Related papers: Data-Driven Filtering of the Spherical Harmonics M…

In this paper the simplified double-spherical harmonics SDPN, approximation of the neutron transport equation is proposed. The SDPN equations are derived from the multi-group DPN equations for N=1,2,3 (comparable to the SP3, SP5, and SP7…

By approximating posterior distributions with weighted samples, particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. While the effectiveness of particle filters has been…

In this study, we introduce a Fourier series-based trainable filter for computed tomography (CT) reconstruction within the filtered backprojection (FBP) framework. This method overcomes the limitation in noise reduction by optimizing…

We extend the finite element interpolated neural network (FEINN) framework from partial differential equations (PDEs) with weak solutions in $H^1$ to PDEs with weak solutions in $H(\textbf{curl})$ or $H(\textbf{div})$. To this end, we…

In this work, we study physics-informed neural networks (PINNs) constrained by partial differential equations (PDEs) and their application in approximating PDEs with two characteristic scales. From a continuous perspective, our formulation…

Filtering for stochastic reaction networks (SRNs) is an important problem in systems/synthetic biology aiming to estimate the state of unobserved chemical species. A good solution to it can provide scientists valuable information about the…

Accurately simulating wave propagation is crucial in fields such as acoustics, electromagnetism, and seismic analysis. Traditional numerical methods, like finite difference and finite element approaches, are widely used to solve governing…

We present a novel approach to define the filter and relax steps in the evolve-filter-relax (EFR) framework for simulating turbulent flows. The EFR main advantages are its ease of implementation and computational efficiency. However, as it…

Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…

Semantic segmentation for spherical data is a challenging problem in machine learning since conventional planar approaches require projecting the spherical image to the Euclidean plane. Representing the signal on a fundamentally different…

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…

Disorder is often considered detrimental to coherence. However, under specific conditions, it can enhance synchronization. We develop a machine-learning framework to design optimal disorder configurations that maximize phase…

Physics-Informed Neural Networks (PINNs) have gained significant attention for their simplicity and flexibility in engineering and scientific computing. In this study, we introduce a normalized PINN (NPINN) framework to solve a class of…

The single image super-resolution task is one of the most examined inverse problems in the past decade. In the recent years, Deep Neural Networks (DNNs) have shown superior performance over alternative methods when the acquisition process…

Physics informed neural network (PINN) based solution methods for differential equations have recently shown success in a variety of scientific computing applications. Several authors have reported difficulties, however, when using PINNs to…

Physics-Informed Neural Networks (PINNs) serve as a flexible alternative for tackling forward and inverse problems in differential equations, displaying impressive advancements in diverse areas of applied mathematics. Despite integrating…

In this paper, numerical methods using Physics-Informed Neural Networks (PINNs) are presented with the aim to solve higher-order ordinary differential equations (ODEs). Indeed, this deep-learning technique is successfully applied for…

Calculating true volatility is an essential task for option pricing and risk management. However, it is made difficult by market microstructure noise. Particle filtering has been proposed to solve this problem as it favorable statistical…

Inverse problems consist of recovering a signal from a collection of noisy measurements. These problems can often be cast as feasibility problems; however, additional regularization is typically necessary to ensure accurate and stable…

Physics-informed neural network architectures have emerged as a powerful tool for developing flexible PDE solvers which easily assimilate data, but face challenges related to the PDE discretization underpinning them. By instead adapting a…