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Nonlinear monotone transformations are used extensively in normalizing flows to construct invertible triangular mappings from simple distributions to complex ones. In existing literature, monotonicity is usually enforced by restricting…

Machine Learning · Computer Science 2022-06-07 Difeng Cai , Yuliang Ji , Huan He , Qiang Ye , Yuanzhe Xi

The AAA algorithm, introduced in 2018, computes best or near-best rational approximations to functions or data on subsets of the real line or the complex plane. It is much faster and more robust than previous algorithms for such problems…

Numerical Analysis · Mathematics 2023-12-07 Yuji Nakatsukasa , Olivier Sete , Lloyd N. Trefethen

We propose an anytime online algorithm for the problem of learning a sequence of adversarial convex cost functions while approximately satisfying another sequence of adversarial online convex constraints. A sequential algorithm is called…

Machine Learning · Computer Science 2025-10-28 Dhruv Sarkar , Abhishek Sinha

In this paper, we consider the integrating factor midpoint method for wave-type equations and derive optimal order a posteriori error estimates. We first introduce an integrating factor midpoint approximation defined by the piecewise linear…

Numerical Analysis · Mathematics 2026-03-03 Xianfa Hu , Fazhan Geng , Wansheng Wang

A way to lower computational cost in large scale inverse problems and problems depending on poorly known model parameters is to replace the detailed model by an approximate one. Inverse problems are typically ill-posed, and the model…

Numerical Analysis · Mathematics 2026-04-30 Daniela Calvetti , Erkki Somersalo

Modular quantum computing architectures require error correction schemes that remain effective in the presense of noisy inter-processor operations. We introduce a distributed quantum error correction framework based on approximate codes to…

Quantum Physics · Physics 2025-11-05 Connor Clayton , Bruno Avritzer

When using the finite element method (FEM) in inverse problems, its discretization error can produce parameter estimates that are inaccurate and overconfident. The Bayesian finite element method (BFEM) provides a probabilistic model for the…

Numerical Analysis · Mathematics 2026-01-26 Anne Poot , Iuri Rocha , Pierre Kerfriden , Frans van der Meer

In this paper, an important discovery has been found for nonconforming immersed finite element (IFE) methods using the integral values on edges as degrees of freedom for solving elliptic interface problems. We show that those IFE methods…

Numerical Analysis · Mathematics 2023-05-17 Haifeng Ji , Feng Wang , Jinru Chen , Zhilin Li

Numerical solutions for flows in partially saturated porous media pose challenges related to the non-linearity and elliptic-parabolic degeneracy of the governing Richards' equation. Iterative methods are therefore required to manage the…

Numerical Analysis · Mathematics 2024-02-02 Nicolae Suciu , Florin A. Radu , Jakob S. Stokke , Emil Cătinaş , Andra Malina

The image quality of the new generation of earthbound Extremely Large Telescopes (ELTs) is heavily influenced by atmospheric turbulences. To compensate these optical distortions a technique called adaptive optics (AO) is used. Many AO…

Numerical Analysis · Mathematics 2020-09-03 Bernadett Stadler , Roberto Biasi , Mauro Manetti , Ronny Ramlau

The efficient resolution of Bayesian inverse problems remains challenging due to the high computational cost of traditional sampling methods. In this paper, we propose a novel framework that integrates Conditional Flow Matching (CFM) with a…

Machine Learning · Computer Science 2025-05-20 Daniil Sherki , Ivan Oseledets , Ekaterina Muravleva

In recent years, machine learning (ML) and neural networks (NNs) have gained widespread use and attention across various domains, particularly in transportation for achieving autonomy, including the emergence of flying taxis for urban air…

Machine Learning · Computer Science 2024-01-17 Fabien Geyer , Johannes Freitag , Tobias Schulz , Sascha Uhrig

Since a long-time, the quantum integrable systems have remained an area where modern mathematical methods have given an access to interesting results in the study of physical systems. The exact computations, both numerical and asymptotic,…

Mathematical Physics · Physics 2020-12-07 Giridhar V. Kulkarni

In the present work, we present a hybrid quantum-classical workflow aimed at improving the accuracy of alchemical free energy (AFE) predictions by incorporating configuration interaction (CI) simulations using the book-ending correction…

Chemical Physics · Physics 2025-06-27 Milana Bazayeva , Zhen Li , Danil Kaliakin , Fangchun Liang , Akhil Shajan , Susanta Das , Kenneth M. Merz

We define a class of machine-learned flow-based sampling algorithms for lattice gauge theories that are gauge-invariant by construction. We demonstrate the application of this framework to U(1) gauge theory in two spacetime dimensions, and…

In this paper, we propose a novel bootstrap algorithm that is more efficient than existing methods for approximating the distribution of the factor-augmented regression estimator for a rotated parameter vector. The regression is augmented…

Methodology · Statistics 2025-10-02 Peiyun Jiang , Takashi Yamagata

We introduce the attention-indexed model (AIM), a theoretical framework for analyzing learning in deep attention layers. Inspired by multi-index models, AIM captures how token-level outputs emerge from layered bilinear interactions over…

Machine Learning · Computer Science 2026-02-03 Fabrizio Boncoraglio , Emanuele Troiani , Vittorio Erba , Lenka Zdeborová

Recently, a new paradigm named \emph{drifting model} has been proposed for mapping distributions, which achieves the SOTA image generation performance over ImageNet via one-step neural functional evaluation (NFE). The basic idea is to…

Machine Learning · Computer Science 2026-05-07 Guoqiang Zhang , Kenta Niwa , W. Bastiaan Kleijn

We consider the Adaptive Antoulas-Anderson (AAA) rational interpolation algorithm recently developed by Trefethen and co-authors, which can be viewed as a type of moment-matching technique for system realization and approximation. We…

Systems and Control · Electrical Eng. & Systems 2023-10-03 Jared Jonas , Bassam Bamieh

In this work we develop and implement a method for calculation of the Bethe logarithm for many-electron atoms. This quantity is required to evaluate the leading-order quantum electrodynamics correction to the energy and properties of atomic…

Atomic Physics · Physics 2023-11-21 Michał Lesiuk , Jakub Lang