Related papers: Learning Hamiltonian flows from numerical integrat…
Quantum process characterization is a fundamental task in quantum information processing, yet conventional methods, such as quantum process tomography, require prohibitive resources and lack scalability. Here, we introduce an efficient…
We propose a novel framework based on neural network that reformulates classical mechanics as an operator learning problem. A machine directly maps a potential function to its corresponding trajectory in phase space without solving the…
Hamiltonian Monte Carlo (HMC) has been progressively incorporated within the statistician's toolbox as an alternative sampling method in settings when standard Metropolis-Hastings is inefficient. HMC generates a Markov chain on an augmented…
The process of transforming observed data into predictive mathematical models of the physical world has always been paramount in science and engineering. Although data is currently being collected at an ever-increasing pace, devising…
Sampling from an unnormalized probability distribution is a fundamental problem in machine learning with applications including Bayesian modeling, latent factor inference, and energy-based model training. After decades of research,…
We propose a methodology to sample from time-integrated stochastic bridges, namely random variables defined as $\int_{t_1}^{t_2} f(Y(t))dt$ conditioned on $Y(t_1)\!=\!a$ and $Y(t_2)\!=\!b$, with $a,b\in R$. The Stochastic Collocation Monte…
The Hamiltonian of a quantum system governs the dynamics of the system via the Schrodinger equation. In this paper, the Hamiltonian is reconstructed in the Pauli basis using measurables on random states forming a time series dataset. The…
We use a data-driven approach to model a three-dimensional turbulent flow using cutting-edge Deep Learning techniques. The deep learning framework incorporates physical constraints on the flow, such as preserving incompressibility and…
The dynamics of information diffusion within graphs is a critical open issue that heavily influences graph representation learning, especially when considering long-range propagation. This calls for principled approaches that control and…
Markov Chain Monte Carlo methods have revolutionised mathematical computation and enabled statistical inference within many previously intractable models. In this context, Hamiltonian dynamics have been proposed as an efficient way of…
We present a method for learning neural representations of flow maps from time-varying vector field data. The flow map is pervasive within the area of flow visualization, as it is foundational to numerous visualization techniques, e.g.…
We train a small message-passing graph neural network to predict Hamiltonian cycles on Erd\H{o}s-R\'enyi random graphs in a critical regime. It outperforms existing hand-crafted heuristics after about 2.5 hours of training on a single GPU.…
A framework for statistical-mechanical analysis of quantum Hamiltonians is introduced. The approach is based upon a gradient flow equation in the space of Hamiltonians such that the eigenvectors of the initial Hamiltonian evolve toward…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
We propose an efficient quantum algorithm for simulating the dynamics of general Hamiltonian systems. Our technique is based on a power series expansion of the time-evolution operator in its off-diagonal terms. The expansion decouples the…
The Hamiltonian Monte Carlo (HMC) sampling algorithm exploits Hamiltonian dynamics to construct efficient Markov Chain Monte Carlo (MCMC), which has become increasingly popular in machine learning and statistics. Since HMC uses the gradient…
Flow-based generative models achieve state-of-the-art sample quality, but require the expensive solution of a differential equation at inference time. Flow map models, commonly known as consistency models, encompass many recent efforts to…
Physics-informed deep learning have recently emerged as an effective tool for leveraging both observational data and available physical laws. Physics-informed neural networks (PINNs) and deep operator networks (DeepONets) are two such…
We present a framework for modeling multi-scale processes, and study its performance in the context of streamflow forecasting in hydrology. Specifically, we propose a novel hierarchical recurrent neural architecture that factorizes the…
We propose a hybrid Monte Carlo (HMC) technique applicable to high-dimensional multivariate normal distributions that effectively samples along chaotic trajectories. The method is predicated on the freedom of choice of the HMC momentum…