arXiv subjects

Stephen Niezgoda

Publications and source records attributed to Stephen Niezgoda.

2 recordsLinked to original sources

arXiv2025

Efficient GPU-computing simulation platform JAX-PF for differentiable phase field model

We present JAX-PF, an open-source, GPU-accelerated, and differentiable Phase Field (PF) software package, supporting both explicit and implicit time stepping schemes. Leveraging the modern computing architecture JAX, JAX-PF achieves high performance through array programming and GPU acceleration, delivering ~5x speedup over PRISMS-PF with MPI (24 CPU cores) for systems with ~4.19 million degrees of freedom using explicit schemes, and scaling efficiently with implicit schemes for large-size problems. Furthermore, a key feature of JAX-PF is automatic differentiation (AD), eliminating manual derivations of free-energy functionals and Jacobians. Beyond forward simulations, JAX-PF demonstrates its potential in inverse design by providing sensitivities for gradient-based optimization. We demonstrate, for the first time, the calibration of PF material parameters using AD-based sensitivities, highlighting its capability for high-dimensional inverse problems. By combining efficiency, flexibility, and full differentiability, JAX-PF offers a fast, practical, and integrated tool for forward simulation and inverse design, advancing co-designing of material and manufacturing processes and supporting the goals of the Materials Genome Initiative.

physics.comp-ph↗

arXiv2020

Bayesian Inference for Polycrystalline Materials

Polycrystalline materials, such as metals, are comprised of heterogeneously oriented crystals. Observed crystal orientations are modelled as a sample from an orientation distribution function (ODF), which determines a variety of material properties and is therefore of great interest to practitioners. Observations consist of quaternions, 4-dimensional unit vectors reflecting both orientation and rotation of a single crystal. Thus, an ODF must account for known crystal symmetries as well as satisfy the unit length constraint. A popular method for estimating ODFs non-parametrically is symmetrized kernel density estimation. However, disadvantages of this approach include difficulty in interpreting results quantitatively, as well as in quantifying uncertainty in the ODF. We propose to use a mixture of symmetric Bingham distributions as a flexible parametric ODF model, inferring the number of mixture components, the mixture weights, and scale and location parameters based on crystal orientation data. Furthermore, our Bayesian approach allows for structured uncertainty quantification of the parameters of interest. We discuss details of the sampling methodology and conclude with analyses of various orientation datasets, interpretations of parameters of interest, and comparison with kernel density estimation methods.

stat.AP↗