相关论文: A hybrid SIAC -- data-driven post-processing filte…

Numerical simulation of time-dependent partial differential equations (PDEs) is central to scientific and engineering applications, but high-fidelity solvers are often prohibitively expensive for long-horizon or time-critical settings.…

Simulations of the dynamics generated by partial differential equations (PDEs) provide approximate, numerical solutions to initial value problems. Such simulations are ubiquitous in scientific computing, but the correctness of the results…

A hybrid simulation code is developed that is suited for fast one-dimensional simulations of shower profiles, including fluctuations. It combines the Monte Carlo simulation of high energy interactions with a fast numerical solution of…

This paper presents an algorithm for the efficient approximation of the saddle-extremum persistence diagram of a scalar field. Vidal et al. introduced recently a fast algorithm for such an approximation (by interrupting a progressive…

Spectral deferred corrections (SDC) is an iterative approach for constructing higher- order accurate numerical approximations of ordinary differential equations. SDC starts with an initial approximation of the solution defined at a set of…

Calibration is crucial in deep learning applications, especially in fields like healthcare and autonomous driving, where accurate confidence estimates are vital for decision-making. However, deep neural networks often suffer from…

Deep Neural Networks (DNN) are nowadays largely adopted in many application domains thanks to their human-like, or even superhuman, performance in specific tasks. However, due to unpredictable/unconsidered operating conditions, unexpected…

We study Bayesian data assimilation (filtering) for time-evolution PDEs, for which the underlying forward problem may be very unstable or ill-posed. Such PDEs, which include the Navier-Stokes equations of fluid dynamics, are characterized…

Recent tropical cyclones, e.g., Hurricane Harvey (2017), have lead to significant rainfall and resulting runoff with accompanying flooding. When the runoff interacts with storm surge, the resulting floods can be greatly amplified and lead…

Many stochastic differential equations (SDEs) in the literature have a superlinearly growing nonlinearity in their drift or diffusion coefficient. Unfortunately, moments of the computationally efficient Euler-Maruyama approximation method…

We present scalable hybrid-parallel algorithms for training large-scale 3D convolutional neural networks. Deep learning-based emerging scientific workflows often require model training with large, high-dimensional samples, which can make…

The existence of redundancy in Convolutional Neural Networks (CNNs) enables us to remove some filters/channels with acceptable performance drops. However, the training objective of CNNs usually tends to minimize an accuracy-related loss…

This study concerns with singularly perturbed systems of second-order reaction-diffusion equations in ODE's. To handle this type of problems, a numerical-asymptotic hybrid method is employed. In this hybrid method, an efficient asymptotic…

Semi-supervised change detection (SSCD) aims to detect changes between bi-temporal remote sensing images by utilizing limited labeled data and abundant unlabeled data. Existing methods struggle in complex scenarios, exhibiting poor…

We investigate the numerical performance of a Discontinuous Galerkin (DG) hydrodynamics implementation when applied to the problem of driven, isothermal supersonic turbulence. While the high-order element-based spectral approach of DG is…

Precise sensing and control of spatial mode content is essential for the performance of precision optical systems, particularly interferometric gravitational-wave detectors, where misalignment and mode mismatch can lead to significant…

We introduce a new sequential methodology to calibrate the fixed parameters and track the stochastic dynamical variables of a state-space system. The proposed method is based on the nested hybrid filtering (NHF) framework of [1], that…

A series of novel filters for probabilistic inference that propose an alternative way of performing Bayesian updates, called particle flow filters, have been attracting recent interest. These filters provide approximate solutions to…

We develop a high-order hybridized discontinuous Galerkin (HDG) method for a linear degenerate elliptic equation arising from a two-phase mixture of mantle convection or glacier dynamics. We show that the proposed HDG method is well-posed…

Model predictive control (MPC) of hybrid dynamical systems is challenging because the associated optimization problem is nonsmooth and the resulting feedback law is discontinuous. This paper develops real-time MPC algorithms for nonlinear…