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We present Neural Quantile Estimation (NQE), a novel Simulation-Based Inference (SBI) method based on conditional quantile regression. NQE autoregressively learns individual one dimensional quantiles for each posterior dimension,…
In the NISQ (Noisy intermediate-scale quantum) area, Quantum computers can be utilized for deep learning by treating variational quantum circuits as neural network models. This can be achieved by first encoding the input data onto quantum…
The use of deep learning has successfully solved several problems in the field of medical imaging. Deep learning has been applied to the CT denoising problem successfully. However, the use of deep learning requires large amounts of data to…
Quantum many-body problems are central to various scientific disciplines, yet their ground-state properties are intrinsically challenging to estimate. Recent advances in deep learning (DL) offer potential solutions in this field,…
New quantum computing architectures consider integrating qubits as sensors to provide actionable information useful for decoherence mitigation on neighboring data qubits, but little work has addressed how such schemes may be efficiently…
Neural Ordinary Differential Equations (NODEs), a framework of continuous-depth neural networks, have been widely applied, showing exceptional efficacy in coping with some representative datasets. Recently, an augmented framework has been…
(Partial) differential equations (PDEs) are fundamental tools for describing natural phenomena, making their solution crucial in science and engineering. While traditional methods, such as the finite element method, provide reliable…
In this paper, we propose and study neural network based methods for solutions of high-dimensional quadratic porous medium equation (QPME). Three variational formulations of this nonlinear PDE are presented: a strong formulation and two…
Hyperspectral sensing provides rich spectral information for scene understanding in urban driving, but its high dimensionality poses challenges for interpretation and efficient learning. We introduce Learnable Quantum Efficiency (LQE), a…
Solving parametric Partial Differential Equations (PDEs) for a broad range of parameters is a critical challenge in scientific computing. To this end, neural operators, which \textcolor{black}{predicts the PDE solution with variable PDE…
Scientific Machine Learning (SciML) is concerned with the development of learned emulators of physical systems governed by partial differential equations (PDE). In application domains such as weather forecasting, molecular dynamics, and…
Finding efficient decoders for quantum error correcting codes adapted to realistic experimental noise in fault-tolerant devices represents a significant challenge. In this paper we introduce several decoding algorithms complemented by deep…
Partial Differential Equations (PDEs) are central to science and engineering. Since solving them is computationally expensive, a lot of effort has been put into approximating their solution operator via both traditional and recently…
Objective: We propose a method for the reconstruction of parameter-maps in Quantitative Magnetic Resonance Imaging (QMRI). Methods: Because different quantitative parameter-maps differ from each other in terms of local features, we propose…
Classical machine learning often struggles with complex, high-dimensional data. Quantum machine learning offers a potential solution, promising more efficient processing. The quantum convolutional neural network (QCNN), a hybrid algorithm,…
Neural Stochastic Differential Equations (NSDEs) model the drift and diffusion functions of a stochastic process as neural networks. While NSDEs are known to make accurate predictions, their uncertainty quantification properties have been…
We propose quadratic residual networks (QRes) as a new type of parameter-efficient neural network architecture, by adding a quadratic residual term to the weighted sum of inputs before applying activation functions. With sufficiently high…
In contexts where relevant problems can easily attain configuration spaces of enormous sizes, solving Linear Differential Equations (LDEs) can become a hard achievement for classical computers; on the other hand, the rise of quantum…
Quantum Amplitude Estimation (QAE) -- a technique by which the amplitude of a given quantum state can be estimated with quadratically fewer queries than by standard sampling -- is a key sub-routine in several important quantum algorithms,…
Quantum computers have been proposed as a solution for efficiently solving non-linear differential equations (DEs), a fundamental task across diverse technological and scientific domains. However, a crucial milestone in this regard is to…