Related papers: Q-Flow: Generative Modeling for Differential Equat…

This contribution reviews the parallel dynamics of Q-Ising neural networks for various architectures: extremely diluted asymmetric, layered feedforward, extremely diluted symmetric, and fully connected. Using a probabilistic signal-to-noise…

Quantum generative models exploit quantum superposition and entanglement to enhance learning efficiency for both classical and quantum data. Recently, inspired by classical diffusion frameworks, the quantum denoising diffusion probabilistic…

We introduce TensorFlow Quantum (TFQ), an open source library for the rapid prototyping of hybrid quantum-classical models for classical or quantum data. This framework offers high-level abstractions for the design and training of both…

Quantum machine learning (QML) based on Noisy Intermediate-Scale Quantum (NISQ) devices hinges on the optimal utilization of limited quantum resources. While gate-based QML models are user-friendly for software engineers, their expressivity…

We report the quantum computing of reacting flows by simulating the Hamiltonian dynamics. The scalar transport equation for reacting flows is transformed into a Hamiltonian system, mapping the dissipative and non-Hermitian problem in…

Recent progress in scientific machine learning (SciML) has opened up the possibility of training novel neural network architectures that solve complex partial differential equations (PDEs). Several (nearly data free) approaches have been…

Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…

The machine learning approaches are applied in the dynamical simulation of open quantum systems. The long short-term memory recurrent neural network (LSTM-RNN) models are used to simulate the long-time quantum dynamics, which are built…

A Normalizing Flow computes a bijective mapping from an arbitrary distribution to a predefined (e.g. normal) distribution. Such a flow can be used to address different tasks, e.g. anomaly detection, once such a mapping has been learned. In…

Open Quantum Walks (OQW) are a type of quantum walk governed by the system's interaction with its environment. We explore the time evolution and the limit behavior of the OQW framework for Quantum Computation and show how we can represent…

We develop a general mathematical framework to analyze scaling regimes and derive explicit analytic solutions for gradient flow (GF) in large learning problems. Our key innovation is a formal power series expansion of the loss evolution,…

Computational Fluid Dynamics (CFD) is central to science and engineering, but faces severe scalability challenges, especially in high-dimensional, multiscale, and turbulent regimes. Traditional numerical methods often become prohibitively…

This paper proposes the TrafficFlowGAN, a physics-informed flow based generative adversarial network (GAN), for uncertainty quantification (UQ) of dynamical systems. TrafficFlowGAN adopts a normalizing flow model as the generator to…

Quantum machine learning (QML) seeks to exploit the intrinsic properties of quantum mechanical systems, including superposition, coherence, and quantum entanglement for classical data processing. However, due to the exponential growth of…

Normalizing flow is a generative modeling approach with efficient sampling. However, Flow-based models suffer two issues: 1) If the target distribution is manifold, due to the unmatch between the dimensions of the latent target distribution…

The modeling of multi-phase flow is very challenging, given the range of scales as well as the diversity of flow regimes that one encounters in this context. We revisit the discrete equation method (DEM) for two-phase flow in the absence of…

Normalizing flows are deep generative models that enable efficient likelihood estimation and sampling through invertible transformations. A key challenge is to design linear layers that enhance expressiveness while maintaining efficient…

We develop general purpose algorithms for computing and utilizing both the Dyson series and Magnus expansion, with the goal of facilitating numerical perturbative studies of quantum dynamics. To enable broad applications to models with…

We present several ideas in direction of physical interpretation of $q$- and $f$-oscillators as a nonlinear oscillators. First we show that an arbitrary one dimensional integrable system in action-angle variables can be naturally…

Diffusion models have demonstrated remarkable success in image generation, but they are computationally intensive and time-consuming to train. In this paper, we introduce a novel diffusion model that benefits from quantum computing…