Solving Stochastic Inverse Problems for Structure-Property Linkages Using Data-Consistent Inversion

Tran, Anh; Wildey, Timothy Michael

doi:10.1007/978-3-030-65261-6_41

Cited by 2 publications

(3 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Constructing an accurate and physically faithful surrogate model is important for uncertainty quantification [51]. Computationally efficient surrogate models are commonly used, for example, in sampling [3,4] or to solve a stochastic inverse problem in structure-property relationship [6,7]. Monotonicity is common in materials science, such as the famous Hall-Petch relationship [2], i.e.…”

Section: Resultsmentioning

confidence: 99%

“…For example, Tallman et al [3,4] used a GP as a surrogate model to bridge microstructure crystallography and homogenized materials properties, where crystal plasticity finite element models are used to construct the database, and Yabansu et al [5] applied GPs to capture the evolution of microstructure statistics. Tran and Wildey [6,7] also used a GP as a surrogate model for structure-property relationship and solved a stochastic inverse problem using the acceptance-rejection sampling method. More examples can be found in [8,9].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Tran

Maupin

Rodgers

2022

Journal of Computing and Information Science in Engineering

Self Cite

View full text Add to dashboard Cite

Physics-constrained machine learning is emerging as an important topic in the field of machine learning for physics. One of the most significant advantages of incorporating physics constraints into machine learning methods is that the resulting model requires significantly less data to train. By incorporating physical rules into the machine learning formulation itself, the predictions are expected to be physically plausible. Gaussian process (GP) is perhaps one of the most common methods in machine learning for small datasets. In this paper, we investigate the possibility of constraining a GP formulation with monotonicity on three different material datasets, where one experimental and two computational datasets are used. The monotonic GP is compared against the regular GP, where significant reduction in the posterior variance is observed. The monotonic GP is strictly monotonic in the interpolation regime, but in the extrapolation regime, the monotonic effect starts fading away as one goes beyond the training dataset. Imposing monotonicity on the GP comes at a small accuracy cost, compared to the regular GP. The monotonic GP is perhaps most useful in applications where data is scarce or when the dimensionality is high, and monotonicity is supported by strong physical evidence.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Tran

Maupin

Rodgers

2022

Journal of Computing and Information Science in Engineering

Self Cite

View full text Add to dashboard Cite

show abstract

“…Bruder et al [17] further extend these ideas by expressing the dependencies between a hierarchy of low and lower-fidelity models using Gaussian processes. These accelerating results led to applications in material sciences [18]. Further, quite recent advances enable the use of stochastic simulation models [19] and Walsh et al [20], as well as Butler et al [21], use the measure-theoretic approach to optimally design experiments.…”

Section: Introductionmentioning

confidence: 99%

Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Wagner,

Castellaz,

Kaiser

et al. 2024

Preprint

View full text Add to dashboard Cite

Advances in measurement technology have led to the generation of increasingly large data sets across various scientific fields. Data that capture the variability of the underlying system or process, such as single-cell or imaging data, are particularly interesting. However, calibrating computational models to explain this type of data remains challenging. We interpret the model calibration as a Stochastic Inverse Problem (SIP), where the measurements are interpreted as probabilistic samples. Our new SIP solution approach, Eulerian Parameter Inference (EPI), only requires data with high variability and a deterministic simulation model that maps model parameters to simulation results. EPI solves the SIP through a change of variables. This computationally efficient approach allows for direct and point-wise evaluation of parameter densities without ever inverting the simulation model. The resulting parameter distribution captures data variability completely, enabling full data reconstruction. Further, estimating multivariate model parameters can bereduced to a series of one-dimensional problems under the assumption of stochasticallyindependent parameters. Particularly for complex simulation models andinvolved problems, this property is vital. With EPI, we explain 1) annual average temperature data of 3,168 weather stations around the world with an arithmetic model, 2) German district-specific COVID-19 infection data through a differential equation model, and 3) artificial data generated via a partial differential equation model with independent parameters. With a robust mathematical foundation and an easily accessible Python package, we provide a versatile solution framework for integrating data with high variability into simulation models that promotes application to various research questions.

show abstract

Solving Stochastic Inverse Problems for Structure-Property Linkages Using Data-Consistent Inversion

Cited by 2 publications

References 39 publications

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Monotonic Gaussian Process for Physics-Constrained Machine Learning With Materials Science Applications

Eulerian Parameter Inference: A Probabilistic Change of Variables for Model-Based Inference with High-Variability Data Sets

Contact Info

Product

Resources

About