相关论文: Space-filling Latin Hypercube Designs based on Ran…

Complex computer codes, for instance simulating physical phenomena, are often too time expensive to be directly used to perform uncertainty, sensitivity, optimization and robustness analyses. A widely accepted method to circumvent this…

Deep learning-based reduced order models (DL-ROMs) have been recently proposed to overcome common limitations shared by conventional ROMs - built, e.g., exclusively through proper orthogonal decomposition (POD) - when applied to nonlinear…

Hyperspherical Prototypical Learning (HPL) is a supervised approach to representation learning that designs class prototypes on the unit hypersphere. The prototypes bias the representations to class separation in a scale invariant and known…

In the paradigm of computer experiments, the choice of an experimental design is an important issue. When no information is available about the black-box function to be approximated, an exploratory design have to be used. In this context,…

Developing and redesigning astrophysical, cosmological, and space plasma numerical codes for existing and next-generation accelerators is critical for enabling large-scale simulations. To address these challenges, the SPACE Center of…

Bayesian optimization (BO) is one of the most effective methods for closed-loop experimental design and black-box optimization. However, a key limitation of BO is that it is an inherently sequential algorithm (one experiment is proposed per…

We prove the existence of quasi-projective coarse moduli spaces parametrising certain complete flags of subschemes of a fixed projective space $\mathbb{P}(V)$ up to projective automorphisms. The flags of subschemes being parametrised are…

Sample efficiency in the face of computationally expensive simulations is a common concern in surrogate modeling. Current strategies to minimize the number of samples needed are not as effective in simulated environments with wide state…

Regular factorial designs with randomization restrictions are widely used in practice. This paper provides a unified approach to the construction of such designs using randomization defining contrast subspaces for the representation of…

Locating arrays (LAs) can be used to detect and identify interaction faults among factors in a component-based system. The optimality and constructions of LAs with a single fault have been investigated extensively under the assumption that…

Cosmological simulations of galaxy formation are limited by finite computational resources. We draw from the ongoing rapid advances in Artificial Intelligence (specifically Deep Learning) to address this problem. Neural networks have been…

Real-world applications of computational fluid dynamics often involve the evaluation of quantities of interest for several distinct geometries that define the computational domain or are embedded inside it. For example, design optimization…

Hardware implementations of complex functions regularly deploy piecewise polynomial approximations. This work determines the complete design space of piecewise polynomial approximations meeting a given accuracy specification. Knowledge of…

The regular polyhedra have the highest order of 3D symmetries and are exceptionally at- tractive templates for (self)-assembly using minimal types of building blocks, from nano-cages and virus capsids to large scale constructions like glass…

Self-orthogonal codes are a subclass of linear codes that are contained within their dual codes. Since self-orthogonal codes are widely used in quantum codes, lattice theory and linear complementary dual (LCD) codes, they have received…

We study the problem of discrete geometric packing. Here, given weighted regions (say in the plane) and points (with capacities), one has to pick a maximum weight subset of the regions such that no point is covered more than its capacity.…

Space-filling designs are popular choices for computer experiments. A sliced design is a design that can be partitioned into several subdesigns. We propose a new type of sliced space-filling design called sliced rotated sphere packing…

This paper presents a novel and lightweight hyperparameter optimization (HPO) method, MOdular FActorial Design (MOFA). MOFA pursues several rounds of HPO, where each round alternates between exploration of hyperparameter space by factorial…

Self-orthogonal codes have received great attention due to their important applications in quantum codes, LCD codes and lattices. Recently, several families of self-orthogonal codes containing the all-$1$ vector were constructed by…

Quantum versions of the hydrogen atom and the harmonic oscillator are studied on non Euclidean spaces of dimension N. 2N-1 integrals, of arbitrary order, are constructed via a multi-dimensional version of the factorization method, thus…