Publications

Compressing large data sets to a manageable number of summaries that are informative about the underlying parameters vastly simplifies both frequentist and Bayesian inference. When only simulations are available, these summaries are typically chosen heuristically, so they may inadvertently miss important information. We introduce a simulation-based machine learning technique that trains artificial neural networks to find nonlinear functionals of data that maximize Fisher information: information maximizing neural networks (IMNNs). In test cases where the posterior can be derived exactly, likelihood-free inference based on automatically derived IMNN summaries produces nearly exact posteriors, showing that these summaries are good approximations to sufficient statistics. In a series of numerical examples of increasing complexity and astrophysical relevance we show that IMNNs are robustly capable of automatically finding optimal, nonlinear summaries of the data even in cases where linear compression fails: inferring the variance of Gaussian signal in the presence of noise, inferring cosmological parameters from mock simulations of the Lyman-α forest in quasar spectra, and inferring frequency-domain parameters from LISA-like detections of gravitational waveforms. In this final case, the IMNN summary outperforms linear data compression by avoiding the introduction of spurious likelihood maxima. We anticipate that the automatic physical inference method described in this paper will be essential to obtain both accurate and precise cosmological parameter estimates from complex and large astronomical data sets, including those from LSST and Euclid.

Multi-epoch radial velocity measurements of stars can be used to identify stellar, sub-stellar, and planetary-mass companions. Even a small number of observation epochs can be informative about companions, though there can be multiple qualitatively different orbital solutions that fit the data. We have custom-built a Monte Carlo sampler (The Joker) that delivers reliable (and often highly multi-modal) posterior samplings for companion orbital parameters given sparse radial-velocity data. Here we use The Joker to perform a search for companions to 96,231 red-giant stars observed in the APOGEE survey (DR14) with ≥3 spectroscopic epochs. We select stars with probable companions by making a cut on our posterior belief about the amplitude of the stellar radial-velocity variation induced by the orbit. We provide (1) a catalog of 320 companions for which the stellar companion properties can be confidently determined, (2) a catalog of 4,898 stars that likely have companions, but would require more observations to uniquely determine the orbital properties, and (3) posterior samplings for the full orbital parameters for all stars in the parent sample. We show the characteristics of systems with confidently determined companion properties and highlight interesting systems with candidate compact object companions.

Machine learning is a promising application of quantum computing, but challenges remain as near-term devices will have a limited number of physical qubits and high error rates. Motivated by the usefulness of tensor networks for machine learning in the classical context, we propose quantum computing approaches to both discriminative and generative learning, with circuits based on tree and matrix product state tensor networks that could have benefits for near-term devices. The result is a unified framework where classical and quantum computing can benefit from the same theoretical and algorithmic developments, and the same model can be trained classically then transferred to the quantum setting for additional optimization. Tensor network circuits can also provide qubit-efficient schemes where, depending on the architecture, the number of physical qubits required scales only logarithmically with, or independently of the input or output data sizes. We demonstrate our proposals with numerical experiments, training a discriminative model to perform handwriting recognition using a optimization procedure that could be carried out on quantum hardware, and testing the noise resilience of the trained model.

We investigate the electronic structure of SrMnO3 with density functional theory plus dynamical mean-field theory (DMFT). Within this scheme the selection of the correlated subspace and the construction of the corresponding Wannier functions is a crucial step. Due to the crystal-field splitting of the Mn-3d orbitals and their separation from the O-2p bands, SrMnO3 is a material where on first sight a three-band d-only model should be sufficient. However, in the present work we demonstrate that the resulting spectrum is considerably influenced by the number of correlated orbitals and the number of bands included in the Wannier function construction. For example, in a d−dp model we observe a splitting of the t2g lower Hubbard band into a more complex spectral structure, not observable in d-only models. To illustrate these high-frequency differences we employ the recently developed fork tensor product state (FTPS) impurity solver, as it provides the necessary spectral resolution on the real-frequency axis. We find that the spectral structure of a five-band d−dp model is in good agreement with PES and XAS experiments. Our results demonstrate that the FTPS solver is capable of performing full five-band DMFT calculations directly on the real-frequency axis.

Ultrafast science offers the prospect of an all-optical design and femtosecond switching of magnetic and topological properties in quantum materials. Floquet topological states were suggested to emerge in photodressed band structures in the presence of periodic laser driving. Here we propose a viable nonthermal route without requiring coherent Floquet states to reach the elusive magnetic Weyl semimetallic phase in pyrochlore iridates by ultrafast modification of the effective electron-electron interaction with short laser pulses. Combining ab initio calculations for a time-dependent self-consistent reduced Hubbard U controlled by laser intensity and nonequilibrium magnetism simulations for quantum quenches, we find dynamically modified magnetic order giving rise to transiently emerging Weyl cones that are probed by time- and angle-resolved photoemission spectroscopy. Our work offers a unique and realistic nonthermal pathway for nonequilibrium materials engineering beyond Floquet physics to create and sustain Weyl semimetals. This may lead to ultrafast, tens-of-femtoseconds switching protocols for light-engineered Berry curvature in combination with ultrafast magnetism.

Standard present day large-scale structure (LSS) analyses make a major assumption in their Bayesian parameter inference --- that the likelihood has a Gaussian form. For summary statistics currently used in LSS, this assumption, even if the underlying density field is Gaussian, cannot be correct in detail. We investigate the impact of this assumption on two recent LSS analyses: the Beutler et al. (2017) power spectrum multipole (Pℓ) analysis and the Sinha et al. (2017) group multiplicity function (ζ) analysis. Using non-parametric divergence estimators on mock catalogs originally constructed for covariance matrix estimation, we identify significant non-Gaussianity in both the Pℓ and ζ likelihoods. We then use Gaussian mixture density estimation and Independent Component Analysis on the same mocks to construct likelihood estimates that approximate the true likelihood better than the Gaussian pseudo-likelihood. Using these likelihood estimates, we accurately estimate the true posterior probability distribution of the Beutler et al. (2017) and Sinha et al. (2017) parameters. Likelihood non-Gaussianity shifts the fσ8 constraint by −0.44σ, but otherwise, does not significantly impact the overall parameter constraints of Beutler et al. (2017). For the ζ analysis, using the pseudo-likelihood significantly underestimates the uncertainties and biases the constraints of Sinha et al. (2017) halo occupation parameters. For logM1 and α, the posteriors are shifted by +0.43σ and −0.51σ and broadened by 42% and 66%, respectively. The divergence and likelihood estimation methods we present provide a straightforward framework for quantifying the impact of likelihood non-Gaussianity and deriving more accurate parameter constraints.

We investigate the dynamics of hydrodynamically interacting motile and non-motile stress-generating swimmers or particles as they invade a surrounding viscous fluid. Colonies of aligned pusher particles are shown to elongate in the direction of particle orientation and undergo a cascade of transverse concentration instabilities. Colonies of aligned puller particles instead are found to elongate in the direction opposite the particle orientation and exhibit dramatic splay as the group moves into the bulk. A linear stability analysis of concentrated line distributions of particles is performed and growth rates are found, using an active slender-body approximation, to match the results of numerical simulations. Thin concentrated bands of aligned pusher particles are always unstable, while bands of aligned puller particles can either be stable (immotile particles) or unstable (motile particles) with a growth rate which is non-monotonic in the force dipole strength. We also prove a surprising "no-flow theorem": a distribution initially isotropic in orientation loses isotropy immediately but in such a way that results in no fluid flow anywhere at any time.

We present a new method for the analysis of electromagnetic scattering from homogeneous penetrable bodies. Our approach is based on a reformulation of the governing Maxwell equations in terms of two uncoupled vector Helmholtz systems: one for the electric feld and one for the magnetic field. This permits the derivation of resonance-free Fredholm equations of the second kind that are stable at all frequencies, insensitive to the genus of the scatterers, and invertible for all passive materials including those with negative permittivities or permeabilities. We refer to these as decoupled field integral equations.

Insights from spectroscopic experiments led to the development of quantum mechanics as the com- mon framework for describing the physical and chemical properties of atoms, molecules and mate- rials. Later, a full quantum description of charged particles, electromagnetic radiation and relativity was developed, leading to quantum-electrodynamics (QED). This is, to our current understanding, the most fundamental theory describing photon-matter interactions in correlated many-body sys- tems. In the low-energy regime, simplified models of QED were developed for describing and an- alyzing spatial and time-resolved spectroscopies encompassing a wide range of energy, time, and space scales as well as physical systems. In this review, we highlight the interrelations and limita- tions of such theoretical models by showing how they appear as low-energy simplifications of the full QED formalism, where anti-particles and the internal structure of the nuclei are neglected. Tak- ing molecular systems as reference, we discuss how the breakdown of some of the well-established simplifications to low-energy QED challenges our conventional understanding of light-matter inter- actions. New features of collective QED effects in complex interacting many-particle systems could become, besides high-precision atomic measurements and simulations of particle-physics problems in solid-state systems, an alternative material-based route to further advance the currently most fun- damental theory for light-matter interactions.

We introduce linear-response theory for non-relativistic quantum-electrodynamics in the long wavelength limit, which allows us to treat correlated excited-state phenomena of matter-photon systems from first principles. By using quantum-electrodynamical density-functional theory we can reformulate the resulting fully coupled photon-matter response equations as a pseudo-eigenvalue problem. This provides a direct extension of the conventional matter-only response theory. Our approach can be solved numerically very efficiently and existing ab-initio density-functional response implementations can be easily extended to take the full photon-matter response into account. We highlight how the coupling between light and matter changes the usual response functions and introduces new types of response functions that measure the matter-photon subsystem responses. We show how correlating light and matter changes the Maxwell equations and highlight how the spectra of real systems are changed upon strongly coupling to the photon field. A key feature of treating the combined matter-photon response is that natural lifetimes of excitations become directly accessible from first principles and no artificial broadening of spectra is required anymore. By introducing a straightforward extension of the random-phase approximation for the coupled matter-photon problem, we are able to present the first ab-initio spectra for a real molecular system that is coupled to the quantized electromagnetic field.