Deep learning as closure for irreversible processes: A data-driven generalized Langevin equation

The ultimate goal of physics is finding a unique equation capable of describing the evolution of any observable quantity in a self-consistent way. Within the field of statistical physics, such an equation is known as the generalized Langevin equation (GLE). Nevertheless, the formal and exact GLE is not particularly useful, since it depends on the complete history of the observable at hand, and on hidden degrees of freedom typically inaccessible from a theoretical point of view. In this work, we propose the use of deep neural networks as a new avenue for learning the intricacies of the unknowns mentioned above. By using machine learning to eliminate the unknowns from GLEs, our methodology outperforms previous approaches (in terms of efficiency and robustness) where general fitting functions were postulated. Finally, our work is tested against several prototypical examples, from a colloidal systems and particle chains immersed in a thermal bath, to climatology and financial models. In all cases, our methodology exhibits an excellent agreement with the actual dynamics of the observables under consideration

Subarcsecond international LOFAR radio images of Arp 220 at 150 MHz: A kpc-scale star forming disk surrounding nuclei with shocked outflows

Context. Arp 220 is the prototypical ultra luminous infrared galaxy (ULIRG). Despite extensive studies, the structure at MHz-frequencies has remained unknown because of limits in spatial resolution. Aims. This work aims to constrain the flux and shape of radio emission from Arp 220 at MHz frequencies. Methods. We analyse new observations with the International Low Frequency Array (LOFAR) telescope, and archival data from the Multi-Element Radio Linked Interferometer Network (MERLIN) and the Karl G. Jansky Very Large Array (VLA). We model the spatially resolved radio spectrum of Arp 220 from 150 MHz to 33 GHz. Results. We present an image of Arp 220 at 150 MHz with resolution 0′. 65 × 0′. 35, sensitivity 0.15 mJy beam, and integrated flux density 394 ± 59 mJy. More than 80% of the detected flux comes from extended (6″∼ 2.2 kpc) steep spectrum (α = -0.7) emission, likely from star formation in the molecular disk surrounding the two nuclei. We find elongated features extending 0.3″ (110 pc) and 0.9″ (330 pc) from the eastern and western nucleus respectively, which we interpret as evidence for outflows. The extent of radio emission requires acceleration of cosmic rays far outside the nuclei. We find that a simple three component model can explain most of the observed radio spectrum of the galaxy. When accounting for absorption at 1.4 GHz, Arp 220 follows the FIR/radio correlation with q = 2.36, and we estimate a star formation rate of 220 M yr. We derive thermal fractions at 1 GHz of less than 1% for the nuclei, which indicates that a major part of the UV-photons are absorbed by dust. Conclusions. International LOFAR observations shows great promise to detect steep spectrum outflows and probe regions of thermal absorption. However, in LIRGs the emission detected at 150 MHz does not necessarily come from the main regions of star formation. This implies that high spatial resolution is crucial for accurate estimates of star formation rates for such galaxies at 150 MHz.A. A. and M.A.P.T. acknowledge support from the Spanish MINECO through grants AYA2012-38491-C02-02 and AYA2015-63939-C2-1-P, partially funded by FEDER funds.The research leading to these results has received funding from the European Commission Seventh Framework Programme (FP/2007-2013) under grant agreement No. 283393 (RadioNet3).Support for MAST for non-HST data is provided by the NASA Office of Space Science via grant NNX09AF08G and by other grants and contracts.Peer Reviewe

Physics-informed Bayesian inference of external potentials in classical density-functional theory

The swift progression of machine learning (ML) has not gone unnoticed in the realm of statistical mechanics. ML techniques have attracted attention by the classical density-functional theory (DFT) community, as they enable discovery of free-energy functionals to determine the equilibrium-density profile of a many-particle system. Within DFT, the external potential accounts for the interaction of the many-particle system with an external field, thus, affecting the density distribution. In this context, we introduce a statistical-learning framework to infer the external potential exerted on a many-particle system. We combine a Bayesian inference approach with the classical DFT apparatus to reconstruct the external potential, yielding a probabilistic description of the external potential functional form with inherent uncertainty quantification. Our framework is exemplified with a grand-canonical one-dimensional particle ensemble with excluded volume interactions in a confined geometry. The required training dataset is generated using a Monte Carlo (MC) simulation where the external potential is applied to the grand-canonical ensemble. The resulting particle coordinates from the MC simulation are fed into the learning framework to uncover the external potential. This eventually allows us to compute the equilibrium density profile of the system by using the tools of DFT. Our approach benchmarks the inferred density against the exact one calculated through the DFT formulation with the true external potential. The proposed Bayesian procedure accurately infers the external potential and the density profile. We also highlight the external-potential uncertainty quantification conditioned on the amount of available simulated data. The seemingly simple case study introduced in this work might serve as a prototype for studying a wide variety of applications, including adsorption and capillarity

A Finite-Volume Method for Fluctuating Dynamical Density Functional Theory

We introduce a finite-volume numerical scheme for solving stochastic gradient-flow equations. Such equations are of crucial importance within the framework of fluctuating hydrodynamics and dynamic density functional theory. Our proposed scheme deals with general free-energy functionals, including, for instance, external fields or interaction potentials. This allows us to simulate a range of physical phenomena where thermal fluctuations play a crucial role, such as nucleation and other energy-barrier crossing transitions. A positivity-preserving algorithm for the density is derived based on a hybrid space discretization of the deterministic and the stochastic terms and different implicit and explicit time integrators. We show through numerous applications that not only our scheme is able to accurately reproduce the statistical properties (structure factor and correlations) of the physical system, but, because of the multiplicative noise, it allows us to simulate energy barrier crossing dynamics, which cannot be captured by mean-field approaches

A Brownian Model for Crystal Nucleation

In this work a phenomenological stochastic differential equation is proposed to model the time evolution of the radius of a pre-critical molecular cluster during nucleation (the classical order parameter). Such a stochastic differential equation constitutes the basis for the calculation of the (nucleation) induction time under Kramers' theory of thermally activated escape processes. Considering the nucleation stage as a Poisson rare-event, analytical expressions for the induction time statistics are deduced for both steady and unsteady conditions, the latter assuming the semiadiabatic limit. These expressions can be used to identify the underlying mechanism of molecular cluster formation (distinguishing between homogeneous or heterogeneous nucleation from the nucleation statistics is possible) as well as to predict induction times and induction time distributions. The predictions of this model are in good agreement with experimentally measured induction times at constant temperature, unlike the values obtained from the classical equation, but agreement is not so good for induction time statistics. Stochastic simulations truncated to the maximum waiting time of the experiments confirm that this fact is due to the time constraints imposed by experiments. Correcting for this effect, the experimental and predicted curves fit remarkably well. Thus, the proposed model seems to be a versatile tool to predict cluster size distributions, nucleation rates, (nucleation) induction time and induction time statistics for a wide range of conditions (e.g. time-dependent temperature, supersaturation, pH, etc.) where classical nucleation theory is of limited applicability.Comment: 20 pages, 3 figure

Total, Bioavailable, and Free Vitamin D Levels and Their Prognostic Value in Pulmonary Arterial Hypertension

Introduction: Epidemiological studies suggest a relationship between vitamin D deficiency and cardiovascular and respiratory diseases. However, whether total, bioavailable, and/or free vitamin D levels have a prognostic role in pulmonary arterial hypertension (PAH) is unknown. We aimed to determine total, bioavailable, and free 25-hydroxy-vitamin D (25(OH)vitD) plasma levels and their prognostic value in PAH patients. Methods: In total, 67 samples of plasma from Spanish patients with idiopathic, heritable, or drug-induced PAH were obtained from the Spanish PH Biobank and compared to a cohort of 100 healthy subjects. Clinical parameters were obtained from the Spanish Registry of PAH (REHAP). Results: Seventy percent of PAH patients had severe vitamin D deficiency (total 25(OH)vitD < 10 ng/mL) and secondary hyperparathyroidism. PAH patients with total 25(OH)vitD plasma above the median of this cohort (7.17 ng/mL) had better functional class and higher 6-min walking distance and TAPSE (tricuspid annular plane systolic excursion). The main outcome measure of survival was significantly increased in these patients (age-adjusted hazard ratio: 5.40 (95% confidence interval: 2.88 to 10.12)). Vitamin D-binding protein (DBP) and albumin plasma levels were downregulated in PAH. Bioavailable 25(OH)vitD was decreased in PAH patients compared to the control cohort. Lower levels of bioavailable 25(OH)vitD (<0.91 ng/mL) were associated with more advanced functional class, lower exercise capacity, and higher risk of mortality. Free 25(OH)vitD did not change in PAH; however, lower free 25(OH)vitD (<1.53 pg/mL) values were also associated with high risk of mortality. Conclusions: Vitamin D deficiency is highly prevalent in PAH, and low levels of total 25(OH)vitD were associated with poor prognosis

General framework for fluctuating dynamic density functional theory

We introduce a versatile bottom-up derivation of a formal theoretical framework to describe (passive) soft-matter systems out of equilibrium subject to fluctuations. We provide a unique connection between the constituent-particle dynamics of real systems and the time evolution equation of their measurable (coarse-grained) quantities, such as local density and velocity. The starting point is the full Hamiltonian description of a system of colloidal particles immersed in a fluid of identical bath particles. Then, we average out the bath via Zwanzig's projection-operator techniques and obtain the stochastic Langevin equations governing the colloidal-particle dynamics. Introducing the appropriate definition of the local number and momentum density fields yields a generalisation of the Dean-Kawasaki (DK) model, which resembles the stochastic Navier-Stokes (NS) description of a fluid. Nevertheless, the DK equation still contains all the microscopic information and, for that reason, does not represent the dynamical law of observable quantities. We address this controversial feature of the DK description by carrying out a nonequilibrium ensemble average. Adopting a natural decomposition into local-equilibrium and nonequilibrium contribution, where the former is related to a generalised version of the canonical distribution, we finally obtain the fluctuating-hydrodynamic equation governing the time-evolution of the mesoscopic density and momentum fields. Along the way, we outline the connection between the ad-hoc energy functional introduced in previous DK derivations and the free-energy functional from classical density-functional theory (DFT). The resultant equation has the structure of a dynamical DFT (DDFT) with an additional fluctuating force coming from the random interactions with the bath. We show that our fluctuating DDFT formalism corresponds to a particular version of the fluctuating NS equations, originally derived by Landau and Lifshitz. Our framework thus provides the formal apparatus for ab-initio derivations of fluctuating DDFT equations capable of describing the dynamics of soft-matter systems in and out of equilibrium. We believe that the derivation offered here represents the current state of the art in the field