Plasma turbulence plays a fundamental role in determining the performances of magnetic confinement fusion devices, such as tokamaks. Advances in computer science, combined with the development of efficient physical models, have significantly improved our u ...
Deep heteroscedastic regression involves jointly optimizing the mean and covariance of the predicted distribution using the negative log-likelihood. However, recent works show that this may result in sub-optimal convergence due to the challenges associated ...
We present a convergence study of the gyromoment (GM) approach, which is based on projecting the gyrokinetic distribution function onto a Hermite–Laguerre polynomial basis, focused on the cyclone base case (CBC) (Lin et al., Phys. Rev. Lett., vol. 83, no. ...
The goal of this thesis is the development and the analysis of numerical methods for problems where the unknown is a curve on a smooth manifold. In particular, the thesis is structured around the three following problems: homotopy continuation, curve inter ...
The goal of this paper is to characterize function distributions that general neural networks trained by descent algorithms (GD/SGD), can or cannot learn in polytime. The results are: (1) The paradigm of general neural networks trained by SGD is poly-time ...
It is well-known that for any integral domain R, the Serre conjecture ring R(X), i.e., the localization of the univariate polynomial ring R[X] at monic polynomials, is a Bezout domain of Krull dimension
We study the existence, uniqueness, and regularity of the solution to the stochastic reaction-diffusion equation (SRDE) with colored noise F-center dot:partial derivative(t)u = aijuxixj +biuxi + cu - bu1+beta +xi u1+gamma F-center dot, (t, x) is ...
Intelligent fault diagnosis has been increasingly improved with the evolution of deep learning (DL) approaches. Recently, the emerging graph neural networks (GNNs) have also been introduced in the field of fault diagnosis with the goal to make better use o ...
We study three convolutions of polynomials in the context of free probability theory. We prove that these convolutions can be written as the expected characteristic polynomials of sums and products of unitarily invariant random matrices. The symmetric addi ...
The celebrated PCP Theorem states that any language in NP can be decided via a verifier that reads O(1) bits from a polynomially long proof. Interactive oracle proofs (IOP), a generalization of PCPs, allow the verifier to interact with the prover for multi ...
