Related papers: UFO: A Domain-Unification-Free Operator Framework …

Neural operator architectures approximate operators between infinite-dimensional Banach spaces of functions. They are gaining increased attention in computational science and engineering, due to their potential both to accelerate…

The Userfault Object (UFO) framework explores avenues of cooperating with the operating system to use memory in non-traditional ways. We implement a framework that employs the Linux kernel's userfault mechanism to fill the contents of…

Learning maps between function spaces with a strong inductive bias is a central challenge in soft computing, especially when training data are scarce and standard deep architectures overfit. We introduce a \emph{neural integral operator}…

gUFO is a lightweight implementation of the Unified Foundational Ontology (UFO) suitable for Semantic Web OWL 2 DL applications. UFO is a mature foundational ontology with a rich axiomatization and that has been employed in a significant…

This work presents UNO, a unified monocular visual odometry framework that enables robust and adaptable pose estimation across diverse environments, platforms, and motion patterns. Unlike traditional methods that rely on deployment-specific…

The classical development of neural networks has primarily focused on learning mappings between finite dimensional Euclidean spaces or finite sets. We propose a generalization of neural networks to learn operators, termed neural operators,…

We introduce an abstract neural flow framework for neural networks and neural operators. The framework contains two continuous-depth models, namely neural flows with composition and separation structures, and covers both finite-dimensional…

Partial differential equations (PDEs) govern a wide variety of dynamical processes in science and engineering, yet obtaining their numerical solutions often requires high-resolution discretizations and repeated evaluations of complex…

Neural operators aim to approximate the solution operator of a system of differential equations purely from data. They have shown immense success in modeling complex dynamical systems across various domains. However, the occurrence of…

Neural operators generalize classical neural networks to maps between infinite-dimensional spaces, e.g., function spaces. Prior works on neural operators proposed a series of novel methods to learn such maps and demonstrated unprecedented…

Neural operators have become increasingly popular in solving \textit{partial differential equations} (PDEs) due to their superior capability to capture intricate mappings between function spaces over complex domains. However, the…

We present a generalized version of the discretization-invariant neural operator and prove that the network is a universal approximation in the operator sense. Moreover, by incorporating additional terms in the architecture, we establish a…

Phase separation in binary mixtures, governed by the Cahn-Hilliard equation, plays a central role in interfacial dynamics across materials science and soft matter. While numerical solvers are accurate, they are often computationally…

Robust uncertainty quantification (UQ) remains a critical barrier to the safe deployment of deep learning in real-time virtual sensing, particularly in high-stakes domains where sparse, noisy, or non-collocated sensor data are the norm. We…

Many people search for foreground objects to use when editing images. While existing methods can retrieve candidates to aid in this, they are constrained to returning objects that belong to a pre-specified semantic class. We instead propose…

Domain shift happens in cross-domain scenarios commonly because of the wide gaps between different domains: when applying a deep learning model well-trained in one domain to another target domain, the model usually performs poorly. To…

In recent years, using a network of autonomous and cooperative unmanned aerial vehicles (UAVs) without command and communication from the ground station has become more imperative, in particular in search-and-rescue operations, disaster…

In scientific and engineering applications, solving partial differential equations (PDEs) across various parameters and domains normally relies on resource-intensive numerical methods. Neural operators based on deep learning offered a…

Many machine learning algorithms can be interpreted as procedures for estimating functions defined on the data distribution. In this paper we present a conceptual framework that formulates a wide range of learning problems as variational…

Obstacle avoidance for small unmanned aircraft is vital for the safety of future urban air mobility (UAM) and Unmanned Aircraft System (UAS) Traffic Management (UTM). There are many techniques for real-time robust drone guidance, but many…