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We present a general and systematic theory of non-equilibrium dynamics of multi-component fluid membranes, in general, and membranes containing transmembrane proteins, in particular. Developed based on a minimal number of principles of…
Particulate Stokesian flows describe the hydrodynamics of rigid or deformable particles in Stokes flows. Due to highly nonlinear fluid-structure interaction dynamics, moving interfaces, and multiple scales, numerical simulations of such…
The purpose of this article is to provide a perspective -- admittedly, a rather subjective one -- of recent developments at the interface of machine learning/data-driven methods and nonlinear wave studies. We review some recent pillars of…
We demonstrate how deep convolutional neural networks can be trained to predict 2+1 D hydrodynamic simulation results for flow coefficients, mean-transverse-momentum and charged particle multiplicity from the initial energy density profile.…
Pseudo-Hamiltonian neural networks (PHNN) were recently introduced for learning dynamical systems that can be modelled by ordinary differential equations. In this paper, we extend the method to partial differential equations. The resulting…
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method (IPM). We utilize the expressiveness…
Fluid dynamics plays a crucial role in various multiphysics applications, including energy systems, electronics cooling, and biomedical engineering. Developing models for complex coupled systems can be challenging and time-consuming. In…
The predictive accuracy of the Navier-Stokes equations is known to degrade at the limits of the continuum assumption, thereby necessitating expensive and often highly approximate solutions to the Boltzmann equation. While tractable in one…
This paper explores the problem of reconstructing temporally consistent surfaces from a 3D point cloud sequence without correspondence. To address this challenging task, we propose DynoSurf, an unsupervised learning framework integrating a…
One of the most promising applications in nanoscience is the design of new materials to improve water permeability and selectivity of nanoporous membranes. Understanding the molecular architecture behind these fascinating structures and how…
The engineering design process often relies on mathematical modeling that can describe the underlying dynamic behavior. In this work, we present a data-driven methodology for modeling the dynamics of nonlinear systems. To simplify this…
Fine-scale simulation of complex systems governed by multiscale partial differential equations (PDEs) is computationally expensive and various multiscale methods have been developed for addressing such problems. In addition, it is…
Flows of particles through bottlenecks are ubiquitous in nature and industry, involving both dry granular materials and suspensions. However, practical limitations of conventional experimental setups hinder the full understanding of these…
We explore how neural differential equations (NDEs) may be trained on highly resolved fluid-dynamical models of unresolved scales providing an ideal framework for data-driven parameterizations in climate models. NDEs overcome some of the…
The existing physical-informed Deep Operator Networks are mostly based on either the well-known mathematical formula of the system or huge amounts of data for different scenarios. However, in some cases, it is difficult to get the exact…
When an ensemble of particles interact hydrodynamically, they generically display large-scale transient structures such as swirls in sedimenting particles [1], or colloidal strings in sheared suspensions [2]. Understanding these…
A substantial number of algorithms exists for the simulation of moving particles suspended in fluids. However, finding the best method to address a particular physical problem is often highly non-trivial and depends on the properties of the…
We introduce a geometric framework to study Newton's equations on infinite-dimensional configuration spaces of diffeomorphisms and smooth probability densities. It turns out that several important PDEs of hydrodynamical origin can be…
Deep learning and the collocation method are merged and used to solve partial differential equations describing structures' deformation. We have considered different types of materials: linear elasticity, hyperelasticity (neo-Hookean) with…
Learning under non-smooth objectives remains a fundamental challenge in machine learning, as abrupt changes in conditioning variables can induce highly non-smooth loss landscapes and destabilize optimization. This difficulty is particularly…