Related papers: A fast multilevel dimension iteration algorithm fo…
We present a high-order method that provides numerical integration on volumes, surfaces, and lines defined implicitly by two smooth intersecting level sets. To approximate the integrals, the method maps quadrature rules defined on…
This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…
One of the main concerns in design and process planning for multi-axis additive and subtractive manufacturing is collision avoidance between moving objects (e.g., tool assemblies) and stationary objects (e.g., a part unified with fixtures).…
Computer-automated design and discovery have led to high-performance nanophotonic devices with diverse functionalities. However, massively multi-channel systems such as metasurfaces controlling many incident angles and photonic-circuit…
In calculating integral or discrete transforms, use has been made of fast algorithms for multiplying vectors by matrices whose elements are specified as values of special (Chebyshev, Legendre, Laguerre, etc.) functions. The currently…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
Convex polytopes have compact representations and exhibit convexity, which makes them suitable for abstracting obstacle-free spaces from various environments. Existing generation methods struggle with balancing high-quality output and…
Many emerging use cases of data mining and machine learning operate on large datasets with data from heterogeneous sources, specifically with both sparse and dense components. For example, dense deep neural network embedding vectors are…
In this paper we present a new method that can accelerate the computation of the PageRank importance vector. Our method, called D-Iteration (DI), is based on the decomposition of the matrix-vector product that can be seen as a fluid…
The theory and computation of tensors with different tensor products play increasingly important roles in scientific computing and machine learning. Different products aim to preserve different algebraic properties from the matrix algebra,…
The Hadamard product of two tensors in the tensor-train (TT) format is a fundamental operation across various applications, such as TT-based function multiplication for nonlinear differential equations or convolutions. However, conventional…
Progressive dimensionality reduction algorithms allow for visually investigating intermediate results, especially for large data sets. While different algorithms exist that progressively increase the number of data points, we propose an…
In this paper we propose a fast optimization algorithm for approximately minimizing convex quadratic functions over the intersection of affine and separable constraints (i.e., the Cartesian product of possibly nonconvex real sets). This…
This paper presents a high-order accurate numerical quadrature algorithm for evaluating integrals over curved surfaces and regions defined implicitly via a level set of a given function restricted to a hyperrectangle. The domain is divided…
Motion planning and control problems are embedded and essential in almost all robotics applications. These problems are often formulated as stochastic optimal control problems and solved using dynamic programming algorithms. Unfortunately,…
In recent years, a new kind of accelerated hardware has gained popularity in the Artificial Intelligence (AI) and Machine Learning (ML) communities which enables extremely high-performance tensor contractions in reduced precision for deep…
Multi-dimensional non-Cartesian MRI encoding using the precomputed interpolator can encounter the curse of dimensionality, in which the interpolator size exceeds the available memory on the parallel accelerators. Here we reformulate the…
Numerically solving multi-marginal optimal transport (MMOT) problems is computationally prohibitive, even for moderate-scale instances involving $l\ge4$ marginals with support sizes of $N\ge1000$. The cost in MMOT is represented as a tensor…
Specialized function gradient computing hardware could greatly improve the performance of state-of-the-art optimization algorithms, e.g., based on gradient descent or conjugate gradient methods that are at the core of control, machine…
Aiming at drastic speedup for point-feature embeddings at test time, we propose a new framework that uses a pair of multi-layer perceptrons (MLP) and a lookup table (LUT) to transform point-coordinate inputs into high-dimensional features.…