arXiv subjects

Luca Magri

Publications and source records attributed to Luca Magri.

At least 73 records · Page 4Linked to original sources

arXiv2023

Compositional noise in nozzles with dissipation

We propose a physical model to predict indirect noise generated by the acceleration of compositional inhomogeneities in nozzles with viscous dissipation (non-isentropic nozzles). First, we derive the quasi-one-dimensional equations from the conservation laws of multicomponent flows. Second, we validate the proposed model with the experimental data available in the literature for binary mixtures of four gases. Third, we calculate the nozzle transfer functions for different Helmholtz numbers and friction factors, in both subsonic and supersonic flows with/without shock waves. We show that friction has a significant effect on the generation of indirect noise, for which the physical mechanism is identified and explained. Fourth, we find a semi-analytical solution with path integrals, which provide an asymptotic expansion with respect to the Helmholtz number. Fifth, we introduce the compositional noise scaling factor, which is applied to quickly estimate compositional noise from the knowledge of only one single-component gas transfer function. The approximation error is less than $1\%$. The proposed low-order model provides accurate estimates of the transfer functions and physical insight into indirect noise for multicomponent gases. This opens up new possibilities to accurately predict, and understand, sound generation in gas turbines.

physics.flu-dyn↗

arXiv2023

A physics-based domain adaptation framework for modelling and forecasting building energy systems

State-of-the-art machine-learning-based models are a popular choice for modeling and forecasting energy behavior in buildings because given enough data, they are good at finding spatiotemporal patterns and structures even in scenarios where the complexity prohibits analytical descriptions. However, their architecture typically does not hold physical correspondence to mechanistic structures linked with governing physical phenomena. As a result, their ability to successfully generalize for unobserved timesteps depends on the representativeness of the dynamics underlying the observed system in the data, which is difficult to guarantee in real-world engineering problems such as control and energy management in digital twins. In response, we present a framework that combines lumped-parameter models in the form of linear time-invariant (LTI) state-space models (SSMs) with unsupervised reduced-order modeling in a subspace-based domain adaptation (SDA) framework. SDA is a type of transfer-learning (TL) technique, typically adopted for exploiting labeled data from one domain to predict in a different but related target domain for which labeled data is limited. We introduce a novel SDA approach where instead of labeled data, we leverage the geometric structure of the LTI SSM governed by well-known heat transfer ordinary differential equations to forecast for unobserved timesteps beyond observed measurement data. Fundamentally, our approach geometrically aligns the physics-derived and data-derived embedded subspaces closer together. In this initial exploration, we evaluate the physics-based SDA framework on a demonstrative heat conduction scenario by varying the thermophysical properties of the source and target systems to demonstrate the transferability of mechanistic models from a physics-based domain to a data domain.

cs.LG↗

arXiv2023

Stability analysis of chaotic systems from data

The prediction of the temporal dynamics of chaotic systems is challenging because infinitesimal perturbations grow exponentially. The analysis of the dynamics of infinitesimal perturbations is the subject of stability analysis. In stability analysis, we linearize the equations of the dynamical system around a reference point, and compute the properties of the tangent space (i.e., the Jacobian). The main goal of this paper is to propose a method that learns the Jacobian, thus, the stability properties, from observables (data). First, we propose the Echo State Network (ESN) with the Recycle Validation as a tool to accurately infer the chaotic dynamics from data. Second, we mathematically derive the Jacobian of the Echo State Network, which provides the evolution of infinitesimal perturbations. Third, we analyse the stability properties of the Jacobian inferred from the ESN, and compare them with the benchmark results obtained by linearizing the equations. The ESN correctly infers the nonlinear solution, and its tangent space with negligible numerical errors. In detail, (i) the long-term statistics of the chaotic state; (ii) the covariant Lyapunov vectors; (ii) the Lyapunov spectrum; (iii) the finite-time Lyapunov exponents; (iv) and the angles between the stable, neutral, and unstable splittings of the tangent space (the degree of hyperbolicity of the attractor). This work opens up new opportunities for the computation of stability properties of nonlinear systems from data, instead of equations.

nlin.AO↗

arXiv2023

Quantum Multi-Model Fitting

Geometric model fitting is a challenging but fundamental computer vision problem. Recently, quantum optimization has been shown to enhance robust fitting for the case of a single model, while leaving the question of multi-model fitting open. In response to this challenge, this paper shows that the latter case can significantly benefit from quantum hardware and proposes the first quantum approach to multi-model fitting (MMF). We formulate MMF as a problem that can be efficiently sampled by modern adiabatic quantum computers without the relaxation of the objective function. We also propose an iterative and decomposed version of our method, which supports real-world-sized problems. The experimental evaluation demonstrates promising results on a variety of datasets. The source code is available at: https://github.com/FarinaMatteo/qmmf.

cs.CV↗

arXiv2023

Data-driven stability analysis of a chaotic time-delayed system

Systems with time-delayed chaotic dynamics are common in nature, from control theory to aeronautical propulsion. The overarching objective of this paper is to compute the stability properties of a chaotic dynamical system, which is time-delayed. The stability analysis is based only on data. We employ the echo state network (ESN), a type of recurrent neural network, and train it on timeseries of a prototypical time-delayed nonlinear thermoacoustic system. By running the trained ESN autonomously, we show that it can reproduce (i) the long-term statistics of the thermoacoustic system's variables, (ii) the physical portion of the Lyapunov spectrum, and (iii) the statistics of the finite-time Lyapunov exponents. This work opens up the possibility to infer stability properties of time-delayed systems from experimental observations.

nlin.AO↗

arXiv2023

Physics-Informed Long Short-Term Memory for Forecasting and Reconstruction of Chaos

We present the Physics-Informed Long Short-Term Memory (PI-LSTM) network to reconstruct and predict the evolution of unmeasured variables in a chaotic system. The training is constrained by a regularization term, which penalizes solutions that violate the system's governing equations. The network is showcased on the Lorenz-96 model, a prototypical chaotic dynamical system, for a varying number of variables to reconstruct. First, we show the PI-LSTM architecture and explain how to constrain the differential equations, which is a non-trivial task in LSTMs. Second, the PI-LSTM is numerically evaluated in the long-term autonomous evolution to study its ergodic properties. We show that it correctly predicts the statistics of the unmeasured variables, which cannot be achieved without the physical constraint. Third, we compute the Lyapunov exponents of the network to infer the key stability properties of the chaotic system. For reconstruction purposes, adding the physics-informed loss qualitatively enhances the dynamical behaviour of the network, compared to a data-driven only training. This is quantified by the agreement of the Lyapunov exponents. This work opens up new opportunities for state reconstruction and learning of the dynamics of nonlinear systems.

cs.LG↗

arXiv2023

Bayesian optimization of the layout of wind farms with a high-fidelity surrogate model

We introduce a gradient-free data-driven framework for optimizing the power output of a wind farm based on a Bayesian approach and large-eddy simulations. In contrast with conventional wind farm layout optimization strategies, which make use of simple wake models, the proposed framework accounts for complex flow phenomena such as wake meandering, local speed-ups and the interaction of the wind turbines with the atmospheric flow. The capabilities of the framework are demonstrated for the case of a small wind farm consisting of five wind turbines. It is shown that it can find optimal designs within a few iterations, while leveraging the above phenomena to deliver increased wind farm performance.

physics.flu-dyn↗

arXiv2023

Indirect noise from weakly reacting inhomogeneities

Indirect noise is a significant contributor to aircraft engine noise, which needs to be minimized in the design of aircraft engines. Indirect noise is caused by the acceleration of flow inhomogeneities through a nozzle. High-fidelity simulations showed that some flow inhomogeneities can be chemically reacting when they leave the combustor and enter the nozzle (Giusti et al., 2019). The state-of-art models, however, are limited to chemically non-reacting (frozen) flows. In this work, first, we propose a low-order model to predict indirect noise in nozzle flows with reacting inhomogeneities. Second, we identify the physical sources of sound, which generate indirect noise via two physical mechanisms: (i) chemical reaction generates compositional perturbations, thereby adding to compositional noise; and (ii) exothermic reaction generates entropy perturbations. Third, we numerically compute the nozzle transfer functions for different frequency ranges (Helmholtz numbers) and reaction rates (Damköhler numbers) in subsonic flows with hydrogen and methane inhomogeneities. Fourth, we extend the model to supersonic flows. We find that hydrogen inhomogeneities have a larger impact to indirect noise than methane inhomogeneities. Both the Damköhler number and the Helmholtz number markedly influence the phase and magnitude of the transmitted and reflected waves, which affect the sound generation and thermoacoustic stability. This work provides a physics-based low-order model, which can open new opportunities for predicting noise emissions and instabilities in aeronautical gas turbines with multi-physics flows.

physics.flu-dyn↗

arXiv2022

On interpretability and proper latent decomposition of autoencoders

The dynamics of a turbulent flow tend to occupy only a portion of the phase space at a statistically stationary regime. From a dynamical systems point of view, this portion is the attractor. The knowledge of the turbulent attractor is useful for two purposes, at least: (i) We can gain physical insight into turbulence (what is the shape and geometry of the attractor?), and (ii) it provides the minimal number of degrees of freedom to accurately describe the turbulent dynamics. Autoencoders enable the computation of an optimal latent space, which is a low-order representation of the dynamics. If properly trained and correctly designed, autoencoders can learn an approximation of the turbulent attractor, as shown by Doan, Racca and Magri (2022). In this paper, we theoretically interpret the transformations of an autoencoder. First, we remark that the latent space is a curved manifold with curvilinear coordinates, which can be analyzed with simple tools from Riemann geometry. Second, we characterize the geometrical properties of the latent space. We mathematically derive the metric tensor, which provides a mathematical description of the manifold. Third, we propose a method -- proper latent decomposition (PLD) -- that generalizes proper orthogonal decomposition of turbulent flows on the autoencoder latent space. This decomposition finds the dominant directions in the curved latent space. This theoretical work opens up computational opportunities for interpreting autoencoders and creating reduced-order models of turbulent flows.

physics.flu-dyn↗

arXiv2022

Modelling spatiotemporal turbulent dynamics with the convolutional autoencoder echo state network

The spatiotemporal dynamics of turbulent flows is chaotic and difficult to predict. This makes the design of accurate and stable reduced-order models challenging. The overarching objective of this paper is to propose a nonlinear decomposition of the turbulent state for a reduced-order representation of the dynamics. We divide the turbulent flow into a spatial problem and a temporal problem. First, we compute the latent space, which is the manifold onto which the turbulent dynamics live (i.e., it is a numerical approximation of the turbulent attractor). The latent space is found by a series of nonlinear filtering operations, which are performed by a convolutional autoencoder (CAE). The CAE provides the decomposition in space. Second, we predict the time evolution of the turbulent state in the latent space, which is performed by an echo state network (ESN). The ESN provides the decomposition in time. Third, by assembling the CAE and the ESN, we obtain an autonomous dynamical system: the convolutional autoncoder echo state network (CAE-ESN). This is the reduced-order model of the turbulent flow. We test the CAE-ESN on a two-dimensional flow. We show that, after training, the CAE-ESN (i) finds a latent-space representation of the turbulent flow that has less than 1% of the degrees of freedom than the physical space; (ii) time-accurately and statistically predicts the flow in both quasiperiodic and turbulent regimes; (iii) is robust for different flow regimes (Reynolds numbers); and (iv) takes less than 1% of computational time to predict the turbulent flow than solving the governing equations. This work opens up new possibilities for nonlinear decompositions and reduced-order modelling of turbulent flows from data.

physics.flu-dyn↗

arXiv2022

Physics-Informed Convolutional Neural Networks for Corruption Removal on Dynamical Systems

Measurements on dynamical systems, experimental or otherwise, are often subjected to inaccuracies capable of introducing corruption; removal of which is a problem of fundamental importance in the physical sciences. In this work we propose physics-informed convolutional neural networks for stationary corruption removal, providing the means to extract physical solutions from data, given access to partial ground-truth observations at collocation points. We showcase the methodology for 2D incompressible Navier-Stokes equations in the chaotic-turbulent flow regime, demonstrating robustness to modality and magnitude of corruption.

physics.flu-dyn↗

arXiv2022

Physics-Informed CNNs for Super-Resolution of Sparse Observations on Dynamical Systems

In the absence of high-resolution samples, super-resolution of sparse observations on dynamical systems is a challenging problem with wide-reaching applications in experimental settings. We showcase the application of physics-informed convolutional neural networks for super-resolution of sparse observations on grids. Results are shown for the chaotic-turbulent Kolmogorov flow, demonstrating the potential of this method for resolving finer scales of turbulence when compared with classic interpolation methods, and thus effectively reconstructing missing physics.

physics.flu-dyn↗

arXiv2022

Data-driven prediction and control of extreme events in a chaotic flow

An extreme event is a sudden and violent change in the state of a nonlinear system. In fluid dynamics, extreme events can have adverse effects on the system's optimal design and operability, which calls for accurate methods for their prediction and control. In this paper, we propose a data-driven methodology for the prediction and control of extreme events in a chaotic shear flow. The approach is based on echo state networks, which are a type of reservoir computing that learn temporal correlations within a time-dependent dataset. The objective is five-fold. First, we exploit ad-hoc metrics from binary classification to analyse (i) how many of the extreme events predicted by the network actually occur in the test set (precision), and (ii) how many extreme events are missed by the network (recall). We apply a principled strategy for optimal hyperparameter selection, which is key to the networks' performance. Second, we focus on the time-accurate prediction of extreme events. We show that echo state networks are able to predict extreme events well beyond the predictability time, i.e., up to more than five Lyapunov times. Third, we focus on the long-term prediction of extreme events from a statistical point of view. By training the networks with datasets that contain non-converged statistics, we show that the networks are able to learn and extrapolate the flow's long-term statistics. In other words, the networks are able to extrapolate in time from relatively short time series. Fourth, we design a simple and effective control strategy to prevent extreme events from occurring. The control strategy decreases the occurrence of extreme events up to one order of magnitude with respect to the uncontrolled system. Finally, we analyse the robustness of the results for a range of Reynolds numbers. We show that the networks perform well across a wide range of regimes.

physics.flu-dyn↗

arXiv2022

Statistical prediction of extreme events from small datasets

We propose Echo State Networks (ESNs) to predict the statistics of extreme events in a turbulent flow. We train the ESNs on small datasets that lack information about the extreme events. We asses whether the networks are able to extrapolate from the small imperfect datasets and predict the heavy-tail statistics that describe the events. We find that the networks correctly predict the events and improve the statistics of the system with respect to the training data in almost all cases analysed. This opens up new possibilities for the statistical prediction of extreme events in turbulence.

physics.flu-dyn↗

arXiv2022

Real-time thermoacoustic data assimilation

Low-order thermoacoustic models are qualitatively correct, but they are typically quantitatively inaccurate. We propose a time-domain bias-aware method to make qualitatively low--order models quantitatively (more) accurate. First, we develop a Bayesian ensemble data assimilation method for a low-order model to self-adapt and self-correct any time that reference data becomes available. Second, we apply the methodology to infer the thermoacoustic states and heat release parameters on the fly without storing data (real-time). We perform twin experiments using synthetic acoustic pressure measurements to analyse the performance of data assimilation in all nonlinear thermoacoustic regimes, from limit cycles to chaos, and interpret the results physically. Third, we propose practical rules for thermoacoustic data assimilation. An increase, reject, inflate strategy is proposed to deal with the rich nonlinear behaviour; and physical time scales for assimilation are proposed in non-chaotic regimes (with the Nyquist-Shannon criterion) and in chaotic regimes (with the Lyapunov time). Fourth, we perform data assimilation using data from a higher-fidelity model. We introduce an echo state network to estimate in real-time the forecast bias, which is the model error of the low-fidelity model. We show that (i) the correct acoustic pressure, parameters, and model bias can be accurately inferred; (ii) the learning is robust as it can tackle large uncertainties in the observations (up to 50% the mean values); (iii) the uncertainty of the prediction and parameters is naturally part of the output; and (iv) both the time-accurate solution and statistics can be successfully inferred. Data assimilation opens up new possibility for real-time prediction of thermoacoustics by synergistically combining physical knowledge and experimental data.

physics.flu-dyn↗

arXiv2022

A physical model for indirect noise in non-isentropic nozzles: Transfer functions and stability

We propose a mathematical model from physical principles to predict the sound generated in nozzles with dissipation. The focus is on the sound generated from the acceleration of temperature inhomogeneities (also known as entropy waves), which is referred to as indirect noise. First, we model the dissipation caused by flow recirculation and wall friction with a friction factor, which enables us to derive quasi-one-dimensional equations from conservation laws. The model is valid for both compact nozzles and nozzles with a spatial extent. Second, the predictions from the proposed model are compared against the experimental data available in the literature. Third, we compute the nozzle transfer functions for a range of Helmholtz numbers and friction factors. It is found that the friction and the Helmholtz number have a significant effect on the gain/phase of the reflected and transmitted waves. The analysis is performed from subsonic to supersonic regimes (with and without shock waves). The acoustic transfer functions vary significantly because of non-isentropic effects and the Helmholtz number, in particular, in the subsonic-choked regime. Finally, we calculate the effect that the friction of a nozzle guide vane has on thermoacoustic stability. It is found that the friction and the Helmholtz number can change thermoacoustic stability from a linearly stable regime to a linearly unstable regime. The study opens up new possibilities for the accurate prediction of indirect noise in realistic nozzles with implications on both noise emissions and thermoacoustic stability. nozzles with implications on both noise emissions and thermoacoustic stability.

physics.flu-dyn↗

arXiv2022

Gradient-free optimization of chaotic acoustics with reservoir computing

We develop a versatile optimization method, which finds the design parameters that minimize time-averaged acoustic cost functionals. The method is gradient-free, model-informed, and data-driven with reservoir computing based on echo state networks. First, we analyse the predictive capabilities of echo state networks both in the short- and long-time prediction of the dynamics. We find that both fully data-driven and model-informed architectures learn the chaotic acoustic dynamics, both time-accurately and statistically. Informing the training with a physical reduced-order model with one acoustic mode markedly improves the accuracy and robustness of the echo state networks, whilst keeping the computational cost low. Echo state networks offer accurate predictions of the long-time dynamics, which would be otherwise expensive by integrating the governing equations to evaluate the time-averaged quantity to optimize. Second, we couple echo state networks with a Bayesian technique to explore the design thermoacoustic parameter space. The computational method is minimally intrusive. Third, we find the set of flame parameters that minimize the time-averaged acoustic energy of chaotic oscillations, which are caused by the positive feedback with a heat source, such as a flame in gas turbines or rocket motors. These oscillations are known as thermoacoustic oscillations. The optimal set of flame parameters is found with the same accuracy as brute-force grid search, but with a convergence rate that is more than one order of magnitude faster. This work opens up new possibilities for non-intrusive ("hands-off") optimization of chaotic systems, in which the cost of generating data, for example from high-fidelity simulations and experiments, is high.

physics.flu-dyn↗

arXiv2021

Short- and long-term prediction of a chaotic flow: A physics-constrained reservoir computing approach

We propose a physics-constrained machine learning method-based on reservoir computing- to time-accurately predict extreme events and long-term velocity statistics in a model of turbulent shear flow. The method leverages the strengths of two different approaches: empirical modelling based on reservoir computing, which it learns the chaotic dynamics from data only, and physical modelling based on conservation laws, which extrapolates the dynamics when training data becomes unavailable. We show that the combination of the two approaches is able to accurately reproduce the velocity statistics and to predict the occurrence and amplitude of extreme events in a model of self-sustaining process in turbulence. In this flow, the extreme events are abrupt transitions from turbulent to quasi-laminar states, which are deterministic phenomena that cannot be traditionally predicted because of chaos. Furthermore, the physics-constrained machine learning method is shown to be robust with respect to noise. This work opens up new possibilities for synergistically enhancing data-driven methods with physical knowledge for the time-accurate prediction of chaotic flows.

physics.flu-dyn↗