampling and surrogate modelling have significantly enhanced the feasibility of Bayesian analysis across engineering fields. However, the selection and integration of surrogate models and cutting-edge MCMC algorithms, often depend on ad-hoc decisions. A systematic assessment of their combined influence on analytical accuracy and efficiency is notably lacking. The present work offers a comprehensive comparative study, employing a scalable case study in computational mechanics focused on the inference of spatially varying material parameters, that sheds light on the impact of methodological choices for surrogate modelling and sampling. We show that a priori training of the surrogate model introduces large errors in the posterior estimation even in low to moderate dimensions. We introduce a simple active learning strategy based on the path of the MCMC algorithm that is superior to all a priori trained models, and determine its training data requirements. We demonstrate that the choice of the MCMC algorithm has only a small influence on the amount of training data but no significant influence on the accuracy of the resulting surrogate model. Further, we show that the accuracy of the posterior estimation largely depends on the surrogate model, but not even a tailored surrogate guarantees convergence of the MCMC.Finally, we identify the forward model as the bottleneck in the inference process, not the MCMC algorithm. While related works focus on employing advanced MCMC algorithms, we demonstrate that the training data requirements render the surrogate modelling approach infeasible before the benefits of these gradient-based MCMC algorithms on cheap models can be reaped.

Related papers

• On Discriminative Probabilistic Modeling for Self-Supervised Representation Learning [85.75164588939185]
  We study the discriminative probabilistic modeling problem on a continuous domain for (multimodal) self-supervised representation learning. We conduct generalization error analysis to reveal the limitation of current InfoNCE-based contrastive loss for self-supervised representation learning.
  arXiv  Detail & Related papers  (2024-10-11T18:02:46Z)
• The Role of Model Architecture and Scale in Predicting Molecular Properties: Insights from Fine-Tuning RoBERTa, BART, and LLaMA [0.0]
  This study introduces a systematic framework to compare the efficacy of Large Language Models (LLMs) for fine-tuning across various cheminformatics tasks. We assessed three well-known models-RoBERTa, BART, and LLaMA-on their ability to predict molecular properties. We found that LLaMA-based models generally offered the lowest validation loss, suggesting their superior adaptability across tasks and scales.
  arXiv  Detail & Related papers  (2024-05-02T02:20:12Z)
• Enhancing Fairness and Performance in Machine Learning Models: A Multi-Task Learning Approach with Monte-Carlo Dropout and Pareto Optimality [1.5498930424110338]
  This study introduces an approach to mitigate bias in machine learning by leveraging model uncertainty. Our approach utilizes a multi-task learning (MTL) framework combined with Monte Carlo (MC) Dropout to assess and mitigate uncertainty in predictions related to protected labels.
  arXiv  Detail & Related papers  (2024-04-12T04:17:50Z)
• Task-optimal data-driven surrogate models for eNMPC via differentiable simulation and optimization [42.72938925647165]
  We present a method for end-to-end learning of Koopman surrogate models for optimal performance in a specific control task. We use a training algorithm that exploits the potential differentiability of environments based on mechanistic simulation models to aid the policy optimization.
  arXiv  Detail & Related papers  (2024-03-21T14:28:43Z)
• Online Variational Sequential Monte Carlo [49.97673761305336]
  We build upon the variational sequential Monte Carlo (VSMC) method, which provides computationally efficient and accurate model parameter estimation and Bayesian latent-state inference. Online VSMC is capable of performing efficiently, entirely on-the-fly, both parameter estimation and particle proposal adaptation.
  arXiv  Detail & Related papers  (2023-12-19T21:45:38Z)
• Learning Energy-Based Prior Model with Diffusion-Amortized MCMC [89.95629196907082]
  Common practice of learning latent space EBMs with non-convergent short-run MCMC for prior and posterior sampling is hindering the model from further progress. We introduce a simple but effective diffusion-based amortization method for long-run MCMC sampling and develop a novel learning algorithm for the latent space EBM based on it.
  arXiv  Detail & Related papers  (2023-10-05T00:23:34Z)
• Data-driven decision-focused surrogate modeling [10.1947610432159]
  We introduce the concept of decision-focused surrogate modeling for solving challenging nonlinear optimization problems in real-time settings. The proposed data-driven framework seeks to learn a simpler, e.g. convex, surrogate optimization model that is trained to minimize the decision prediction error. We validate our framework through numerical experiments involving the optimization of common nonlinear chemical processes.
  arXiv  Detail & Related papers  (2023-08-23T14:23:26Z)
• A Deep Learning Method for Comparing Bayesian Hierarchical Models [1.6736940231069393]
  We propose a deep learning method for performing Bayesian model comparison on any set of hierarchical models. Our method enables efficient re-estimation of posterior model probabilities and fast performance validation prior to any real-data application.
  arXiv  Detail & Related papers  (2023-01-27T17:27:07Z)
• Stochastic Methods for AUC Optimization subject to AUC-based Fairness Constraints [51.12047280149546]
  A direct approach for obtaining a fair predictive model is to train the model through optimizing its prediction performance subject to fairness constraints. We formulate the training problem of a fairness-aware machine learning model as an AUC optimization problem subject to a class of AUC-based fairness constraints. We demonstrate the effectiveness of our approach on real-world data under different fairness metrics.
  arXiv  Detail & Related papers  (2022-12-23T22:29:08Z)
• When to Update Your Model: Constrained Model-based Reinforcement Learning [50.74369835934703]
  We propose a novel and general theoretical scheme for a non-decreasing performance guarantee of model-based RL (MBRL) Our follow-up derived bounds reveal the relationship between model shifts and performance improvement. A further example demonstrates that learning models from a dynamically-varying number of explorations benefit the eventual returns.
  arXiv  Detail & Related papers  (2022-10-15T17:57:43Z)
• Knowledge Removal in Sampling-based Bayesian Inference [86.14397783398711]
  When single data deletion requests come, companies may need to delete the whole models learned with massive resources. Existing works propose methods to remove knowledge learned from data for explicitly parameterized models. In this paper, we propose the first machine unlearning algorithm for MCMC.
  arXiv  Detail & Related papers  (2022-03-24T10:03:01Z)

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.