Extending a Physics-Based Constitutive Model using Genetic Programming
- URL: http://arxiv.org/abs/2108.01595v4
- Date: Fri, 19 Nov 2021 14:08:31 GMT
- Title: Extending a Physics-Based Constitutive Model using Genetic Programming
- Authors: Gabriel Kronberger, Evgeniya Kabliman, Johannes Kronsteiner, Michael
Kommenda
- Abstract summary: We present a new approach that identifies the functional dependency of calibration parameters from processing conditions based on genetic programming.
We propose two (explicit and implicit) methods to identify these dependencies and generate short interpretable expressions.
Our results show that the implicit method is more expensive than the explicit approach but also produces significantly better results.
- Score: 0.0
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: In material science, models are derived to predict emergent material
properties (e.g. elasticity, strength, conductivity) and their relations to
processing conditions. A major drawback is the calibration of model parameters
that depend on processing conditions. Currently, these parameters must be
optimized to fit measured data since their relations to processing conditions
(e.g. deformation temperature, strain rate) are not fully understood. We
present a new approach that identifies the functional dependency of calibration
parameters from processing conditions based on genetic programming. We propose
two (explicit and implicit) methods to identify these dependencies and generate
short interpretable expressions. The approach is used to extend a physics-based
constitutive model for deformation processes. This constitutive model operates
with internal material variables such as a dislocation density and contains a
number of parameters, among them three calibration parameters. The derived
expressions extend the constitutive model and replace the calibration
parameters. Thus, interpolation between various processing parameters is
enabled.
Our results show that the implicit method is computationally more expensive
than the explicit approach but also produces significantly better results.
Related papers
- Variational Bayesian surrogate modelling with application to robust design optimisation [0.9626666671366836]
Surrogate models provide a quick-to-evaluate approximation to complex computational models.
We consider Bayesian inference for constructing statistical surrogates with input uncertainties and dimensionality reduction.
arXiv Detail & Related papers (2024-04-23T09:22:35Z) - Joint Parameter and Parameterization Inference with Uncertainty Quantification through Differentiable Programming [0.20530463088872453]
We introduce a novel framework for the joint estimation of physical parameters and machine learning parameterizations with uncertainty quantification.
Our framework incorporates online training and efficient Bayesian inference within a high-dimensional parameter space, facilitated by differentiable programming.
arXiv Detail & Related papers (2024-03-04T17:02:23Z) - Data-freeWeight Compress and Denoise for Large Language Models [101.53420111286952]
We propose a novel approach termed Data-free Joint Rank-k Approximation for compressing the parameter matrices.
We achieve a model pruning of 80% parameters while retaining 93.43% of the original performance without any calibration data.
arXiv Detail & Related papers (2024-02-26T05:51:47Z) - 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) - Conditional Korhunen-Lo\'{e}ve regression model with Basis Adaptation
for high-dimensional problems: uncertainty quantification and inverse
modeling [62.997667081978825]
We propose a methodology for improving the accuracy of surrogate models of the observable response of physical systems.
We apply the proposed methodology to constructing surrogate models via the Basis Adaptation (BA) method of the stationary hydraulic head response.
arXiv Detail & Related papers (2023-07-05T18:14:38Z) - FAENet: Frame Averaging Equivariant GNN for Materials Modeling [123.19473575281357]
We introduce a flexible framework relying on frameaveraging (SFA) to make any model E(3)-equivariant or invariant through data transformations.
We prove the validity of our method theoretically and empirically demonstrate its superior accuracy and computational scalability in materials modeling.
arXiv Detail & Related papers (2023-04-28T21:48:31Z) - On the Effectiveness of Parameter-Efficient Fine-Tuning [79.6302606855302]
Currently, many research works propose to only fine-tune a small portion of the parameters while keeping most of the parameters shared across different tasks.
We show that all of the methods are actually sparse fine-tuned models and conduct a novel theoretical analysis of them.
Despite the effectiveness of sparsity grounded by our theory, it still remains an open problem of how to choose the tunable parameters.
arXiv Detail & Related papers (2022-11-28T17:41:48Z) - Surrogate Modeling for Physical Systems with Preserved Properties and
Adjustable Tradeoffs [0.0]
We present a model-based and a data-driven strategy to generate surrogate models.
The latter generates interpretable surrogate models by fitting artificial relations to a presupposed topological structure.
Our framework is compatible with various spatial discretization schemes for distributed parameter models.
arXiv Detail & Related papers (2022-02-02T17:07:02Z) - Bayesian Calibration of imperfect computer models using Physics-informed
priors [0.0]
We introduce a computational efficient data-driven framework suitable for quantifying the uncertainty in physical parameters of computer models.
We extend this into a fully Bayesian framework which allows quantifying the uncertainty of physical parameters and model predictions.
This work is motivated by the need for interpretable parameters for the hemodynamics of the heart for personal treatment of hypertension.
arXiv Detail & Related papers (2022-01-17T15:16:26Z) - A data-driven peridynamic continuum model for upscaling molecular
dynamics [3.1196544696082613]
We propose a learning framework to extract, from molecular dynamics data, an optimal Linear Peridynamic Solid model.
We provide sufficient well-posedness conditions for discretized LPS models with sign-changing influence functions.
This framework guarantees that the resulting model is mathematically well-posed, physically consistent, and that it generalizes well to settings that are different from the ones used during training.
arXiv Detail & Related papers (2021-08-04T07:07:47Z) - Post-mortem on a deep learning contest: a Simpson's paradox and the
complementary roles of scale metrics versus shape metrics [61.49826776409194]
We analyze a corpus of models made publicly-available for a contest to predict the generalization accuracy of neural network (NN) models.
We identify what amounts to a Simpson's paradox: where "scale" metrics perform well overall but perform poorly on sub partitions of the data.
We present two novel shape metrics, one data-independent, and the other data-dependent, which can predict trends in the test accuracy of a series of NNs.
arXiv Detail & Related papers (2021-06-01T19:19:49Z)
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.