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Related papers: Verifiable Error Bounds for Physics-Informed Neura…

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Motivated by the recent successful application of physics-informed neural networks (PINNs) to solve Boltzmann-type equations [S. Jin, Z. Ma, and K. Wu, J. Sci. Comput., 94 (2023), pp. 57], we provide a rigorous error analysis for PINNs in…

Numerical Analysis · Mathematics 2025-11-20 Elie Abdo , Lihui Chai , Ruimeng Hu , Xu Yang

Several recent works in communication systems have proposed to leverage the power of neural networks in the design of encoders and decoders. In this approach, these blocks can be tailored to maximize the transmission rate based on…

Information Theory · Computer Science 2020-07-15 Sina Molavipour , Germán Bassi , Mikael Skoglund

This paper investigates the robot state estimation problem within a non-inertial environment. The proposed state estimation approach relaxes the common assumption of static ground in the system modeling. The process and measurement models…

Robotics · Computer Science 2024-03-26 Zijian He , Sangli Teng , Tzu-Yuan Lin , Maani Ghaffari , Yan Gu

We study the performance of efficient quantum state tomography methods based on neural network quantum states using measured data from a two-photon experiment. Machine learning inspired variational methods provide a promising route towards…

We use statistical learning methods to construct an adaptive state estimator for nonlinear stochastic systems. Optimal state estimation, in the form of a Kalman filter, requires knowledge of the system's process and measurement uncertainty.…

Machine Learning · Statistics 2014-11-05 Michael Busch , Jeff Moehlis

Estimating the Kullback-Leibler (KL) divergence between random variables is a fundamental problem in statistical analysis. For continuous random variables, traditional information-theoretic estimators scale poorly with dimension and/or…

Machine Learning · Computer Science 2025-10-08 Mikil Foss , Andrew Lamperski

Physics Informed Neural Networks (PINNs) have frequently been used for the numerical approximation of Partial Differential Equations (PDEs). The goal of this paper is to construct PINNs along with a computable upper bound of the error,…

Numerical Analysis · Mathematics 2022-12-19 Lewin Ernst , Karsten Urban

We introduce a generalisation of quantum error correction, relaxing the requirement that a code should identify and correct a set of physical errors on the Hilbert space of a quantum computer exactly, instead allowing recovery up to a…

Quantum Physics · Physics 2023-10-17 Daniel Zhang , Toby Cubitt

Quantum Extreme Learning Machines (QELMs) have emerged as a potent tool for various quantum information processing tasks. We present a QELM protocol for estimating the amount of entanglement in Werner states. The protocol requires the…

Quantum Physics · Physics 2025-11-04 Hajar Assil , Abderrahim El Allati , Gian Luca Giorgi

The number of parameters describing a quantum state is well known to grow exponentially with the number of particles. This scaling clearly limits our ability to do tomography to systems with no more than a few qubits and has been used to…

Trustworthiness in neural networks is crucial for their deployment in critical applications, where reliability, confidence, and uncertainty play pivotal roles in decision-making. Traditional performance metrics such as accuracy and…

Machine Learning · Computer Science 2025-09-05 Koffi Ismael Ouattara , Ioannis Krontiris , Theo Dimitrakos , Frank Kargl

Classical state estimation algorithms rely on predefined target's state-space model, which complicates model derivation and limits adaptability when system dynamics change. Neural network based estimators offer a data-driven alternative,…

Signal Processing · Electrical Eng. & Systems 2025-10-01 Minxing Sun , Li Miao , Qingyu Shen , Yao Mao , Qiliang Bao

We build a general quantum state tomography framework that makes use of machine learning techniques to reconstruct quantum states from a given set of coincidence measurements. For a wide range of pure and mixed input states we demonstrate…

Quantum Physics · Physics 2020-06-09 Sanjaya Lohani , Brian T. Kirby , Michael Brodsky , Onur Danaci , Ryan T. Glasser

I propose quantum versions of the Ziv-Zakai bounds as alternatives to the widely used quantum Cram\'er-Rao bounds for quantum parameter estimation. From a simple form of the proposed bounds, I derive both a "Heisenberg" error limit that…

Quantum Physics · Physics 2012-06-07 Mankei Tsang

We design specific neural networks (NNs) for the identification of switching nonlinear systems in the state-space form, which explicitly model the switching behavior and address the inherent coupling between system parameters and switching…

Systems and Control · Electrical Eng. & Systems 2025-03-14 Yanxin Zhang , Chengpu Yu , Filippo Fabiani

The Koml\'os$\unicode{x2013}$Major$\unicode{x2013}$Tusn\'ady (KMT) inequality for partial sums is one of the most celebrated results in probability theory. Yet its practical application has been hindered by a lack of practical constants.…

Statistics Theory · Mathematics 2026-05-19 Haoyu Ye , Morgane Austern

Near-term quantum computers must protect fragile coherence against decoherence to deliver useful results. Catalytic quantum error correction (CQEC) addresses this challenge by amplifying residual coherence with a reusable catalyst,…

Quantum Physics · Physics 2026-05-11 Hikaru Wakaura

Interpretability techniques in NLP have mainly focused on understanding individual predictions using attention visualization or gradient-based saliency maps over tokens. We propose using k nearest neighbor (kNN) representations to identify…

Computation and Language · Computer Science 2020-10-20 Nazneen Fatema Rajani , Ben Krause , Wengpeng Yin , Tong Niu , Richard Socher , Caiming Xiong

A novel approach to the problem of partial state estimation of nonlinear systems is proposed. The main idea is to translate the state estimation problem into one of estimation of constant, unknown parameters related to the systems initial…

Systems and Control · Computer Science 2016-04-08 Ortega Romeo , Bobtsov Alexey , Pyrkin Anton , Aranovskiy Stanislav

Existing generalization theories of supervised learning typically take a holistic approach and provide bounds for the expected generalization over the whole data distribution, which implicitly assumes that the model generalizes similarly…

Machine Learning · Computer Science 2024-01-08 Firas Laakom , Yuheng Bu , Moncef Gabbouj