Physics-Informed Neural Networks for Quantum Control.

Quantum control is a ubiquitous research field that has enabled physicists to delve into the dynamics and features of quantum systems, delivering powerful applications for various atomic, optical, mechanical, and solid-state systems. In recent years, traditional control techniques based on optimization processes have been translated into efficient artificial intelligence algorithms. Here, we introduce a computational method for optimal quantum control problems via physics-informed neural networks (PINNs). We apply our methodology to open quantum systems by efficiently solving the state-to-state transfer problem with high probabilities, short-time evolution, and using low-energy consumption controls. Furthermore, we illustrate the flexibility of PINNs to solve the same problem under changes in physical parameters and initial conditions, showing advantages in comparison with standard control techniques.

Modeling the effect of the vaccination campaign on the COVID-19 pandemic.

Population-wide vaccination is critical for containing the SARS-CoV-2 (COVID-19) pandemic when combined with restrictive and prevention measures. In this study we introduce SAIVR, a mathematical model able to forecast the COVID-19 epidemic evolution during the vaccination campaign. SAIVR extends the widely used Susceptible-Infectious-Removed (SIR) model by considering the Asymptomatic (A) and Vaccinated (V) compartments. The model contains several parameters and initial conditions that are estimated by employing a semi-supervised machine learning procedure. After training an unsupervised neural network to solve the SAIVR differential equations, a supervised framework then estimates the optimal conditions and parameters that best fit recent infectious curves of 27 countries. Instructed by these results, we performed an extensive study on the temporal evolution of the pandemic under varying values of roll-out daily rates, vaccine efficacy, and a broad range of societal vaccine hesitancy/denial levels. The concept of herd immunity is questioned by studying future scenarios which involve different vaccination efforts and more infectious COVID-19 variants.

LAN: A Materials Notation for Two-Dimensional Layered Assemblies.

Two-dimensional (2D) layered materials offer intriguing possibilities for novel physics and applications. Before any attempt at exploring the materials space in a systematic fashion, or combining insights from theory, computation, and experiment, a formal description of information about an assembly of arbitrary composition is required. Here, we introduce a domain-generic notation that is used to describe the space of 2D layered materials from monolayers to twisted assemblies of arbitrary composition, existent or not yet fabricated. The notation corresponds to a theoretical materials concept of stepwise assembly of layered structures using a sequence of rotation, vertical stacking, and other operations on individual 2D layers. Its scope is demonstrated with a number of example structures using common single-layer materials as building blocks. This work overall aims to contribute to the systematic codification, capture, and transfer of materials knowledge in the area of 2D layered materials.

Hamiltonian neural networks for solving equations of motion.

There has been a wave of interest in applying machine learning to study dynamical systems. We present a Hamiltonian neural network that solves the differential equations that govern dynamical systems. This is an equation-driven machine learning method where the optimization process of the network depends solely on the predicted functions without using any ground truth data. The model learns solutions that satisfy, up to an arbitrarily small error, Hamilton's equations and, therefore, conserve the Hamiltonian invariants. The choice of an appropriate activation function drastically improves the predictability of the network. Moreover, an error analysis is derived and states that the numerical errors depend on the overall network performance. The Hamiltonian network is then employed to solve the equations for the nonlinear oscillator and the chaotic Hénon-Heiles dynamical system. In both systems, a symplectic Euler integrator requires two orders more evaluation points than the Hamiltonian network to achieve the same order of the numerical error in the predicted phase space trajectories.

Susceptibility to Resurgent COVID-19 Outbreaks Following Vaccine Rollouts: A Modeling Study.

Using the recently proposed Susceptible-Asymptomatic-Infected-Vaccinated-Removed (SAIVR) model, we study the impact of key factors affecting COVID-19 vaccine rollout effectiveness and the susceptibility to resurgent epidemics. The SAIVR model expands the widely used Susceptible-Infectious-Removed (SIR) model for describing epidemics by adding compartments to include the asymptomatic infected (A) and the vaccinated (V) populations. We solve the model numerically to make predictions on the susceptibility to resurgent COVID-19 epidemics depending on initial vaccination coverage, importation loads, continuing vaccination, and more contagious SARS-CoV-2 variants, under persistent immunity and immunity waning conditions. The parameters of the model represent reported epidemiological characteristics of the SARS-CoV-2 virus such as the disease spread in countries with high levels of vaccination coverage. Our findings help explain how the combined effects of different vaccination coverage levels and waning immunity lead to distinct patterns of resurgent COVID-19 epidemics (either surges or endemic), which are observed in countries that implemented different COVID-19 health policies and achieved different vaccinated population plateaus after the vaccine rollouts in the first half of 2021.

Variational integrator graph networks for learning energy-conserving dynamical systems.

Recent advances show that neural networks embedded with physics-informed priors significantly outperform vanilla neural networks in learning and predicting the long-term dynamics of complex physical systems from noisy data. Despite this success, there has only been a limited study on how to optimally combine physics priors to improve predictive performance. To tackle this problem we unpack and generalize recent innovations into individual inductive bias segments. As such, we are able to systematically investigate all possible combinations of inductive biases of which existing methods are a natural subset. Using this framework we introduce variational integrator graph networks-a novel method that unifies the strengths of existing approaches by combining an energy constraint, high-order symplectic variational integrators, and graph neural networks. We demonstrate, across an extensive ablation, that the proposed unifying framework outperforms existing methods, for data-efficient learning and in predictive accuracy, across both single- and many-body problems studied in the recent literature. We empirically show that the improvements arise because high-order variational integrators combined with a potential energy constraint induce coupled learning of generalized position and momentum updates which can be formalized via the partitioned Runge-Kutta method.

Port-Hamiltonian neural networks for learning explicit time-dependent dynamical systems.

Accurately learning the temporal behavior of dynamical systems requires models with well-chosen learning biases. Recent innovations embed the Hamiltonian and Lagrangian formalisms into neural networks and demonstrate a significant improvement over other approaches in predicting trajectories of physical systems. These methods generally tackle autonomous systems that depend implicitly on time or systems for which a control signal is known a priori. Despite this success, many real world dynamical systems are nonautonomous, driven by time-dependent forces and experience energy dissipation. In this study, we address the challenge of learning from such nonautonomous systems by embedding the port-Hamiltonian formalism into neural networks, a versatile framework that can capture energy dissipation and time-dependent control forces. We show that the proposed port-Hamiltonian neural network can efficiently learn the dynamics of nonlinear physical systems of practical interest and accurately recover the underlying stationary Hamiltonian, time-dependent force, and dissipative coefficient. A promising outcome of our network is its ability to learn and predict chaotic systems such as the Duffing equation, for which the trajectories are typically hard to learn.

In situ nanoscale imaging of moiré superlattices in twisted van der Waals heterostructures.

Direct visualization of nanometer-scale properties of moiré superlattices in van der Waals heterostructure devices is a critically needed diagnostic tool for study of the electronic and optical phenomena induced by the periodic variation of atomic structure in these complex systems. Conventional imaging methods are destructive and insensitive to the buried device geometries, preventing practical inspection. Here we report a versatile scanning probe microscopy employing infrared light for imaging moiré superlattices of twisted bilayers graphene encapsulated by hexagonal boron nitride. We map the pattern using the scattering dynamics of phonon polaritons launched in hexagonal boron nitride capping layers via its interaction with the buried moiré superlattices. We explore the origin of the double-line features imaged and show the mechanism of the underlying effective phase change of the phonon polariton reflectance at domain walls. The nano-imaging tool developed provides a non-destructive analytical approach to elucidate the complex physics of moiré engineered heterostructures.