Related papers: IKNO: Infinite-order Kernel Neural Operators
We propose an Indirect Quantum Approximate Optimization Algorithm (referred to as IQAOA) where the Quantum Alternating Operator Ansatz takes into consideration a general parameterized family of unitary operators to efficiently model the…
Quantum kernels hold great promise for offering computational advantages over classical learners, with the effectiveness of these kernels closely tied to the design of the quantum feature map. However, the challenge of designing effective…
A plentitude of applications in scientific computing requires the approximation of mappings between Banach spaces. Recently introduced Fourier Neural Operator (FNO) and Deep Operator Network (DeepONet) can provide this functionality. For…
This paper introduces HyperNOs, a PyTorch library designed to streamline and automate the process of exploring neural operators, with a special focus on hyperparameter optimization for comprehensive and exhaustive exploration. Indeed,…
Neural operators have emerged as powerful tools for learning nonlinear mappings between function spaces, enabling real-time prediction of complex dynamics in diverse scientific and engineering applications. With their growing adoption in…
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
Neural ODEs are increasingly used as continuous-time models for scientific and sensor data, but unconstrained neural ODEs can drift and violate domain invariants (e.g., conservation laws), yielding physically implausible solutions. In turn,…
Deep neural networks, despite their success in numerous applications, often function without established theoretical foundations. In this paper, we bridge this gap by drawing parallels between deep learning and classical numerical analysis.…
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…
Neural operators, such as Fourier Neural Operators (FNO), form a principled approach for learning solution operators for PDEs and other mappings between function spaces. However, many real-world problems require high-resolution training…
We implement an all-optical setup demonstrating kernel-based quantum machine learning for two-dimensional classification problems. In this hybrid approach, kernel evaluations are outsourced to projective measurements on suitably designed…
Neural operators are capable of capturing nonlinear mappings between infinite-dimensional functional spaces, offering a data-driven approach to modeling complex functional relationships in classical density functional theory (cDFT). In this…
A wide range of scientific problems, such as those described by continuous-time dynamical systems and partial differential equations (PDEs), are naturally formulated on function spaces. While function spaces are typically…
Improved performance in higher-order spectral density estimation is achieved using a general class of infinite-order kernels. These estimates are asymptotically less biased but with the same order of variance as compared to the classical…
Kernel methods provide a principled way to perform non linear, nonparametric learning. They rely on solid functional analytic foundations and enjoy optimal statistical properties. However, at least in their basic form, they have limited…
We propose an extended Fourier neural operator (FNO) architecture for learning state and linear quadratic additive optimal control of systems governed by partial differential equations. Using the Ehrenpreis-Palamodov fundamental principle,…
This research introduces an improved framework for constructing matrix product operators (MPOs) and tree tensor network operators (TTNOs), crucial tools in quantum simulations. A given (Hamiltonian) operator typically has a known symbolic…
This article presents an input convex neural network architecture using Kolmogorov-Arnold networks (ICKAN). Two specific networks are presented: the first is based on a low-order, linear-by-part, representation of functions, and a universal…
In this paper, we considered the problem of the simultaneous approximation of a function and its derivatives by means of the well-known neural network (NN) operators activated by sigmoidal function. Other than a uniform convergence theorem…
The end-to-end neural combinatorial optimization (NCO) method shows promising performance in solving complex combinatorial optimization problems without the need for expert design. However, existing methods struggle with large-scale…