Related papers: Mathematical artificial data for operator learning

We present a framework for recovering/approximating unknown time-dependent partial differential equation (PDE) using its solution data. Instead of identifying the terms in the underlying PDE, we seek to approximate the evolution operator of…

During the past decade, metal additive manufacturing (MAM) has experienced significant developments and gained much attention due to its ability to fabricate complex parts, manufacture products with functionally graded materials, minimize…

Solving optimization problems in which functions are blackboxes and variables involve different types poses significant theoretical and algorithmic challenges. Nevertheless, such settings frequently occur in simulation-based engineering…

Neural operators have emerged as promising surrogate models for solving partial differential equations (PDEs), but struggle to generalise beyond training distributions and are often constrained to a fixed temporal discretisation. This work…

The rapid expansion of data from diverse sources has made anomaly detection (AD) increasingly essential for identifying unexpected observations that may signal system failures, security breaches, or fraud. As datasets become more complex…

Deep learning and deep architectures are emerging as the best machine learning methods so far in many practical applications such as reducing the dimensionality of data, image classification, speech recognition or object segmentation. In…

Modeling the dynamics of real-world physical systems is critical for spatiotemporal prediction tasks, but challenging when data is limited. The scarcity of real-world data and the difficulty in reproducing the data distribution hinder…

Unstructured grid data are essential for modelling complex geometries and dynamics in computational physics. Yet, their inherent irregularity presents significant challenges for conventional machine learning (ML) techniques. This paper…

Automatic machine learning (\AML) is a family of techniques to automate the process of training predictive models, aiming to both improve performance and make machine learning more accessible. While many recent works have focused on aspects…

The order/dimension of models derived on the basis of data is commonly restricted by the number of observations, or in the context of monitored systems, sensing nodes. This is particularly true for structural systems (e.g., civil or…

Real-world machine learning applications often face simultaneous covariate and semantic shifts, challenging traditional domain generalization and out-of-distribution (OOD) detection methods. We introduce Meta-learned Across Domain…

Synthetic data generation is an appealing tool for augmenting and enriching datasets, playing a crucial role in advancing artificial intelligence (AI) and machine learning (ML). Not only does synthetic data help build robust AI/ML datasets…

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…

Partial differential equations (PDEs) govern physical phenomena across the full range of scientific scales, yet their computational solution remains one of the defining challenges of modern science. This critical review examines two mature…

Contemporary machine learning paradigm excels in statistical data analysis, solving problems that classical AI couldn't. However, it faces key limitations, such as a lack of integration with planning, incomprehensible internal structure,…

The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…

In this era of digital information explosion, an abundance of data from numerous modalities is being generated as well as archived everyday. However, most problems associated with training Deep Neural Networks still revolve around lack of…

Supervised learning in function spaces is an emerging area of machine learning research with applications to the prediction of complex physical systems such as fluid flows, solid mechanics, and climate modeling. By directly learning maps…

Compared to physics-based computational manufacturing, data-driven models such as machine learning (ML) are alternative approaches to achieve smart manufacturing. However, the data-driven ML's "black box" nature has presented a challenge to…

Training neural operators to approximate mappings between infinite-dimensional function spaces often requires extensive datasets generated by either demanding experimental setups or computationally expensive numerical solvers. This…