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Saumik Dana

Publications and source records attributed to Saumik Dana.

13 recordsLinked to original sources
arXiv2022

Comparison of LSTM autoencoder based deep learning enabled Bayesian inference using two time series reconstruction approaches

In this work, we use a combination of Bayesian inference, Markov chain Monte Carlo and deep learning in the form of LSTM autoencoders to build and test a framework to provide robust estimates of injection rate from ground surface data in coupled flow and geomechanics problems. We use LSTM autoencoders to reconstruct the displacement time series for grid points on the top surface of a faulting due to water injection problem. We then deploy this LSTM autoencoder based model instead of the high fidelity model in the Bayesian inference framework to estimate injection rate from displacement input.

cs.LG↗
arXiv2021

Bayesian inference and Markov chain Monte Carlo based estimation of a geoscience model parameter

The critical slip distance in rate and state model for fault friction in the study of potential earthquakes can vary wildly from micrometers to few meters depending on the length scale of the critically stressed fault. This makes it incredibly important to construct an inversion framework that provides good estimates of the critical slip distance purely based on the observed acceleration at the seismogram. The framework is based on Bayesian inference and Markov chain Monte Carlo. The synthetic data is generated by adding noise to the acceleration output of spring-slider-damper idealization of the rate and state model as the forward model.

physics.geo-ph↗
arXiv2021

A fault slip model to study earthquakes due to pore pressure perturbations

The burgeoning need to sequester anthropogenic CO$_2$ for climate mitigation and the need for energy sustenance leading upto enhanced geothermal energy production has made it incredibly critical to study potential earthquakes due to fluid activity in the subsurface. These earthquakes result from reactivation of faults in the subsurface due to pore pressure perturbations. In this work, we provide a framework to model fault slip due to pore pressure change leading upto quantifying the earthquake magnitude.

physics.geo-ph↗
arXiv2021

A machine learning accelerated FE$^2$ homogenization algorithm for elastic solids

The FE$^2$ homogenization algorithm for multiscale modeling iterates between the macroscale and the microscale (represented by a representative volume element) till convergence is achieved at every increment of macroscale loading. The information exchange between the two scales occurs at the gauss points of the macroscale finite element discretization. The microscale problem is also solved using finite elements on-the-fly thus rendering the algorithm computationally expensive for complex microstructures. We invoke machine learning to establish the input-output causality of the RVE boundary value problem using a neural network framework. This renders the RVE as a blackbox which gets the information from the macroscale as an input and gives information back to the macroscale as output, thereby eliminating the need for on-the-fly finite element solves at the RVE level. This framework has the potential to significantly accelerate the FE$^2$ algorithm.

cs.CE↗
arXiv2021

Design of convergence criterion for fixed stress split iterative scheme for small strain anisotropic poroelastoplasticity coupled with single phase flow

We arrive at convergence criterion for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The analysis is based on studying the equations satisfied by the difference of iterates to show that the iterative scheme is contractive. The contractivity is based on driving a term to as small a value as possible (ideally zero). This condition is rendered as the convergence criterion of the algorithm.

math.NA↗
arXiv2021

An efficient algorithm for numerical homogenization of fluid filled porous solids: part-I

The concept of representative volume element or RVE is invoked to develop an algorithm for numerical homogenization of fluid filled porous solids. RVE based methods decouple analysis of a composite material into analyses at the local and global levels. The local level analysis models the microstructural details to determine effective properties by applying boundary conditions to the RVE and solving the resultant boundary value problem. The composite structure is then replaced by an equivalent homogeneous material having the calculated effective properties. We combine the features of two techniques: one is the definition of a displacement field for the fluid phase to allow for a definition of a continuous displacement field across the microstructure and the other is the $FE^2$ numerical homogenization that couples the macroscale with the RVE scale via gauss points.

cs.CE↗
arXiv2021

A simple framework for arriving at bounds on effective moduli in heterogeneous anisotropic poroelastic solids

The concepts of representative volume element (RVE), statistical homogeneity and homogeneous boundary conditions are invoked to arrive at bounds on effective moduli for heterogeneous anisotropic poroelastic solids. The homogeneous displacement boundary condition applicable to linear elasticity is replaced by a homogeneous displacement-pressure boundary condition to arrive at an upper bound within the RVE while the homogeneous traction boundary condition applicable to linear elasticity is replaced by a homogeneous traction-fluid content boundary condition to arrive at a lower bound within the RVE. Statistical homogeneity is then invoked to argue that the bounds obtained over the RVE are representative of the bounds obtained over the whole heterogeneous poroelastic solid.

cs.CE↗
arXiv2021

Augmented Lagrangian for treatment of hanging nodes in hexahedral meshes

The surge of activity in the resolution of fine scale features in the field of earth sciences over the past decade necessitates the development of robust yet simple algorithms that can tackle the various drawbacks of in silico models developed hitherto. One such drawback is that of the restrictive computational cost of finite element method in rendering resolutions to the fine scale features, while at the same time keeping the domain being modeled sufficiently large. We propose the use of the augmented lagrangian method commonly used in the treatment of hanging nodes in contact mechanics in tackling the drawback. An interface is introduced in a typical finite element mesh across which an aggressive coarsening of the finite elements is possible. The method is based upon minimizing an augmented potential energy which factors in the constraint that exists at the hanging nodes on that interface. This allows for a significant reduction in the number of finite elements comprising the mesh with concomitant reduction in the computational expense.

math.NA↗
arXiv2021

Uncertainty Quantification in Friction Model for Earthquakes using Bayesian inference

This work presents a framework to inversely quantify uncertainty in the model parameters of the friction model using earthquake data via the Bayesian inference. The forward model is the popular rate- and state- friction (RSF) model along with the spring slider damper idealization. The inverse model is to determine the model parameters using the earthquake data as the response of the RSF model. The conventional solution to the inverse problem is the deterministic parameter values, which may not represent the true value, and quantifying uncertainty in the model parameters increases confidence in the estimation. The uncertainty in the model parameters is estimated by the posterior distribution obtained through the Bayesian inversion.

cs.CE↗
arXiv2021

Two-grid method on unstructured tetrahedra: Applying computational geometry to staggered solution of coupled flow and mechanics problems

We develop a computational framework that leverages the features of sophisticated software tools and numerics to tackle some of the pressing issues in the realm of earth sciences. The algorithms to handle the physics of multiphase flow, concomitant geomechanics all the way to the surface of the earth and the complex geometries of field cases with surfaces of discontinuity are stacked on top of each other in a modular fashion which allows for easy use to the end user. The current focus of the framework is to provide the user with tools for assessing seismic risks associated with energy technologies as well as for use in generating forward simulations in inversion analysis from data obtained using GPS and InSAR. In this work, we focus on one critical aspect in the development of the framework: the use of computational geometry in a two-grid method for unstructured tetrahedral meshes

cs.CE↗
arXiv2018

The correspondence between Voigt and Reuss bounds and the decoupling constraint in a two-grid staggered solution algorithm to coupled flow and deformation in heterogeneous poroelastic media

We perform a convergence analysis of a two-grid staggered solution algorithm for the Biot system modeling coupled flow and deformation in heterogeneous poroelastic media. The algorithm first solves the flow subproblem on a fine grid using a mixed finite element method (by freezing a certain measure of the mean stress) followed by the poromechanics subproblem on a coarse grid using a conforming Galerkin method. Restriction operators map the fine scale flow solution to the coarse scale poromechanical grid and prolongation operators map the coarse scale poromechanical solution to the fine scale flow grid. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The analysis is based on studying the equations satisfied by the difference of iterates to show that the two-grid scheme is a contraction map under certain conditions. Those conditions are used to construct the restriction and prolongation operators as well as arrive at coarse scale elastic properties in terms of the fine scale data. We show that the adjustable parameter in the measure of the mean stress is linked to the Voigt and Reuss bounds frequently encountered in computational homogenization of multiphase composites.

math.NA↗
arXiv2018

Convergence analysis of fixed stress split iterative scheme for small strain anisotropic poroelastoplasticity: a primer

This work serves as a primer to our efforts in arriving at convergence estimates for the fixed stress split iterative scheme for single phase flow coupled with small strain anisotropic poroelastoplasticity. The fixed stress split iterative scheme solves the flow subproblem with stress tensor fixed using a mixed finite element method, followed by the poromechanics subproblem using a conforming Galerkin method in every coupling iteration at each time step. The coupling iterations are repeated until convergence and Backward Euler is employed for time marching. The convergence analysis is based on studying the equations satisfied by the difference of iterates to show that the iterative scheme is contractive.

math.NA↗