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We study the dynamics of membrane vesicle motor transport into dendritic spines, which are bulbous intracellular compartments in neurons that play a key role in transmitting signals between neurons. We consider the stochastic analog of the…
We present a linear, second order fully discrete numerical scheme on a staggered grid for a thermodynamically consistent hydrodynamic phase field model of binary compressible fluid flow mixtures derived from the generalized Onsager…
High-dimensional recordings of dynamical processes are often characterized by a much smaller set of effective variables, evolving on low-dimensional manifolds. Identifying these latent dynamics requires solving two intertwined problems:…
Stochastic gradient descent (SGD) has been widely used in machine learning due to its computational efficiency and favorable generalization properties. Recently, it has been empirically demonstrated that the gradient noise in several deep…
We study the noisy nonequilibrium dynamics of a conserved density that is driven by a fluctuating surface governed by the conserved Kardar-Parisi-Zhang equation. We uncover the universal scaling properties of the conserved density. We…
We present a statistical learning framework for robust identification of partial differential equations from noisy spatiotemporal data. Extending previous sparse regression approaches for inferring PDE models from simulated data, we address…
A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the…
Stochastic differential equations (SDEs) are popular tools to analyse time series data in many areas, such as mathematical finance, physics, and biology. They provide a mechanistic description of the phenomeon of interest, and their…
When solving partial differential equations (PDEs), classical numerical methods often require fine mesh grids and small time stepping to meet stability, consistency, and convergence conditions, leading to high computational cost. Recently,…
This paper presents a geometric-variational approach to continuous and discrete mechanics and field theories. Using multisymplectic geometry, we show that the existence of the fundamental geometric structures as well as their preservation…
A variety of real-world applications are modeled via hyperbolic conservation laws. To account for uncertainties or insufficient measurements, random coefficients may be incorporated. These random fields may depend discontinuously on the…
This paper introduces a new approach to Large-Eddy Simulation (LES) where subgrid-scale (SGS) dissipation is applied proportionally to the degree of local spectral broadening, hence mitigated or deactivated in regions dominated by…
In this paper, we discuss information-theoretic tools for obtaining optimized coarse-grained molecular models for both equilibrium and non-equilibrium molecular dynamics. The latter are ubiquitous in physicochemical and biological…
We propose a sampling algorithm relying on a collective variable (CV) of mid-size dimension modelled by a normalizing flow and using non-equilibrium dynamics to propose full configurational moves from the proposition of a refreshed value of…
We present a new approach to coarse-graining of variables describing dust flow in GR. It is based on assigning quasi-local shear, twist and expansion to 2-dimensional surfaces with the help of isometric embeddings into the 3-dimensional…
The weakly compressible Smoothed Particle Hydrodynamics (SPH) is known to suffer from the pressure oscillation, which would undermine the simulation stability and accuracy. To address this issue, we propose a generalized density dissipation…
Numerous processes across both the physical and biological sciences are driven by diffusion. Partial differential equations (PDEs) are a popular tool for modelling such phenomena deterministically, but it is often necessary to use…
Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and…
This study addresses the inverse problem of parameter estimation for Stochastic Differential Equations (SDEs) by minimizing a regularized discrepancy functional via Stochastic Gradient Descent (SGD). To achieve computational efficiency, we…
Diffeomorphic matching (only one of several names for this technique) is a technique for non-rigid registration of curves and surfaces in which the curve or surface is embedded in the flow of a time-series of vector fields. One seeks the…