Related papers: Operator Learning Renormalization Group
We present incomplete gamma kernels, a generalization of Locally Optimal Projection (LOP) operators. In particular, we reveal the relation of the classical localized $ L_1 $ estimator, used in the LOP operator for point cloud denoising, to…
We present a unified framework for renormalization group methods, including Wilson's numerical renormalization group (NRG) and White's density-matrix renormalization group (DMRG), within the language of matrix product states. This allows…
Methods for electronic structure based on Gaussian and molecular orbital discretizations offer a well established, compact representation that forms much of the foundation of correlated quantum chemistry calculations on both classical and…
The density matrix renormalization group (DMRG) has been extended to study quantum phase transitions on random graphs of fixed connectivity. As a relevant example, we have analysed the random Ising model in a transverse field. If the…
Much recent work has addressed the solution of a family of partial differential equations by computing the inverse operator map between the input and solution space. Toward this end, we incorporate function-valued reproducing kernel Hilbert…
The advancement of foundation models fosters new initiatives for policy learning in achieving safe and efficient autonomous driving. However, a critical bottleneck lies in the manual engineering of reward functions and training curricula…
We propose a data-driven and machine-learning-based approach to compute non-Galerkin coarse-grid operators in algebraic multigrid (AMG) methods, addressing the well-known issue of increasing operator complexity. Guided by the AMG theory on…
Modern techniques of the renormalization group (RG) combined with effective field theory (EFT) methods are revolutionizing nuclear many-body physics. In these lectures we will explore the motivation for RG in low-energy nuclear systems and…
The Wilsonian renormalization group (RG) method is applied to finite temperature systems for the study of non-perturbative methods in the field theory. We choose the O(N) linear sigma model as the first step. Under the local potential…
Understanding the dynamics of nonequilibrium quantum many-body systems is an important research topic in a wide range of fields across condensed matter physics, quantum optics, and high-energy physics. However, numerical studies of…
The logarithm-determinant is an widely-present operation in many areas of physics and computer science. Derivatives of the logarithm-determinant compute physically relevant quantities in statistical physics models, quantum field theories,…
SLAM (Simultaneous Localisation and Mapping) is a crucial component for robotic systems, providing a map of an environment, the current location and previous trajectory of a robot. While 3D LiDAR SLAM has received notable improvements in…
The ordered weighted $\ell_1$ norm (OWL) was recently proposed, with two different motivations: its good statistical properties as a sparsity promoting regularizer; the fact that it generalizes the so-called {\it octagonal shrinkage and…
Large Language Model (LLM)-based multi-agent systems show promise for automating real-world tasks but struggle to transfer across domains due to their domain-specific nature. Current approaches face two critical shortcomings: they require…
We propose an iterative algorithm to simulate the dynamics generated by any $n$-qubit Hamiltonian. The simulation entails decomposing the unitary time evolution operator $U$ (unitary) into a product of different time-step unitaries. The…
An efficient numerical method is developed using the matrix product formalism for computing the properties at finite energy densities in one-dimensional (1D) many-body localized (MBL) systems. Arguing that any efficient (possibly quantum)…
We introduce a simple, exactly solvable strong-randomness renormalization group (RG) model for the many-body localization (MBL) transition in one dimension. Our approach relies on a family of RG flows parametrized by the asymmetry between…
Quantum learning encounters fundamental challenges when estimating non-linear properties, owing to the inherent linearity of quantum mechanics. Although recent advances in single-copy randomized measurement protocols have achieved optimal…
We ask whether the Hamiltonian, interaction geometry, and symmetries of a quantum many-body system can be inferred from a few low-lying eigenstates without knowing which sites interact with each other. Directly solving the eigenvalue…
We propose a computational framework for replacing the repeated numerical solution of differential Riccati equations in finite-horizon Linear Quadratic Regulator (LQR) problems by a learned operator surrogate. Instead of solving a nonlinear…