Related papers: A Position-Free Path Integral for Homogeneous Slab…
Rendering algorithms typically integrate light paths over path space. However, integrating over this one unified space is not necessarily the most efficient approach, and we show that partitioning path space and integrating each of these…
We study the numerical integration of functions from isotropic Sobolev spaces $W_p^s([0,1]^d)$ using finitely many function evaluations within randomized algorithms, aiming for the smallest possible probabilistic error guarantee…
In traffic flow modeling, incorporating uncertainty is crucial for accurately capturing the complexities of real-world scenarios. In this work we focus on kinetic models of traffic flow, where a key step is to design effective numerical…
High-dimensional distributions, especially those with heavy tails, are notoriously difficult for off-the-shelf MCMC samplers: the combination of unbounded state spaces, diminishing gradient information, and local moves results in…
Partial differential equations (PDEs) with spatially-varying coefficients arise throughout science and engineering, modeling rich heterogeneous material behavior. Yet conventional PDE solvers struggle with the immense complexity found in…
We propose to use deep neural networks for generating samples in Monte Carlo integration. Our work is based on non-linear independent components estimation (NICE), which we extend in numerous ways to improve performance and enable its…
Path-Guiding algorithms for sampling scattering directions can drastically decrease the variance of Monte Carlo estimators of Light Transport Equation, but their usage was limited to offline rendering because of memory and computational…
This paper investigates the use of stratified sampling as a variance reduction technique for approximating integrals over large dimensional spaces. The accuracy of this method critically depends on the choice of the space partition, the…
We consider the problem of propagating the uncertainty from a possibly large number of random inputs through a computationally expensive model. Stratified sampling is a well-known variance reduction strategy, but its application, thus far,…
The Multilevel Monte Carlo method is an efficient variance reduction technique. It uses a sequence of coarse approximations to reduce the computational cost in uncertainty quantification applications. The method is nowadays often considered…
We present a novel hybrid computational method to simulate accurately dendritic solidification in the low undercooling limit where the dendrite tip radius is one or more orders of magnitude smaller than the characteristic spatial scale of…
Rendering volumetric scattering media, including clouds, fog, smoke, and other complex materials, is crucial for realism in computer graphics. Traditional path tracing, while unbiased, requires many long path samples to converge in scenes…
Interactive global illumination remains a challenge in radiometrically- and geometrically-complex scenes. Specialized sampling strategies are effective for specular and near-specular transport because the scattering has relatively low…
Hybrid methods for simulating rarefied gas flows reduce computational cost by coupling a particle-based model, typically the direct simulation Monte Carlo (DSMC) method, to a continuum-based solver, i.e. a computational fluid dynamics (CFD)…
The path integral of a quantum system with an exact symmetry can be written as a sum of functional integrals each giving the contribution from quantum states with definite symmetry properties. We propose a strategy to compute each of them,…
Discontinuous visibility changes remain a major bottleneck when optimizing surfaces within a physically-based inverse renderer. Many previous works have proposed sophisticated algorithms and data structures to sample visibility silhouettes…
The efficient evaluation of high-dimensional integrals is of importance in both theoretical and practical fields of science, such as data science, statistical physics, and machine learning. However, exact computation methods suffer from the…
We consider the scattering of neutrons and photons on solid volume rectangular targets. It is common to treat this problem using the Maxwell Boltzmann Transport Equation and to use underlying symmetries to simplify the calculation. For…
We present an experimental investigation of multiple scattering in photonic-crystal-based topological edge states with and without engineered random disorder. We map the spatial distribution of light as it propagates along a so-called…
We present a multiple time step algorithm for hybrid path integral Monte Carlo simulations involving rigid linear rotors. We show how to calculate the quantum torques needed in the simulation from the rotational density matrix, for which we…