Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions

• URL: http://arxiv.org/abs/2307.13149v4
• Date: Thu, 1 Feb 2024 15:24:08 GMT
• Title: Discovering interpretable elastoplasticity models via the neural polynomial method enabled symbolic regressions
• Authors: Bahador Bahmani, Hyoung Suk Suh and WaiChing Sun
• Abstract summary: Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Conventional neural network elastoplasticity models are often perceived as lacking interpretability. This paper introduces a two-step machine learning approach that returns mathematical models interpretable by human experts. In particular, we introduce a surrogate model where yield surfaces are expressed in terms of a set of single-variable feature mappings obtained from supervised learning. A post-processing step is then used to re-interpret the set of single-variable neural network mapping functions into mathematical form through symbolic regression. This divide-and-conquer approach provides several important advantages. First, it enables us to overcome the scaling issue of symbolic regression algorithms. From a practical perspective, it enhances the portability of learned models for partial differential equation solvers written in different programming languages. Finally, it enables us to have a concrete understanding of the attributes of the materials, such as convexity and symmetries of models, through automated derivations and reasoning. Numerical examples have been provided, along with an open-source code to enable third-party validation.

Related papers

• Scaling and renormalization in high-dimensional regression [72.59731158970894]
  This paper presents a succinct derivation of the training and generalization performance of a variety of high-dimensional ridge regression models. We provide an introduction and review of recent results on these topics, aimed at readers with backgrounds in physics and deep learning.
  arXiv  Detail & Related papers  (2024-05-01T15:59:00Z)
• Discovering Interpretable Physical Models using Symbolic Regression and Discrete Exterior Calculus [55.2480439325792]
  We propose a framework that combines Symbolic Regression (SR) and Discrete Exterior Calculus (DEC) for the automated discovery of physical models. DEC provides building blocks for the discrete analogue of field theories, which are beyond the state-of-the-art applications of SR to physical problems. We prove the effectiveness of our methodology by re-discovering three models of Continuum Physics from synthetic experimental data.
  arXiv  Detail & Related papers  (2023-10-10T13:23:05Z)
• PROSE: Predicting Operators and Symbolic Expressions using Multimodal Transformers [5.263113622394007]
  We develop a new neural network framework for predicting differential equations. By using a transformer structure and a feature fusion approach, our network can simultaneously embed sets of solution operators for various parametric differential equations. The network is shown to be able to handle noise in the data and errors in the symbolic representation, including noisy numerical values, model misspecification, and erroneous addition or deletion of terms.
  arXiv  Detail & Related papers  (2023-09-28T19:46:07Z)
• A Recursive Bateson-Inspired Model for the Generation of Semantic Formal Concepts from Spatial Sensory Data [77.34726150561087]
  This paper presents a new symbolic-only method for the generation of hierarchical concept structures from complex sensory data. The approach is based on Bateson's notion of difference as the key to the genesis of an idea or a concept. The model is able to produce fairly rich yet human-readable conceptual representations without training.
  arXiv  Detail & Related papers  (2023-07-16T15:59:13Z)
• Toward Physically Plausible Data-Driven Models: A Novel Neural Network Approach to Symbolic Regression [2.7071541526963805]
  This paper proposes a novel neural network-based symbolic regression method. It constructs physically plausible models based on even very small training data sets and prior knowledge about the system. We experimentally evaluate the approach on four test systems: the TurtleBot 2 mobile robot, the magnetic manipulation system, the equivalent resistance of two resistors in parallel, and the longitudinal force of the anti-lock braking system.
  arXiv  Detail & Related papers  (2023-02-01T22:05:04Z)
• Variational Hierarchical Mixtures for Probabilistic Learning of Inverse Dynamics [20.953728061894044]
  Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. We consider a probabilistic hierarchical modeling paradigm that combines the benefits of both worlds to deliver computationally efficient representations with inherent complexity regularization. We derive two efficient variational inference techniques to learn these representations and highlight the advantages of hierarchical infinite local regression models.
  arXiv  Detail & Related papers  (2022-11-02T13:54:07Z)
• Dynamically-Scaled Deep Canonical Correlation Analysis [77.34726150561087]
  Canonical Correlation Analysis (CCA) is a method for feature extraction of two views by finding maximally correlated linear projections of them. We introduce a novel dynamic scaling method for training an input-dependent canonical correlation model.
  arXiv  Detail & Related papers  (2022-03-23T12:52:49Z)
• Model-agnostic multi-objective approach for the evolutionary discovery of mathematical models [55.41644538483948]
  In modern data science, it is more interesting to understand the properties of the model, which parts could be replaced to obtain better results. We use multi-objective evolutionary optimization for composite data-driven model learning to obtain the algorithm's desired properties.
  arXiv  Detail & Related papers  (2021-07-07T11:17:09Z)
• Improving the Reconstruction of Disentangled Representation Learners via Multi-Stage Modeling [54.94763543386523]
  Current autoencoder-based disentangled representation learning methods achieve disentanglement by penalizing the ( aggregate) posterior to encourage statistical independence of the latent factors. We present a novel multi-stage modeling approach where the disentangled factors are first learned using a penalty-based disentangled representation learning method. Then, the low-quality reconstruction is improved with another deep generative model that is trained to model the missing correlated latent variables.
  arXiv  Detail & Related papers  (2020-10-25T18:51:15Z)
• Learning a Formula of Interpretability to Learn Interpretable Formulas [1.7616042687330642]
  We show that an ML model of non-objective Proxies of Human Interpretability can be learned from human feedback. We show this for evolutionary symbolic regression. Our approach represents an important stepping stone for the design of next-generation interpretable (evolutionary) ML algorithms.
  arXiv  Detail & Related papers  (2020-04-23T13:59:49Z)

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.