Related papers: A regularized model for wetting/dewetting problems…
Hypothesis Emerging energy-related technologies deal with multiscale hierarchical structures, intricate surface morphology, non-axisymmetric interfaces, and complex contact lines where wetting is difficult to quantify with classical…
We develop a mesoscale computational model to describe the interaction of a droplet with a solid. The model is based on the hybrid combination of the immersed boundary and the lattice Boltzmann computational schemes: the former is used to…
We investigate theoretically the possibility of a wetting transition induced by geometric roughness of a solid substrate for the case where the flat substrate does not show a wetting layer. Our approach makes use of a novel closed-form…
Gradient, chemically modified, flat surfaces enable directed transport of droplets. Calculation of apparent contact angles inherent for gradient surfaces is challenging even for atomically flat ones. Wetting of gradient, flat solid surfaces…
We propose a general framework for regularization in M-estimation problems under time dependent (absolutely regular-mixing) data which encompasses many of the existing estimators. We derive non-asymptotic concentration bounds for the…
Optimization, a key tool in machine learning and statistics, relies on regularization to reduce overfitting. Traditional regularization methods control a norm of the solution to ensure its smoothness. Recently, topological methods have…
A new modeling approach for large-eddy simulation (LES) is obtained by combining a `regularization principle' with an explicit filter and its inversion. This regularization approach allows a systematic derivation of the implied…
Image restoration is one of the most important areas in imaging science. Mathematical tools have been widely used in image restoration, where wavelet frame based approach is one of the successful examples. In this paper, we introduce a…
Decentralized optimization is a powerful paradigm that finds applications in engineering and learning design. This work studies decentralized composite optimization problems with non-smooth regularization terms. Most existing gradient-based…
Over-parameterized neural network models often lead to significant performance discrepancies between training and test sets, a phenomenon known as overfitting. To address this, researchers have proposed numerous regularization techniques…
This paper exploits the theory of geometric gradient flows to introduce an alternative regularization of the thin-film equation. The solution properties of this regularization are investigated via a sequence of numerical simulations whose…
Improved estimation of hydrometeorological states from down-sampled observations and background model forecasts in a noisy environment, has been a subject of growing research in the past decades. Here, we introduce a unified framework that…
In this work, we consider the solid-state dewetting of an axisymmetric thin film on a curved-surface substrate, with the assumption that the substrate morphology is also axisymmetric. Under the assumptions of axisymmetry, the surface…
This paper proposes a new way of regularizing an inverse problem in imaging (e.g., deblurring or inpainting) by means of a deep generative neural network. Compared to end-to-end models, such approaches seem particularly interesting since…
In many applications where collecting data is expensive, for example neuroscience or medical imaging, the sample size is typically small compared to the feature dimension. It is challenging in this setting to train expressive, non-linear…
We propose finite difference methods for degenerate fully nonlinear elliptic equations and prove the convergence of the schemes. Our focus is on the pure equation and a related free boundary problem of transmission type. The cornerstone of…
The purpose of this work is to develop and study a distributed strategy for Pareto optimization of an aggregate cost consisting of regularized risks. Each risk is modeled as the expectation of some loss function with unknown probability…
The problem of contact angle and hysteresis determination has direct implications for engineering applications of wetting, colloid and surface science. Significant technical challenges can arise under real-world operating conditions,…
Recent studies show that transformer-based architectures emulate gradient descent during a forward pass, contributing to in-context learning capabilities - an ability where the model adapts to new tasks based on a sequence of prompt…
We present a new approach for the mechanically consistent modelling and simulation of fluid-structure interactions with contact. The fundamental idea consists of combining a relaxed contact formulation with the modelling of seepage through…