Related papers: FIAT: improving performance and accuracy for high-…
Chain-of-Thought (CoT) reasoning enhances the decision-making capabilities of vision-language-action models in autonomous driving, but its autoregressive nature introduces significant inference latency, making it impractical for real-time…
Partition refinement is a method for minimizing automata and transition systems of various types. Recently, we have developed a partition refinement algorithm that is generic in the transition type of the given system and matches the run…
Alloy discovery is constrained by vast compositional spaces, competing objectives, and prohibitive experimental costs. Although simulations and machine learning have each accelerated parts of this process, unifying scientific knowledge,…
We develop an efficient $hp$-finite element method for piecewise-smooth differential equations with periodic boundary conditions, using orthogonal polynomials defined on circular arcs. The operators derived from this basis are banded and…
This paper presents the first family of conforming finite element divdiv complexes on tetrahedral grids in three dimensions. In these complexes, finite element spaces of $H(\text{divdiv},\Omega;\mathbb{S})$ are from a current preprint [Chen…
Finite-state models are widely used in software engineering, especially in control systems development. Commonly, in control applications such models are developed manually, hence, keeping them up-to-date requires extra effort. To simplify…
The nonlinear Fourier transform (NFT) has recently gained significant attention in fiber optic communications and other engineering fields. Although several numerical algorithms for computing the NFT have been published, the design of…
We introduce a novel method for bounding high-order multi-dimensional polynomials in finite element approximations. The method involves precomputing optimal piecewise-linear bounding boxes for polynomial basis functions, which can then be…
Low-bit floating-point (FP) formats, such as FP8, provide significant acceleration and memory savings in model training thanks to native hardware support on modern GPUs and NPUs. However, we analyze that FP8 quantization offers speedup…
We consider finite approximations of a fractal generated by an iterated function system of affine transformations on $\mathbb{R}^d$ as a discrete set of data points. Considering a signal supported on this finite approximation, we propose a…
We construct a finite element like scheme for fully non-linear integro-partial differential equations arising in optimal control of jump-processes. Special cases of these equations include optimal portfolio and option pricing equations in…
In the analysis of composite materials with heterogeneous microstructures, full resolution of the heterogeneities using classical numerical approaches can be computationally prohibitive. This paper presents a micromechanics-enhanced finite…
Since the 1960's the finite element method emerged as a powerful tool for the numerical simulation of countless physical phenomena or processes in applied sciences. One of the reasons for this undeniable success is the great versatility of…
We introduce a new paradigm for immersed finite element and isogeometric methods based on interpolating function spaces from an unfitted background mesh into Lagrange finite element spaces defined on a foreground mesh that captures the…
We present Pylot, a platform for autonomous vehicle (AV) research and development, built with the goal to allow researchers to study the effects of the latency and accuracy of their models and algorithms on the end-to-end driving behavior…
Reliable and interpretable traffic crash modeling is essential for understanding causality and improving road safety. This study introduces a novel approach to predicting collision types by utilizing a comprehensive dataset fused from…
In this paper, we present explicit expressions for conforming finite element function spaces, basis functions, and degrees of freedom on the pentatope and tetrahedral prism elements. More generally, our objective is to construct finite…
As a key step towards a complete automation of the finite element method, we present a new algorithm for automatic and efficient evaluation of multilinear variational forms. The algorithm has been implemented in the form of a compiler, the…
Instruction fine-tuning stands as a crucial advancement in leveraging large language models (LLMs) for enhanced task performance. However, the annotation of instruction datasets has traditionally been expensive and laborious, often relying…
We propose a matrix-free finite element (FE) homogenization scheme that is considerably more efficient than generic FE implementations. The efficiency of our scheme follows from a preconditioned well-scaled reformulation allowing for the…