arXiv subjects

Patrick Cook

Publications and source records attributed to Patrick Cook.

5 recordsLinked to original sources

arXiv2026

Parametric Matrix Models for Emulation in Nuclear and Many-Body Physics

Progress in nuclear and many-body physics today is predicated on the ability to solve large-scale, strongly correlated quantum many-body problems. As the theoretical models become more sophisticated, they also become more computationally complex. Simultaneously, quantifying uncertainty in model predictions and fitting free parameters to experimental observations requires repeated evaluation of these expensive models. Surrogate models---known as emulators---provide the means of accomplishing these goals. This thesis provides an introduction into the current state of emulation in nuclear and many-body physics. The motivations, goals, and origins of currently popular emulation methods are discussed along with selected examples. We see how many methods are closely mathematically related and how trade-offs are made to optimize specific properties or applications. The central work in this thesis is the method of parametric matrix models (PMMs), an emulation and general machine learning framework which combines aspects of traditional reduced basis method with modern parametric machine learning. PMMs are able to retain as much or as little physical information about the underlying system as desired, yielding not only excellent performance but also nearly unparalleled adaptability, interpretability, and trustworthiness as an emulation method. A formal mathematical framework for PMMs is developed and accompanied by practical step-by-step procedures for the application of the method. As part of this thesis, the open-source pyPMM package was developed. This package enables any researcher to construct, train, share, and deploy PMM-based emulators with modular, extendable, and graphics processing unit (GPU)-optimized code. All PMM examples in this thesis were created using this package.

nucl-th↗

arXiv2026

PMM-IMSRG emulator for the nuclear equation of state with quantified uncertainties

We introduce a hybrid emulator for in-medium similarity renormalization group (IMSRG) calculations of nuclear matter, based on chiral nucleon-nucleon and three-nucleon interactions and an implicit-reduced-basis method emulator constructed from parametric matrix models (PMMs) which is capable of rigorously estimating its uncertainties via conformal predictions. The resulting PMM-IMSRG emulator enables fast and accurate predictions with trustworthy confidence intervals of the nuclear equation of state (EOS) across a wide range of input parameters, including low-energy couplings, IMSRG flow parameters, densities, and basis sizes. This framework provides the foundation for principled uncertainty quantification of the nuclear EOS and enables computationally demanding applications such as Bayesian parameter estimation using our IMSRG calculations. As a first application, we present results for the coupling constants of the two quark-mass-dependent three-nucleon interactions, recently identified to contribute at next-to-next-to-leading order in the chiral expansion based on a renormalization-group analysis, by fitting them to empirical saturation properties. We then propagate both parametric and emulator uncertainties to the EOS in the limits of pure neutron matter and symmetric nuclear matter.

nucl-th↗

arXiv2024

Tractable $\textit{a}$ $\textit{priori}$ Dimensionality Reduction for Quantum Dynamics

In this short letter, I present a powerful application in dimensionality reduction of the lesser-used Jacobi-Davidson algorithm for the generalized eigenvalue decomposition. When combined with matrix-free implementations of relevant operators, this technique allows for the computation of the dynamics of an arbitrary quantum state to be done in $\mathcal{O}(n)$ time, where $n$ is the size of the original Hilbert space.

quant-ph↗

arXiv2024

Parametric Matrix Models

We present a general class of machine learning algorithms called parametric matrix models. In contrast with most existing machine learning models that imitate the biology of neurons, parametric matrix models use matrix equations that emulate physical systems. Similar to how physics problems are usually solved, parametric matrix models learn the governing equations that lead to the desired outputs. Parametric matrix models can be efficiently trained from empirical data, and the equations may use algebraic, differential, or integral relations. While originally designed for scientific computing, we prove that parametric matrix models are universal function approximators that can be applied to general machine learning problems. After introducing the underlying theory, we apply parametric matrix models to a series of different challenges that show their performance for a wide range of problems. For all the challenges tested here, parametric matrix models produce accurate results within an efficient and interpretable computational framework that allows for input feature extrapolation.

cs.LG↗

arXiv2023

Non-equilibrium critical scaling and universality in a quantum simulator

Universality and scaling laws are hallmarks of equilibrium phase transitions and critical phenomena. However, extending these concepts to non-equilibrium systems is an outstanding challenge. Despite recent progress in the study of dynamical phases, the universality classes and scaling laws for non-equilibrium phenomena are far less understood than those in equilibrium. In this work, using a trapped-ion quantum simulator with single-spin resolution, we investigate the non-equilibrium nature of critical fluctuations following a quantum quench to the critical point. We probe the scaling of spin fluctuations after a series of quenches to the critical Hamiltonian of a long-range Ising model. With systems of up to 50 spins, we show that the amplitude and timescale of the post-quench fluctuations scale with system size with distinct universal critical exponents, depending on the quench protocol. While a generic quench can lead to thermal critical behavior, we find that a second quench from one critical state to another (i.e.~a double quench) results in a new universal non-equilibrium behavior, identified by a set of critical exponents distinct from their equilibrium counterparts. Our results demonstrate the ability of quantum simulators to explore universal scaling beyond equilibrium.

quant-ph↗