Related papers: LLM-Guided Evolutionary Program Synthesis for Quas…
Quasi-Monte Carlo algorithms are studied for designing discrete approximations of two-stage linear stochastic programs. Their integrands are piecewise linear, but neither smooth nor lie in the function spaces considered for QMC error…
Monte Carlo (MC) and Quasi-Monte Carlo (QMC) methods are classical approaches for the numerical integration of functions $f$ over $[0,1]^d$. While QMC methods can achieve faster convergence rates than MC in moderate dimensions, their…
Low-discrepancy (LD) sequences have been extensively used as efficient experimental designs across many scientific disciplines. QMCPy (https://qmcsoftware.github.io/QMCSoftware/) is an accessible Python library which provides a unified…
In this paper, we study quasi-Monte Carlo (QMC) integration in weighted Sobolev spaces. In contrast to many previous results the QMC algorithms considered here are of open type, i.e., they are extensible in the number of sample points…
LLM-driven program evolution has emerged as a powerful tool for automated scientific discovery, yet existing frameworks offer no principled guide for designing their individual components and provide no guarantee that the search converges.…
Large Language Models exhibit mode collapse, producing homogeneous outputs that fail to explore valid solution spaces. We present QD-LLM, a framework for parameter-efficient neuroevolution that evolves prompt embeddings, compact neural…
Quasi-Monte Carlo methods have become the industry standard in computer graphics. For that purpose, efficient algorithms for low discrepancy sequences are discussed. In addition, numerical pitfalls encountered in practice are revealed. We…
The efficient approximation of quantity of interest derived from PDEs with lognormal diffusivity is a central challenge in uncertainty quantification. In this study, we propose a multilevel quasi-Monte Carlo framework to approximate…
Quasi-Monte Carlo (QMC) methods are applied to multi-level Finite Element (FE) discretizations of elliptic partial differential equations (PDEs) with a random coefficient, to estimate expected values of linear functionals of the solution.…
We study signal processing tasks in which the signal is mapped via some generalized time-frequency transform to a higher dimensional time-frequency space, processed there, and synthesized to an output signal. We show how to approximate such…
This paper introduces quasi-Monte Carlo latent variable models (QLVMs): a class of deep generative models that are specialized for finding extremely low-dimensional and interpretable embeddings of high-dimensional datasets. Unlike standard…
We compare the integration error of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods for approximating the normalizing constant of posterior distributions and certain marginal likelihoods. In doing so, we characterize the dependency of…
We consider the problem of improving the efficiency of randomized Fourier feature maps to accelerate training and testing speed of kernel methods on large datasets. These approximate feature maps arise as Monte Carlo approximations to…
In many financial applications Quasi Monte Carlo (QMC) based on Sobol low-discrepancy sequences (LDS) outperforms Monte Carlo showing faster and more stable convergence. However, unlike MC QMC lacks a practical error estimate. Randomized…
The L infinity star discrepancy is a measure for how uniformly a point set is distributed in a given space. Point sets of low star discrepancy are used as designs of experiments, as initial designs for Bayesian optimization algorithms, for…
We present precision Monte Carlo calculations solving the QCD evolution equations up to the next-to-leading-order (NLO) level. They employ forward Markovian Monte Carlo (FMC) algorithms, which provide the rigorous solutions of the QCD…
Quasi-Monte Carlo (QMC) method is a useful numerical tool for pricing and hedging of complex financial derivatives. These problems are usually of high dimensionality and discontinuities. The two factors may significantly deteriorate the…
This study presents a comparative analysis of Monte Carlo (MC) and quasi-Monte Carlo (QMC) methods in the context of derivative pricing, emphasizing convergence rates and the curse of dimensionality. After a concise overview of traditional…
This paper investigates the construction of space-filling designs for computer experiments. The space-filling property is characterized by the covering and separation radii of a design, which are integrated through the unified criterion of…
Large Language Models (LLMs) have recently advanced many applications on software engineering tasks, particularly the potential for code generation. Among contemporary challenges, code generated by LLMs often suffers from inaccuracies and…