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Neural networks predictions are unreliable when the input sample is out of the training distribution or corrupted by noise. Being able to detect such failures automatically is fundamental to integrate deep learning algorithms into robotics.…
In Reinforcement Learning (RL), agents aim at maximizing cumulative rewards in a given environment. During the learning process, RL agents face the dilemma of exploitation and exploration: leveraging existing knowledge to acquire rewards or…
We propose a novel data-lean operator learning algorithm, the Reduced Basis Neural Operator (ReBaNO), to solve a group of PDEs with multiple distinct inputs. Inspired by the Reduced Basis Method and the recently introduced Generative…
We introduce a novel deep operator network (DeepONet) framework that incorporates generalised variational inference (GVI) using R\'enyi's $\alpha$-divergence to learn complex operators while quantifying uncertainty. By incorporating…
This paper explores Neural Operators to predict turbulent flows, focusing on the Fourier Neural Operator (FNO) model. It aims to develop reduced-order/surrogate models for turbulent flow simulations using Machine Learning. Different model…
Neural Operators (NOs) are machine learning models designed to solve partial differential equations (PDEs) by learning to map between function spaces. Neural Operators such as the Deep Operator Network (DeepONet) and the Fourier Neural…
Prediction deviations of different uncertainties have varying impacts on downstream decision-making. Improving the prediction accuracy of critical uncertainties with significant impacts on decision-making quality yields better optimization…
Regularization plays a pivotal role in integrating prior information into inverse problems. While many deep learning methods have been proposed to solve inverse problems, determining where to apply regularization remains a crucial…
Unsupervised learning with functional data is an emerging paradigm of machine learning research with applications to computer vision, climate modeling and physical systems. A natural way of modeling functional data is by learning operators…
This paper introduces the Kernel Neural Operator (KNO), a provably convergent operator-learning architecture that utilizes compositions of deep kernel-based integral operators for function-space approximation of operators (maps from…
Neural operators, which can act as implicit solution operators of hidden governing equations, have recently become popular tools for learning the responses of complex real-world physical systems. Nevertheless, most neural operator…
Pretraining methods gain increasing attraction recently for solving PDEs with neural operators. It alleviates the data scarcity problem encountered by neural operator learning when solving single PDE via training on large-scale datasets…
This paper proposes a new data-driven method for the reliable prediction of power system post-fault trajectories. The proposed method is based on the fundamentally new concept of Deep Operator Networks (DeepONets). Compared to traditional…
Physics-Informed Neural Operators provide efficient, high-fidelity simulations for systems governed by partial differential equations (PDEs). However, most existing studies focus only on multi-scale, multi-physics systems within a single…
Signal denoising is a key preprocessing step for many applications, as the performance of a learning task is closely related to the quality of the input data. In this paper, we apply a signal processing based deep neural network…
Simulating and controlling physical systems described by partial differential equations (PDEs) are crucial tasks across science and engineering. Recently, diffusion generative models have emerged as a competitive class of methods for these…
The success of building a high-resolution velocity model using machine learning is hampered by generalization limitations that often limit the success of the approach on field data. This is especially true when relying on neural operators…
The predictive accuracy of operator learning frameworks depends on the quality and quantity of available training data (input-output function pairs), often requiring substantial amounts of high-fidelity data, which can be challenging to…
Solving parametric partial differential equations (PDEs) and associated PDE-based, inverse problems is a central task in engineering and physics, yet existing neural operator methods struggle with high-dimensional, discontinuous inputs and…
Parametric differential equations of the form du/dt = f(u, x, t, p) are fundamental in science and engineering. While deep learning frameworks such as the Fourier Neural Operator (FNO) can efficiently approximate solutions, they struggle…