Related papers: Active Learning for Neural PDE Solvers

Training a quantum machine learning model generally requires a large labeled dataset, which incurs high labeling and computational costs. To reduce such costs, a selective training strategy, called active learning (AL), chooses only a…

Behavioral models are the key enablers for behavioral analysis of Software Product Lines (SPL), including testing and model checking. Active model learning comes to the rescue when family behavioral models are non-existent or outdated. A…

Learning solution operators for differential equations with neural networks has shown great potential in scientific computing, but ensuring their stability under input perturbations remains a critical challenge. This paper presents a robust…

Many problems in science and engineering can be represented by a set of partial differential equations (PDEs) through mathematical modeling. Mechanism-based computation following PDEs has long been an essential paradigm for studying topics…

When we can not assume a large amount of annotated data , active learning is a good strategy. It consists in learning a model on a small amount of annotated data (annotation budget) and in choosing the best set of points to annotate in…

Nonlinear PDE solvers require fine space-time discretizations and local linearizations, leading to high memory cost and slow runtimes. Neural operators such as FNOs and DeepONets offer fast single-shot inference by learning…

Active Learning (AL) is a family of machine learning (ML) algorithms that predates the current era of artificial intelligence. Unlike traditional approaches that require labeled samples for training, AL iteratively selects unlabeled samples…

In recent years, data-driven methods have been developed to learn dynamical systems and partial differential equations (PDE). The goal of such work is discovering unknown physics and the corresponding equations. However, prior to achieving…

Even though Active Learning (AL) is widely studied, it is rarely applied in contexts outside its own scientific literature. We posit that the reason for this is AL's high computational cost coupled with the comparatively small lifts it is…

Neural networks can be used to learn the solution of partial differential equations (PDEs) on arbitrary domains without requiring a computational mesh. Common approaches integrate differential operators in training neural networks using a…

Across numerous applications, forecasting relies on numerical solvers for partial differential equations (PDEs). Although the use of deep-learning techniques has been proposed, actual applications have been restricted by the fact the…

Developing efficient numerical algorithms for the solution of high dimensional random Partial Differential Equations (PDEs) has been a challenging task due to the well-known curse of dimensionality. We present a new solution framework for…

High-performance scientific simulations, important for comprehension of complex systems, encounter computational challenges especially when exploring extensive parameter spaces. There has been an increasing interest in developing deep…

Deep Operator Networks are emerging as fundamental tools among various neural network types to learn mappings between function spaces, and have recently gained attention due to their ability to approximate nonlinear operators. In…

Mainstream numerical Partial Differential Equation (PDE) solvers require discretizing the physical domain using a mesh. Mesh movement methods aim to improve the accuracy of the numerical solution by increasing mesh resolution where the…

Recent advances in scientific machine learning (SciML) have enabled neural operators (NOs) to serve as powerful surrogates for modeling the dynamic evolution of physical systems governed by partial differential equations (PDEs). While…

Deep Active Learning (DAL) aims to reduce labeling costs in neural-network training by prioritizing the most informative unlabeled samples for annotation. Beyond selecting which samples to label, several DAL approaches further enhance data…

Active learning (AL) seeks to reduce annotation costs by selecting the most informative samples for labeling, making it particularly valuable in resource-constrained settings. However, traditional evaluation methods, which focus solely on…

The costly human effort required to prepare the training data of machine learning (ML) models hinders their practical development and usage in software engineering (ML4Code), especially for those with limited budgets. Therefore, efficiently…

Active learning (AL) is a human-and-model-in-the-loop paradigm that iteratively selects informative unlabeled data for human annotation, aiming to improve over random sampling. However, performing AL experiments with human annotations…