Related papers: Operator learning on domain boundary through combi…

In this paper, we introduce Masked Anomaly Detection (MAD), a general self-supervised learning task for multivariate time series anomaly detection. With the increasing availability of sensor data from industrial systems, being able to…

While many problems in machine learning focus on learning mappings between finite-dimensional spaces, scientific applications require approximating mappings between function spaces, i.e., operators. We study the problem of learning…

The Monte Carlo-type Neural Operator (MCNO) introduces a framework for learning solution operators of one-dimensional partial differential equations (PDEs) by directly learning the kernel function and approximating the associated integral…

We propose a hybrid solver that fuses the dimensionality-reduction strengths of the Method of Lines (MOL) with the flexibility of Physics-Informed Neural Networks (PINNs). Instead of approximating spatial derivatives with fixed…

Solving partial differential equations (PDEs) is a required step in the simulation of natural and engineering systems. The associated computational costs significantly increase when exploring various scenarios, such as changes in initial or…

Operator learning is a rising field of scientific computing where inputs or outputs of a machine learning model are functions defined in infinite-dimensional spaces. In this paper, we introduce NEON (Neural Epistemic Operator Networks), an…

Finding tight bounds on the optimal solution is a critical element of practical solution methods for discrete optimization problems. In the last decade, decision diagrams (DDs) have brought a new perspective on obtaining upper and lower…

In this paper, we propose Neumann Series Neural Operator (NSNO) to learn the solution operator of Helmholtz equation from inhomogeneity coefficients and source terms to solutions. Helmholtz equation is a crucial partial differential…

Performing anomaly detection in hybrid systems is a challenging task since it requires analysis of timing behavior and mutual dependencies of both discrete and continuous signals. Typically, it requires modeling system behavior, which is…

Depth prediction is a critical problem in robotics applications especially autonomous driving. Generally, depth prediction based on binocular stereo matching and fusion of monocular image and laser point cloud are two mainstream methods.…

Neural operators are a new type of models that can map between function spaces, allowing trained models to emulate the solution operators of partial differential equations (PDEs). This paper proposes a multigrid Fourier neural operator…

Deep Neural Networks (DNNs) have demonstrated exceptional recognition capabilities in traditional computer vision (CV) tasks. However, existing CV models often suffer a significant decrease in accuracy when confronted with…

Neural operators (NOs) are designed to learn maps between infinite-dimensional function spaces. We propose a novel reframing of their use. By introducing an auxiliary base-space, any finite-dimensional function can be viewed as an operator…

Neural ordinary differential equations (NODEs), one of the most influential works of the differential equation-based deep learning, are to continuously generalize residual networks and opened a new field. They are currently utilized for…

Machine learning has witnessed substantial growth, leading to the development of advanced artificial intelligence models crafted to address a wide range of real-world challenges spanning various domains, such as computer vision, natural…

In this study, we propose a novel approach, termed boundary integrated neural networks (BINNs), for analyzing in-plane crack problems within the framework of linear elastic fracture mechanics. The proposed approach integrates artificial…

We study Consensus-Based Optimization (CBO) for two-layer neural network training. We compare the performance of CBO against Adam on two test cases and demonstrate how a hybrid approach, combining CBO with Adam, provides faster convergence…

Solving inverse problems governed by partial differential equations (PDEs) is central to science and engineering, yet remains challenging when measurements are sparse, noisy, or when the underlying coefficients are high-dimensional or…

Neural operators have emerged as powerful tools for learning solution operators of partial differential equations. However, in time-dependent problems, standard training strategies such as teacher forcing introduce a mismatch between…

Deep Operator Networks (DeepONets) and their physics-informed variants have shown significant promise in learning mappings between function spaces of partial differential equations, enhancing the generalization of traditional neural…