arXiv subjects

Simon Lang

Publications and source records attributed to Simon Lang.

29 records · Page 2Linked to original sources

arXiv2024

AIFS -- ECMWF's data-driven forecasting system

Machine learning-based weather forecasting models have quickly emerged as a promising methodology for accurate medium-range global weather forecasting. Here, we introduce the Artificial Intelligence Forecasting System (AIFS), a data driven forecast model developed by the European Centre for Medium-Range Weather Forecasts (ECMWF). AIFS is based on a graph neural network (GNN) encoder and decoder, and a sliding window transformer processor, and is trained on ECMWF's ERA5 re-analysis and ECMWF's operational numerical weather prediction (NWP) analyses. It has a flexible and modular design and supports several levels of parallelism to enable training on high-resolution input data. AIFS forecast skill is assessed by comparing its forecasts to NWP analyses and direct observational data. We show that AIFS produces highly skilled forecasts for upper-air variables, surface weather parameters and tropical cyclone tracks. AIFS is run four times daily alongside ECMWF's physics-based NWP model and forecasts are available to the public under ECMWF's open data policy.

physics.ao-ph↗

arXiv2024

Data driven weather forecasts trained and initialised directly from observations

Skilful Machine Learned weather forecasts have challenged our approach to numerical weather prediction, demonstrating competitive performance compared to traditional physics-based approaches. Data-driven systems have been trained to forecast future weather by learning from long historical records of past weather such as the ECMWF ERA5. These datasets have been made freely available to the wider research community, including the commercial sector, which has been a major factor in the rapid rise of ML forecast systems and the levels of accuracy they have achieved. However, historical reanalyses used for training and real-time analyses used for initial conditions are produced by data assimilation, an optimal blending of observations with a physics-based forecast model. As such, many ML forecast systems have an implicit and unquantified dependence on the physics-based models they seek to challenge. Here we propose a new approach, training a neural network to predict future weather purely from historical observations with no dependence on reanalyses. We use raw observations to initialise a model of the atmosphere (in observation space) learned directly from the observations themselves. Forecasts of crucial weather parameters (such as surface temperature and wind) are obtained by predicting weather parameter observations (e.g. SYNOP surface data) at future times and arbitrary locations. We present preliminary results on forecasting observations 12-hours into the future. These already demonstrate successful learning of time evolutions of the physical processes captured in real observations. We argue that this new approach, by staying purely in observation space, avoids many of the challenges of traditional data assimilation, can exploit a wider range of observations and is readily expanded to simultaneous forecasting of the full Earth system (atmosphere, land, ocean and composition).

physics.ao-ph↗

arXiv2024

On $\ell_2$-performance of weakly-hard real-time control systems

This paper considers control systems with failures in the feedback channel, that occasionally lead to loss of the control input signal. A useful approach for modeling such failures is to consider window-based constraints on possible loss sequences, for example that at least r control attempts in every window of s are successful. A powerful framework to model such constraints are weakly-hard real-time constraints. Various approaches for stability analysis and the synthesis of stabilizing controllers for such systems have been presented in the past. However, existing results are mostly limited to asymptotic stability and rarely consider performance measures such as the resulting $\ell_2$-gain. To address this problem, we adapt a switched system description where the switching sequence is constrained by a graph that captures the loss information. We present an approach for $\ell_2$-performance analysis involving linear matrix inequalities (LMI). Further, leveraging a system lifting method, we propose an LMI-based approach for synthesizing state-feedback controllers with guaranteed $\ell_2$-performance. The results are illustrated by a numerical example.

eess.SY↗

arXiv2021

Nonergodicity parameters of confined hard-sphere glasses

Within a recently developed mode-coupling theory for fluids confined to a slit we elaborate numerical results for the long-time limits of suitably generalized intermediate scattering functions. The theory requires as input the density profile perpendicular to the plates, which we obtain from density functional theory within the fundamental-measure framework, as well as symmetry-adapted static structure factors which can be calculated relying on the inhomogeneous Percus-Yevick closure. Our calculations for the nonergodicity parameters for both the collective as well as for the self motion are in qualitative agreement with our extensive event-driven molecular dynamics simulations for the intermediate scattering functions for slightly polydisperse hard-sphere systems at high packing fraction. We show that the variation of the nonergodicity parameters as a function of the wavenumber correlates with the in-plane static structure factors, while subtle effects become apparent in the structure factors and relaxation times of higher mode-indices. A criterion to predict the multiple reentrant from the variation of the in-plane static structure is presented.

cond-mat.soft↗

arXiv2015

Glassy dynamics in confinement: Planar and bulk limit of the mode-coupling theory

We demonstrate how the matrix-valued mode-coupling theory of the glass transition and glassy dynamics in planar confinement converges to the corresponding theory for two-dimensional (2D) planar and the three-dimensional bulk liquid, provided the wall potential satisfies certain conditions. Since the mode-coupling theory relies on the static properties as input, the emergence of a homogeneous limit for the matrix-valued intermediate scattering functions is directly connected to the convergence of the corresponding static quantities to their conventional counterparts. We show that the 2D limit is more subtle than the bulk limit, in particular, the in-planar dynamics decouples from the motion perpendicular to the walls. We investigate the frozen-in parts of the intermediate scattering function in the glass state and find that the limits time $t\to \infty$ and effective wall separation $L\to 0$ do not commute due to the mutual coupling of the residual transversal and lateral force kernels.

cond-mat.soft↗

arXiv2014

Tagged-particle motion in a dense confined liquid

We investigate the dynamics of a tagged particle embedded in a strongly interacting confined liquid enclosed between two opposing flat walls. Using the Zwanzig-Mori projection operator formalism we obtain an equation of motion for the incoherent scattering function suitably generalized to account for the lack of translational symmetry. We close the equations of motion by a self-consistent mode-coupling ansatz. The interaction of the tracer with the surrounding liquid is encoded in generalized direct correlation functions. We extract the in-plane dynamics and provide a microscopic expression for the diffusion coefficient parallel to the walls. The solute particle may differ in size or interaction from the surrounding host-liquid constituents offering the possibility of a systematic analysis of dynamic effects on the tagged-particle motion in confinement.

cond-mat.soft↗

arXiv2014

Structural quantities of quasi-two-dimensional fluids

Quasi-two-dimensional fluids can be generated by confining a fluid between two parallel walls with narrow separation. Such fluids exhibit an inhomogeneous structure perpendicular to the walls due to the loss of translational symmetry. Taking the transversal degrees of freedom as a perturbation to an appropriate 2D reference fluid we provide a systematic expansion of the $m$-particle density for arbitrary $m$. To leading order in the slit width this density factorizes into the densities of the transversal and lateral degrees of freedom. Explicit expressions for the next-to-leading order terms are elaborated analytically quantifying the onset of inhomogeneity. The case $m=1$ yields the density profile with a curvature given by an integral over the pair-distribution function of the corresponding 2D reference fluid, which reduces to its 2D contact value in the case of pure excluded-volume interactions. Interestingly, we find that the 2D limit is subtle and requires stringent conditions on the fluid-wall interactions. We quantify the rapidity of convergence for various structural quantities to their 2D counterparts.

cond-mat.soft↗

arXiv2014

Mode-coupling theory for multiple decay channels

We investigate the properties of a class of mode-coupling equations for the glass transition where the density mode decays into multiple relaxation channels. We prove the existence and uniqueness of the solutions for Newtonian as well as Brownian dynamics and demonstrate that they fulfill the requirements of correlation functions, in the latter case the solutions are purely relaxational. Furthermore, we construct an effective mode-coupling functional which allows to map the theory to the case of a single decay channel, such that the covariance principle found for the mode-coupling theory for simple liquids is properly generalized. This in turn allows establishing the maximum theorem stating that long-time limits of mode-coupling solutions can be calculated as maximal solutions of a fixed-point equation without relying on the dynamic solutions.

cond-mat.soft↗

arXiv2013

Fluids in Extreme Confinement

For extremely confined fluids with two-dimensional density $n$ in slit geometry of accessible width $L$, we prove that in the limit $L\to 0$ the lateral and transversal degrees of freedom decouple, and the latter become ideal-gas-like. For small wall separation the transverse degrees of freedom can be integrated out and renormalize the interaction potential. We identify $n L^2 $ as hidden smallness parameter of the confinement problem and evaluate the effective two-body potential analytically, which allows calculating the leading correction to the free energy exactly. Explicitly, we map a fluid of hard spheres in extreme confinement onto a 2d-fluid of disks with an effective hard-core diameter and a soft boundary layer. Two-dimensional phase transitions are robust and the transition point experiences a shift ${\cal O}(n L^2)$.

cond-mat.soft↗

arXiv2012

Mode-coupling theory of the glass transition for confined fluids

We present a detailed derivation of a microscopic theory for the glass transition of a liquid enclosed between two parallel walls relying on a mode-coupling approximation. This geometry lacks translational invariance perpendicular to the walls, which implies that the density profile and the density-density correlation function depends explicitly on the distances to the walls. We discuss the residual symmetry properties in slab geometry and introduce a symmetry adapted complete set of two-point correlation functions. Since the currents naturally split into components parallel and perpendicular to the walls the mathematical structure of the theory differs from the established mode-coupling equations in bulk. We prove that the equations for the nonergodicity parameters still display a covariance property similar to bulk liquids.

cond-mat.soft↗

arXiv2010

Glass Transition in Confined Geometry

Extending mode-coupling theory, we elaborate a microscopic theory for the glass transition of liquids confined between two parallel flat hard walls. The theory contains the standard MCT equations in bulk and in two dimensions as limiting cases and requires as input solely the equilibrium density profile and the structure factors of the fluid in confinement. We evaluate the phase diagram as a function of the distance of the plates for the case of a hard sphere fluid and obtain an oscillatory behavior of the glass transtion line as a result of the structural changes related to layering.

cond-mat.soft↗