相关论文: CUQIpy: II. Computational uncertainty quantificati…

State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we…

We introduce the Suggest-and-Improve framework for general nonconvex quadratically constrained quadratic programs (QCQPs). Using this framework, we generalize a number of known methods and provide heuristics to get approximate solutions to…

Optimal uncertainty quantification (OUQ) is a framework for numerical extreme-case analysis of stochastic systems with imperfect knowledge of the underlying probability distribution. This paper presents sufficient conditions under which an…

In principle, deep learning models trained on medical time-series, including wearable photoplethysmography (PPG) sensor data, can provide a means to continuously monitor physiological parameters outside of clinical settings. However, there…

Distribution estimation for noisy data via density deconvolution is a notoriously difficult problem for typical noise distributions like Gaussian. We develop a density deconvolution estimator based on quadratic programming (QP) that can…

Quantum Physics-Informed Neural Networks (QPINNs) integrate quantum computing and machine learning to impose physical biases on the output of a quantum neural network, aiming to either solve or discover differential equations. The approach…

Quantum machine learning seeks to leverage quantum computers to improve upon classical machine learning algorithms. Currently, robust uncertainty quantification methods remain underdeveloped in the quantum domain, despite the critical need…

We consider the Bayesian approach to linear inverse problems when the underlying operator depends on an unknown parameter. Allowing for finite dimensional as well as infinite dimensional parameters, the theory covers several models with…

Uncertainty Quantification (UQ) is a promising approach to improve model reliability, yet quantifying the uncertainty of Large Language Models (LLMs) is non-trivial. In this work, we establish a connection between the uncertainty of LLMs…

Nonlinear Optical Spectroscopy is a well-developed field with theoretical and experimental advances that have aided multiple fields including chemistry, biology and physics. However, accurate quantum dynamical simulations based on model…

A template-based generic programming approach was presented in a previous paper that separates the development effort of programming a physical model from that of computing additional quantities, such as derivatives, needed for embedded…

Modern control theory provides us with a spectrum of methods for studying the interconnection of dynamic systems using input-output properties of the interconnected subsystems. Perhaps the most advanced framework for such input-output…

Well-established methods for the solution of stochastic partial differential equations (SPDEs) typically struggle in problems with high-dimensional inputs/outputs. Such difficulties are only amplified in large-scale applications where even…

We introduce GenAI4UQ, a software package for inverse uncertainty quantification in model calibration, parameter estimation, and ensemble forecasting in scientific applications. GenAI4UQ leverages a generative artificial intelligence (AI)…

Uncertainty Quantification (UQ) presents a pivotal challenge in the field of Artificial Intelligence (AI), profoundly impacting decision-making, risk assessment and model reliability. In this paper, we introduce Credal and Interval Deep…

Partial differential equations (PDEs) are widely used across the physical and computational sciences. Decades of research and engineering went into designing fast iterative solution methods. Existing solvers are general purpose, but may be…

Accurate estimation of uncertainty in deep learning is critical for deploying models in high-stakes domains such as medical diagnosis and autonomous decision-making, where overconfident predictions can lead to harmful outcomes. In practice,…

Nonlinear programming is explicitly analyzed via a novel perspective/method and from a bottom-up manner. The philosophy is based on the recent findings on convex quadratic equation (CQE), which help clarify a geometric interpretation that…

The combination of machine learning and physical laws has shown immense potential for solving scientific problems driven by partial differential equations (PDEs) with the promise of fast inference, zero-shot generalisation, and the ability…