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Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…
In this work, we introduce two novel reformulations of a recent weakly hyperbolic model for two-phase flow with surface tension. In the model, the tracking of phase boundaries is achieved by using a vector interface field, rather than a…
Filtering and smoothing algorithms for linear discrete-time state-space models with skewed and heavy-tailed measurement noise are presented. The algorithms use a variational Bayes approximation of the posterior distribution of models that…
Predicting the behavior of a dynamical system from noisy observations of its past outputs is a classical problem encountered across engineering and science. For linear systems with Gaussian inputs, the Kalman filter -- the best linear…
Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the…
Pore-resolved direct numerical simulations of turbulent open channel flow are performed comparing the structure and dynamics of turbulence over impermeable rough and smooth walls to a porous sediment bed at permeability Reynolds number…
In operational scenarios, steganographers use sets of covers from various sensors and processing pipelines that differ significantly from those used by researchers to train steganalysis models. This leads to an inevitable performance gap…
We study the homogenization of a steady diffusion equation in a highly heterogeneous medium made of two subregions separated by a periodic barrier through which the flow is proportional to the jump of the temperature by a layer conductance…
We consider the problem of minimizing the sum of non-smooth convex functions in non-Euclidean spaces, e.g., probability simplex, via only local computation and communication on an undirected graph. We propose two algorithms motivated by…
Transmembrane ion flow through channel proteins undergoing density fluctuations may cause lateral gradients of the electrical potential across the membrane giving rise to electrophoresis of charged channels. A model for the dynamics of the…
The ability of streamwise-travelling waves of spanwise velocity to reduce the turbulent skin friction drag is assessed in the compressible regime. Direct numerical simulations are carried out to compare drag reduction in subsonic, transonic…
Motivated by a constrained minimization problem, it is studied the gradient flows with respect to Hessian Riemannian metrics induced by convex functions of Legendre type. The first result characterizes Hessian Riemannian structures on…
A purpose-built permeameter was used to explore the transient evolution of porosity during the mixing process in filtration experiments. The experiments considered upward seepage flow and explored the influence of base and filter particle…
By analogy to the terminology of curved exponential families in statistics, we define curved Bregman divergences as Bregman divergences restricted to non-affine parameter subspaces and sub-dimensional Bregman divergences when the…
Probabilistic Circuits (PCs) are a class of generative models that allow exact and tractable inference for a wide range of queries. While recent developments have enabled the learning of deep and expressive PCs, this increased capacity can…
We propose a general approach to the higher-order homogenization of discrete elastic networks made up of linear elastic beams or springs in dimension 2 or 3. The network may be nearly (rather than exactly) periodic: its elastic and…
This study proposes an algorithm for modeling compressible flows in spherical shells in nearly incompressible and weakly compressible regimes based on an implicit direction splitting approach. The method retains theoretically expected…
A method for density-based topology optimization of heat exchangers with two fluids is proposed. The goal of the optimization process is to maximize the heat transfer from one fluid to the other, under maximum pressure drop constraints for…
Fluid deformation and strain history are central to wide range of fluid mechanical phenomena ranging from fluid mixing and particle transport to stress development in complex fluids and the formation of Lagrangian coherent structures…
There is a need for numerical models capable of predicting local accumulation of hydrogen near stress concentrators and crack tips to prevent and mitigate hydrogen assisted fracture in steels. The experimental characterisation of trapping…