All Outputs (23)

Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization (2024)
Journal Article

Using quasi-Newton methods in stochastic optimization is not a trivial task given the difficulty of extracting curvature information from the noisy gradients. Moreover, pre-conditioning noisy gradient observations tend to amplify the noise. We propos... Read More about Approximating Hessian matrices using Bayesian inference: a new approach for quasi-Newton methods in stochastic optimization.

A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness (2024)
Journal Article

In this continuum theory, we propose a mathematical framework to study the mechanical interplay of bulk-surface materials undergoing deformation and phase segregation. To this end, we devise a principle of virtual powers with a bulk-surface dynamics,... Read More about A bulk-surface continuum theory for fluid flows and phase segregation with finite surface thickness.

Mechanics and Geometry of Enriched Continua (2023)
Book

Correction to: A continuum framework for phase field with bulk-surface dynamics (2023)
Journal Article

Corrigendum to “Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty” [Comput. Methods Appl. Mech. Engrg. 399 (2022) 115320] (Computer Methods in Applied Mechanics and Engineering (2022) 399, (S0045782522004194), (10.1016/j.cma.2022.115320)) (2023)
Journal Article

The authors regret that because of the condensed notation in Eq. (21), we failed to keep track of the dependence of the correction term [Formula presented] on the parameters of interest [Formula presented] entering through [Formula presented] in Sect... Read More about Corrigendum to “Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty” [Comput. Methods Appl. Mech. Engrg. 399 (2022) 115320] (Computer Methods in Applied Mechanics and Engineering (2022) 399, (S0045782522004194), (10.1016/j.cma.2022.115320)).

The effects of chemical and mechanical interactions on the thermodynamic pressure for mineral solid solutions (2023)
Journal Article

We use a coupled thermodynamically consistent framework to model reactive chemo-mechanical responses of solid solutions. Specifically, we focus on chemically active solid solutions that are subject to mechanical effects due to heterogeneous stress di... Read More about The effects of chemical and mechanical interactions on the thermodynamic pressure for mineral solid solutions.

A continuum framework for phase field with bulk-surface dynamics (2022)
Journal Article

This continuum mechanical theory aims at detailing the underlying rational mechanics of dynamic boundary conditions proposed by Fischer et al. (Phys Rev Lett 79:893, 1997), Goldstein et al. (Phys D Nonlinear Phenom 240:754–766, 2011), and Knopf et al... Read More about A continuum framework for phase field with bulk-surface dynamics.

Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty (2022)
Journal Article

Calculating the expected information gain in optimal Bayesian experimental design typically relies on nested Monte Carlo sampling. When the model also contains nuisance parameters, which are parameters that contribute to the overall uncertainty of th... Read More about Small-noise approximation for Bayesian optimal experimental design with nuisance uncertainty.

Localized folding of thick layers (2022)
Journal Article

We describe the localized folding of thick layers embedded in a viscoelastic framework. Higher-order partial differential equations such as the Swift-Hohenberg equation are standard for modelling the folding process. Using a high-order shear theory,... Read More about Localized folding of thick layers.

Direct numerical simulations of intrusive density- and particle-driven gravity currents (2022)
Journal Article

In the present study, mesopycnal flows are investigated using direct numerical simulations. In particular, intrusive density- and particle-driven gravity currents in the lock exchange setup are simulated with the high-order finite-difference framewor... Read More about Direct numerical simulations of intrusive density- and particle-driven gravity currents.

A spatio-temporal adaptive phase-field fracture method (2022)
Journal Article

We present an energy-preserving mechanic formulation for dynamic quasi-brittle fracture in an Eulerian–Lagrangian formulation, where a second-order phase-field equation controls the damage evolution. The numerical formulation adapts in space and time... Read More about A spatio-temporal adaptive phase-field fracture method.

Estimating divergence‐free flows via neural networks (2021)
Journal Article

We apply neural networks to the problem of estimating divergence-free velocity flows from given sparse observations. Following the modern trend of combining data and models in physics-informed neural networks, we reconstruct the velocity flow by trai... Read More about Estimating divergence‐free flows via neural networks.

Statistical learning for fluid flows: Sparse Fourier divergence-free approximations (2021)
Journal Article

We reconstruct the velocity field of incompressible flows given a finite set of measurements. For the spatial approximation, we introduce the Sparse Fourier divergence-free approximation based on a discrete L2 projection. Within this physics-informed... Read More about Statistical learning for fluid flows: Sparse Fourier divergence-free approximations.

Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems (2021)
Journal Article

At high temperature and pressure, solid diffusion and chemical reactions between rock minerals lead to phase transformations. Chemical transport during uphill diffusion causes phase separation, that is, spinodal decomposition. Thus, to describe the c... Read More about Extended Larché–Cahn framework for reactive Cahn–Hilliard multicomponent systems.

A continuum theory for mineral solid solutions undergoing chemo-mechanical processes (2021)
Journal Article

Recent studies on metamorphic petrology as well as microstructural observations suggest the influence of mechanical effects upon chemically active metamorphic minerals. Thus, the understanding of such a coupling is crucial to describe the dynamics of... Read More about A continuum theory for mineral solid solutions undergoing chemo-mechanical processes.

Phase-field gradient theory (2021)
Journal Article

We propose a phase-field theory for enriched continua. To generalize classical phase-field models, we derive the phase-field gradient theory based on balances of microforces, microtorques, and mass. We focus on materials where second gradients of the... Read More about Phase-field gradient theory.

On the control volume arbitrariness in the Navier-Stokes equation (2021)
Journal Article

We present a continuum theory to demonstrate the implications of considering general tractions developed on arbitrary control volumes where the surface enclosing it lacks smoothness. We then tailor these tractions to recover the Navier-Stokes-αβ equa... Read More about On the control volume arbitrariness in the Navier-Stokes equation.

Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory (2020)
Journal Article

The principle of virtual power is used derive a microforce balance for a second-gradient phase-field theory. In conjunction with constitutive relations consistent with a free-energy imbalance, this balance yields a broad generalization of the Swift–H... Read More about Generalized Swift–Hohenberg and phase-field-crystal equations based on a second-gradient phase-field theory.

Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design (2020)
Journal Article

An optimal experimental set-up maximizes the value of data for statistical inferences. The efficiency of strategies for finding optimal experimental set-ups is particularly important for experiments that are time-consuming or expensive to perform. In... Read More about Multilevel double loop Monte Carlo and stochastic collocation methods with importance sampling for Bayesian optimal experimental design.

Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization (2020)
Journal Article

Finding the best setup for experiments is the primary concern for Optimal Experimental Design (OED). Here, we focus on the Bayesian experimental design problem of finding the setup that maximizes the Shannon expected information gain. We use the stoc... Read More about Nesterov-aided stochastic gradient methods using Laplace approximation for Bayesian design optimization.