Related papers: Highly efficient exponential scalar auxiliary vari…

We present a parametric family of semi-implicit second order accurate numerical methods for non-conservative and conservative advection equation for which the numerical solutions can be obtained in a fixed number of forward and backward…

Numerical stabilization techniques are often employed in under-resolved simulations of convection-dominated flows to improve accuracy and mitigate spurious oscillations. Specifically, the evolve--filter--relax (EFR) algorithm is a framework…

Learning in models with discrete latent variables is challenging due to high variance gradient estimators. Generally, approaches have relied on control variates to reduce the variance of the REINFORCE estimator. Recent work (Jang et al.…

Sharpness-aware Minimization (SAM) has been proposed recently to improve model generalization ability. However, SAM calculates the gradient twice in each optimization step, thereby doubling the computation costs compared to stochastic…

The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter Q for the orientational order is coupled with a real scalar…

We present a fast, unconditionally energy-stable numerical scheme for simulating vesicle deformation under osmotic pressure using a phase-field approach. The model couples an Allen-Cahn equation for the biomembrane interface with a…

Bilevel optimization is a fundamental tool in hierarchical decision-making and has been widely applied to machine learning tasks such as hyperparameter tuning, meta-learning, and continual learning. While significant progress has been made…

We propose a new, more general approach to the design of stochastic gradient-based optimization methods for machine learning. In this new framework, optimizers assume access to a batch of gradient estimates per iteration, rather than a…

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains…

Variance-reduced gradient estimators for policy gradient methods have been one of the main focus of research in the reinforcement learning in recent years as they allow acceleration of the estimation process. We propose a variance-reduced…

In this study, a fast and stable machine-learned hybrid algorithm implemented in TensorFlow for the integration of stiff chemical kinetics is introduced. Numerical solutions to differential equations are at the core of computational fluid…

Collective variable (CV) or order parameter based enhanced sampling algorithms have achieved great success due to their ability to efficiently explore the rough potential energy landscapes of complex systems. However, the degeneracy of…

The Smectic-A (SmA) phase is modeled by a modified Landau-de Gennes (mLdG) model proposed by Xia et al. [Phys. Rev. Lett., 126 (2021), 177801], in which a tensor order parameter $\mathbf{Q}$ for the orientational order is coupled with a…

In this work, we investigate the use of data-driven equation discovery for dynamical systems to model and forecast continuous-time dynamics of unconstrained optimization problems. To avoid expensive evaluations of the objective function and…

Reducing the variance of the gradient estimator is known to improve the convergence rate of stochastic gradient-based optimization and sampling algorithms. One way of achieving variance reduction is to design importance sampling strategies.…

We focus on the numerical approximation of the Cahn-Hilliard type equations, and present a family of second-order unconditionally energy-stable schemes. By reformulating the equation into an equivalent system employing a scalar auxiliary…

In today's cyber-enabled smart grids, high penetration of uncertain renewables, purposeful manipulation of meter readings, and the need for wide-area situational awareness, call for fast, accurate, and robust power system state estimation.…

In this paper, we present two multiple scalar auxiliary variable (MSAV)-based, finite element numerical schemes for the Abels-Garcke-Gr{\"u}n (AGG) model, which is a thermodynamically consistent phase field model of two-phase incompressible…

We propose in this paper efficient first/second-order time-stepping schemes for the evolutional Navier-Stokes-Nernst-Planck-Poisson equations. The proposed schemes are constructed using an auxiliary variable reformulation and sophisticated…

We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…