A generalized Bayesian approach to model calibration

Tohme, Tony; Vanslette, Kevin

doi:10.1016/j.ress.2020.107141

Cited by 12 publications

(5 citation statements)

References 44 publications

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“…Symbolic regression is challenging to tackle with hand-designed operators, due to non-locality and discontinuities in the space of expressions. Existing symbolic regression approaches use carefullydeveloped representations, genetic operators, and auxiliary methods like gradient-based/convex coefficient optimization [13,39,79] to construct the right kind of search process for reaching highperforming expressions that look like the kinds of expressions the experimenter is interested in. With LMX, these challenges can be avoided by simply feeding parent expressions into the language model.…”

Section: Symbolic Regressionmentioning

confidence: 99%

Language Model Crossover: Variation through Few-Shot Prompting

Meyerson¹,

Nelson²,

Bradley³

et al. 2023

Preprint

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This paper pursues the insight that language models naturally enable an intelligent variation operator similar in spirit to evolutionary crossover. In particular, language models of sufficient scale demonstrate in-context learning, i.e. they can learn from associations between a small number of input patterns to generate outputs incorporating such associations (also called few-shot prompting). This ability can be leveraged to form a simple but powerful variation operator, i.e. to prompt a language model with a few text-based genotypes (such as code, plain-text sentences, or equations), and to parse its corresponding output as those genotypes' offspring. The promise of such language model crossover (which is simple to implement and can leverage many different open-source language models) is that it enables a simple mechanism to evolve semantically-rich text representations (with few domain-specific tweaks), and naturally benefits from current progress in language models. Experiments in this paper highlight the versatility of language-model crossover, through evolving binary bit-strings, sentences, equations, text-toimage prompts, and Python code. The conclusion is that language model crossover is a promising method for evolving genomes representable as text. CCS CONCEPTS• Computing methodologies → Neural networks.

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Section: Symbolic Regressionmentioning

confidence: 99%

Language Model Crossover: Variation through Few-Shot Prompting

Meyerson¹,

Nelson²,

Bradley³

et al. 2023

Preprint

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“…The Bayesian Validation Metric (BVM) is a general model validation and testing tool that was shown to generalize Bayesian model testing and regression (Vanslette, Tohme, and Youcef-Toumi 2020;Tohme, Vanslette, and Youcef-Toumi 2020). The BVM measures the probability of agreement A between the model M and the data D given the Boolean agreement function B, denoted as 0 ≤ p(A|M, D, B) ≤ 1.…”

Section: The Bayesian Validation Metricmentioning

confidence: 99%

Improving Regression Uncertainty Estimation Under Statistical Change

Tohme¹,

Vanslette²

2021

Preprint

Self Cite

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While deep neural networks are highly performant and successful in a wide range of real-world problems, estimating their predictive uncertainty remains a challenging task. To address this challenge, we propose and implement a loss function for regression uncertainty estimation based on the Bayesian Validation Metric (BVM) framework while using ensemble learning. A series of experiments on indistribution data show that the proposed method is competitive with existing state-of-the-art methods. In addition, experiments on out-of-distribution data show that the proposed method is robust to statistical change and exhibits superior predictive capability.

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“…It can be performed by comparison with data from experiments or atomistic simulations, and the development of machine learning approaches is highly relevant in this field. A powerful tool for doing this is the Bayesian statistical method [ 52 ], consisting of the random enumeration of parameter sets and the estimation of a quasi-probability of each set according to the correspondence between the model predictions and the training data. Walters et al [ 53 ] successfully employed the plate impact experiments and Bayesian method to calibrate the Johnson-Cook strength model; a fast emulator (Gaussian regression model) was trained to predict the hydrocode model outputs in order to substitute the model in the Bayesian algorithm and to speed up the optimization process.…”

Section: Introductionmentioning

confidence: 99%

Modified Taylor Impact Tests with Profiled Copper Cylinders: Experiment and Optimization of Dislocation Plasticity Model

et al. 2023

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Current progress in numerical simulations and machine learning allows one to apply complex loading conditions for the identification of parameters in plasticity models. This possibility expands the spectrum of examined deformed states and makes the identified model more consistent with engineering practice. A combined experimental-numerical approach to identify the model parameters and study the dynamic plasticity of metals is developed and applied to the case of cold-rolled OFHC copper. In the experimental part, profiled projectiles (reduced cylinders or cones in the head part) are proposed for the Taylor impact problem for the first time for material characterization. These projectiles allow us to reach large plastic deformations with true strains up to 1.3 at strain rates up to 105 s−1 at impact velocities below 130 m/s. The experimental results are used for the optimization of parameters of the dislocation plasticity model implemented in 3D with the numerical scheme of smoothed particle hydrodynamics (SPH). A Bayesian statistical method in combination with a trained artificial neural network as an SPH emulator is applied to optimize the parameters of the dislocation plasticity model. It is shown that classical Taylor cylinders are not enough for a univocal selection of the model parameters, while the profiled cylinders provide better optimization even if used separately. The combination of different shapes and an increase in the number of experiments increase the quality of optimization. The optimized numerical model is successfully validated by the experimental data about the shock wave profiles in flyer plate experiments from the literature. In total, a cheap, simple, but efficient route for optimizing a dynamic plasticity model is proposed. The dislocation plasticity model is extended to estimate grain refinement and volume fractions of weakened areas in comparison with experimental observations.

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A generalized Bayesian approach to model calibration

Cited by 12 publications

References 44 publications

Language Model Crossover: Variation through Few-Shot Prompting

Language Model Crossover: Variation through Few-Shot Prompting

Improving Regression Uncertainty Estimation Under Statistical Change

Modified Taylor Impact Tests with Profiled Copper Cylinders: Experiment and Optimization of Dislocation Plasticity Model

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