相关论文: Spectral and Nilpotent Matrix Orderings: Compariso…

SPARC processors have many applications in mission-critical industries such as aviation and space engineering. Hence, it is important to provide formal frameworks that facilitate the verification of hardware and software that run on or…

We devise and evaluate numerically Hybrid High-Order (HHO) methods for hyperelastic materials undergoing finite deformations. The HHO methods use as discrete unknowns piecewise polynomials of order $k\ge1$ on the mesh skeleton, together…

Spectral behaviors have been widely discussed in machine learning, yet the optimizer's own spectral bias remains unclear. We argue that first-order optimizers exhibit an intrinsic frequency preference that significantly reshapes the…

Entropy conditions play a crucial role in the extraction of a physically relevant solution for systems of conservation laws, thus motivating the construction of entropy stable schemes that satisfy a discrete analogue of such conditions.…

In this work, we study optimization methods that leverage the linear minimization oracle (LMO) over a norm-ball. We propose a new stochastic family of algorithms that uses the LMO to adapt to the geometry of the problem and, perhaps…

Scientific machine learning has seen significant progress with the emergence of operator learning. However, existing methods encounter difficulties when applied to problems on unstructured grids and irregular domains. Spatial graph neural…

Given pairwise comparisons between multiple items, how to rank them so that the ranking matches the observations? This problem, known as rank aggregation, has found many applications in sports, recommendation systems, and other web…

Neural network (NN) controllers achieve strong empirical performance on nonlinear dynamical systems, yet deploying them in safety-critical settings requires robustness to disturbances and uncertainty. We present a method for jointly…

While many visual odometry (VO), visual-inertial odometry (VIO), and SLAM systems achieve high accuracy, the majority of existing methods miss to assess risks at runtime. This paper presents SUPER (Sensitivity-based Uncertainty-aware…

We study the impact of different discretization choices on the accuracy of SPH and we explore them in a large number of Newtonian and special-relativistic benchmark tests. As a first improvement, we explore a gradient prescription that…

Subgraph query is a critical task in graph analysis with a wide range of applications across various domains. Most existing methods rely on heuristic vertex matching orderings, which may significantly degrade enumeration performance for…

In this work, we present a numerical implementation to compute the atom centered descriptors introduced by Bartok et al (Phys. Rev. B, 87, 184115, 2013) based on the harmonic analysis of the atomic neighbor density function. Specifically,…

Determination of the neutrino mass ordering (NMO) is one of the biggest priorities in the intensity frontier of high energy particle physics. To accomplish that goal a lot of efforts are being put together with the atmospheric, solar,…

Characterizing the long term behavior of dynamical systems given limited measurements is a common challenge throughout the physical and biological sciences. This is a challenging task due to the sparsity and noise inherent to empirical…

Optimizing costly black-box functions within a constrained evaluation budget presents significant challenges in many real-world applications. Surrogate Optimization (SO) is a common resolution, yet its proprietary nature introduced by the…

We explore what may be deduced about the neutrino mass ordering problem from the observation of core-collapse supernova burst neutrinos in modern terrestrial detectors. We employ ternary plots in a novel way to visualize the time evolution…

We propose the *State Space Neural Operator* (SS-NO), a compact architecture for learning solution operators of time-dependent partial differential equations (PDEs). Our formulation extends structured state space models (SSMs) to joint…

Nonnegative matrix factorization (NMF) under the separability assumption can provably be solved efficiently, even in the presence of noise, and has been shown to be a powerful technique in document classification and hyperspectral unmixing.…

The matrix spectral and nuclear norms appear in enormous applications. The generalizations of these norms to higher-order tensors is becoming increasingly important but unfortunately they are NP-hard to compute or even approximate. Although…

We show that nilpotent matrices that yield the Schrodinger equation from its first order form encode the fingerprints of grand unified theories. We perform a rigorous search for all such nilpotent matrices and find that the resulting…