Related papers: Introducing Interval Neural Networks for Uncertain…

Reliable uncertainty quantification (UQ) is essential for developing machine-learned interatomic potentials (MLIPs) in predictive atomistic simulations. Conformal prediction (CP) is a statistical framework that constructs prediction…

Scientific machine learning for inferring dynamical systems combines data-driven modeling, physics-based modeling, and empirical knowledge. It plays an essential role in engineering design and digital twinning. In this work, we primarily…

The modeling and simulation of high-dimensional multiscale systems is a critical challenge across all areas of science and engineering. It is broadly believed that even with today's computer advances resolving all spatiotemporal scales…

The steady incompressible Navier--Stokes equations pose significant computational challenges due to their nonlinear convective terms and pressure--velocity coupling. Physics-informed neural networks (PINNs) provide a mesh-free framework for…

We propose a numerical method for discovering unknown parameterized dynamical systems by using observational data of the state variables. Our method is built upon and extends the recent work of discovering unknown dynamical systems, in…

This paper considers the generation of prediction intervals (PIs) by neural networks for quantifying uncertainty in regression tasks. It is axiomatic that high-quality PIs should be as narrow as possible, whilst capturing a specified…

Large language models (LLMs) have transformed natural language processing, but their reliable deployment requires effective uncertainty quantification (UQ). Existing UQ methods are often heuristic and lack a probabilistic interpretation.…

Integrating domain knowledge into neural networks is a central challenge in scientific machine learning. Three paradigms have emerged -- data-driven (Neural Ordinary Differential Equations, NODEs), soft-constrained (Physics-Informed Neural…

Neural Linear Models (NLM) are deep Bayesian models that produce predictive uncertainty by learning features from the data and then performing Bayesian linear regression over these features. Despite their popularity, few works have focused…

Large Language Models (LLMs) have demonstrated remarkable capabilities across various tasks due to large training datasets and powerful transformer architecture. However, the reliability of responses from LLMs remains a question.…

Large Language Diffusion Models (LLDMs) are emerging as an alternative to autoregressive models, offering faster inference through higher parallelism. Similar to autoregressive LLMs, they remain prone to hallucinations, making reliable…

Deep Neural Networks (DNNs) have demonstrated remarkable performance across various domains, including computer vision and natural language processing. However, they often struggle to accurately quantify the uncertainty of their…

Reliable uncertainty estimation has become a crucial requirement for the industrial deployment of deep learning algorithms, particularly in high-risk applications such as autonomous driving and medical diagnosis. However, mainstream…

Deploying machine learning-based intrusion detection systems (IDSs) on hardware devices is challenging due to their limited computational resources, power consumption, and network connectivity. Hence, there is a significant need for robust,…

The ability to accurately model interatomic interactions in large-scale systems is fundamental to understanding a wide range of physical and chemical phenomena, from drug-protein binding to the behavior of next-generation materials. While…

The paper presents an efficient and robust data-driven deep learning (DL) computational framework developed for linear continuum elasticity problems. The methodology is based on the fundamentals of the Physics Informed Neural Networks…

This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Given a neural network, we use an existing…

This work presents novel extensions for combining two frameworks for quantifying both aleatoric (i.e., irreducible) and epistemic (i.e., reducible) sources of uncertainties in the modeling of engineered systems. The data-consistent (DC)…

Quantifying uncertainties for machine learning (ML) models is a foundational challenge in modern data analysis. This challenge is compounded by at least two key aspects of the field: (a) inconsistent terminology surrounding uncertainty and…

We present the application of a class of deep learning, known as Physics Informed Neural Networks (PINN), to learning and discovery in solid mechanics. We explain how to incorporate the momentum balance and constitutive relations into PINN,…