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The stochastic gradient descent (SGD) method is a widely used approach for solving stochastic optimization problems, but its convergence is typically slow. Existing variance reduction techniques, such as SAGA, improve convergence by…
We present an implicit method for solving the diffusion equation for the evolution of the dust fraction in the terminal velocity approximation using dust-as-mixture smoothed particle hydrodynamics (SPH). The numerical scheme involves…
We present a novel approach to investigate the long-time stochastic dynamics of multi-dimensional classical systems, in contact with a heat-bath. When the potential energy landscape is rugged, the kinetics displays a decoupling of short and…
We develop a fully-coupled, fully-implicit approach for phase-field modeling of solidification in metals and alloys. Predictive simulation of solidification in pure metals and metal alloys remains a significant challenge in the field of…
In this work we investigate the practicality of stochastic gradient descent and recently introduced variants with variance-reduction techniques in imaging inverse problems. Such algorithms have been shown in the machine learning literature…
The theoretical analysis of many problems in physics, astronomy and applied mathematics requires an efficient numerical exploration of multimodal parameter spaces that exhibit broken ergodicity. Monte Carlo methods are widely used to deal…
Ensuring the safe and reliable operation of integrated electricity and gas systems (IEGS) requires dynamic energy flow (DEF) simulation tools that achieve high accuracy and computational efficiency. However, the inherent strong nonlinearity…
Investigating the dynamical evolution of dust grains in proto-planetary disks is a key issue to understand how planets should form. We identify under which conditions dust settling can be constrained by high angular resolution observations…
Stochastic nested optimization, including stochastic compositional, min-max and bilevel optimization, is gaining popularity in many machine learning applications. While the three problems share the nested structure, existing works often…
We introduce a novel method for non-convex optimization, called Swarm-based Simulated Annealing (SSA), which is at the interface between the swarm-based gradient-descent (SBGD) [J. Lu et. al., ArXiv:2211.17157; E.Tadmor and A. Zenginoglu,…
We propose a statistical adaptive procedure called SALSA for automatically scheduling the learning rate (step size) in stochastic gradient methods. SALSA first uses a smoothed stochastic line-search procedure to gradually increase the…
We present an explicit second order staggered finite difference (FD) discretization scheme for forward simulation of natural gas transport in pipeline networks. By construction, this discretization approach guarantees that the conservation…
This paper aims to enhance the efficiency of validation and verification campaigns involving fuel sloshing phenomena. Our first contribution is the development of an open-source, high-fidelity and computationally efficient two-dimensional…
Interstellar dust is an important component of the galactic ecosystem, playing a key role in multiple galaxy formation processes. We present a novel numerical framework for the dynamics and size evolution of dust grains implemented in the…
The characterization of the spectral energy distribution (SED) of dust emission has become a critical issue in the quest for primordial B-modes. The dust SED is often approximated by a modified black body (MBB) emission law but the extent…
We describe a numerical scheme for magnetohydrodynamics simulations of dust-gas mixture by extending smoothed particle magnetohydrodynamics. We employ the single-species particle approach to describe dust-gas mixture with several…
We describe a new implementation of the one-fluid method in the SPH code Phantom to simulate the dynamics of dust grains in gas protoplanetary discs. We revise and extend previously developed algorithms by computing the evolution of a new…
Forming macroscopic solid bodies in circumstellar discs requires local dust concentration levels significantly higher than the mean. Interactions of the dust particles with the gas must serve to augment local particle densities, and…
Existing offline hierarchical reinforcement learning methods rely on high-level policy learning to generate subgoal sequences. However, their efficiency degrades as task horizons increase, and they lack effective strategies for stitching…
Recent years have shown many advances in our knowledge of the collisional evolution of protoplanetary dust. Based on a variety of dust-collision experiments in the laboratory, our view of the growth of dust aggregates in protoplanetary…