Discovery of deformation mechanisms of soft material
Z. Wang, J.B. Estrada, E.M. Arruda, K. Garikipati, "Discovery of deformation mechanisms and constitutive response of soft material surrogates of biological tissue by full-field characterization and data-driven variational system identification ", 2020, [BioRiv]
System identification by VSI
A set of spatio-temporal partial differential equations (PDEs) is the most common mathematical form used to model phase separation including biologic pattern development and precipitate morphology in alloy systems. For first-order dynamics, which govern materials physics, PDEs describe the time derivatives of concentrations or of order parameters in the system as a algebraic function of its current state, which could be coupled with various derivative terms. Similar contributions from other species' concentrations could also be included. It is compelling to attempt to discover the analytic forms of PDEs from data.Z. Wang, X. Huan, K. Garikipati, "Variational system identification of the partial differential equations governing pattern-forming physics: Inference under varying fidelity and noise", Computer Methods in Applied Mechanics and Engineering, Vol 353, 201-216, 2019, doi.org/10.1016/j.cma.2019.05.019, [journal] [arXiv]Z. Wang, B. Wu, K. Garikipati, X. Huan, "A Perspective on Regression and Bayesian Approaches for System Identification of Pattern Formation Dynamics", Theoretical and Applied Mechanics Letters, 2020 [arXiv]Z. Wang, X. Huan, K. Garikipati, "Variational system identification of the partial differential equations governing microstructure evolution in materials: Inference over sparse and spatially unrelated data", 2020, [arXiv]
Machine Learning in Physics
Machine learning has been achieving tremendous success. Can we use this to help us analyze physical phenomena? Like learning/representing some highly nonlinear profiles (e.g. free energy function), predicting trends and find local minimum? Can we come up data driven model to bridge multi-scale modeling? In essential can we relate machine learning technique like neutral network to traditional numerical methods?
RNN and time series data --- learn the system dynamics
Recently I am particular interesting in Recurrent Neural Network for time series data: data that collected by traditional numerical method (time and space discretization).
CNN and image-based physics learning
Brain Morphology & Inverse Problem
We use MRI data from an atlas of fetal brains, and perform image registration on them to obtain displacement vector fields describing morphogenesis of averaged fetal brains. Inverse solutions are sought for the distribution of proliferating and migrating neurons, whose accumulation in the cortex and tangential intercalation there leads to folding. We focus on the formation of the highly robust primary folds.
Z. Wang, B. Martin, J. Weickenmeier, K. Garikipati, "An inverse modelling study for the local volume changes during early growth of the fetal human brain", 2020, [BioRiv]
Battery System Modeling
Lithium-ion battery can be broadly classified at three different levels: battery pack level, sandwich level (homogeneous model) and particle scale level. We focus on battery microstructure problem in these porous material fulfilled with electrolyte, and electrochemistry-mechanics process in battery. They are highly coupled and driven from continuum physics, including structure-fluid interaction (ALE), electrochemistry and thermodynamics. Variational methods are usually applied to form numerical formulation of governing equations.
Z. Wang and K. Garikipati, “A multi-physics battery model with particle scale resolution of evolving porosity and electrolyte flow”, Journal of the Electrochemical Society, Vol. 165: A2421-A438, 2018, doi:10.1149/2.0141811jes [journal] [arXiv]
Z. Wang, J. Siegel, K. Garikipati, "Intercalation driven porosity effects in coupled continuum models for the electrical, chemical, thermal and mechanical response of battery electrode materials", Journal of the Electrochemical Society, Vol. 164: A2199-A2212, 2017, doi:10.1149/2.0081712jes [arXiv]
strain gradient elasticity
Classical elasticity is scale invariant: it does not admit length scales intrinsic to the material. The only length scale which may manifest itself arises from the problem geometry. However, real materials do posses intrinsic length scales (i.e., interatomic distance, dislocation cells, grain sizes, etc). If the deformation varies on these scales, size effects may arise. They mollify singularities that otherwise appear, for instance in classical elastic descriptions of defects such as cracks, point defects, dislocations and grain boundaries. They also arise as essential elements to the formation of strain-driven microstructure. One framework that is appropriate for treating such problems is the strain gradient formulation of elasticity, which is a natural extension of classical elasticity by a Taylor series expansion of the deformation map to include gradients of strain.
Z. Wang, S. Rudraraju, K. Garikipati, "A three dimensional field formulation, and isogeometric solutions to point and line defects using Toupin's theory of gradient elasticity at finite strains'', Journal of the Mechanics and Physics of Solids, Vol. 94: 336-361, 2016, doi:10.1016/j.jmps.2016.03.028 [journal] [arXiv]