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Register a new userAnalysis of a bistable climate toy model with physics-based machine learning methods
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We propose a comprehensive framework able to address both the predictability of the first and of the second kind for high-dimensional chaotic models. For this purpose, we analyse the properties of a newly introduced multistable climate toy model constructed by coupling the Lorenz 96 model with a zero-dimensional energy balance model. First, the attractors of the system are identified with Monte Carlo Basin Bifurcation Analysis. Additionally, we are able to detect the Melancholia state separating the two attractors. Then, Neural Ordinary Differential Equations are applied in order to predict the future state of the system in both of the identified attractors.
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Data assimilation (DA) aims at optimally merging observational data and model outputs to create a coherent statistical and dynamical picture of the system under investigation. Indeed, DA aims at minimizing the effect of observational and model error, and at distilling the correct ingredients of its dynamics. DA is of critical importance for the analysis of systems featuring sensitive dependence on the initial conditions, as chaos wins over any finitely accurate knowledge of the state of the system, even in absence of model error. Clearly, the skill of DA is guided by the properties of dynamical system under investigation, as merging optimally observational data and model outputs is harder when strong instabilities are present. In this paper we reverse the usual angle on the problem and show that it is indeed possible to use the skill of DA to infer some basic properties of the tangent space of the system, which may be hard to compute in very high-dimensional systems. Here, we focus our attention on the first Lyapunov exponent and the Kolmogorov-Sinai entropy, and perform numerical experiments on the Vissio-Lucarini 2020 model, a recently proposed generalisation of the Lorenz 1996 model that is able to describe in a simple yet meaningful way the interplay between dynamical and thermodynamical variables.
The many ways in which machine and deep learning are transforming the analysis and simulation of data in particle physics are reviewed. The main methods based on boosted decision trees and various types of neural networks are introduced, and cutting-edge applications in the experimental and theoretical/phenomenological domains are highlighted. After describing the challenges in the application of these novel analysis techniques, the review concludes by discussing the interactions between physics and machine learning as a two-way street enriching both disciplines and helping to meet the present and future challenges of data-intensive science at the energy and intensity frontiers.
New heterogeneous computing paradigms on dedicated hardware with increased parallelization, such as Field Programmable Gate Arrays (FPGAs), offer exciting solutions with large potential gains. The growing applications of machine learning algorithms in particle physics for simulation, reconstruction, and analysis are naturally deployed on such platforms. We demonstrate that the acceleration of machine learning inference as a web service represents a heterogeneous computing solution for particle physics experiments that potentially requires minimal modification to the current computing model. As examples, we retrain the ResNet-50 convolutional neural network to demonstrate state-of-the-art performance for top quark jet tagging at the LHC and apply a ResNet-50 model with transfer learning for neutrino event classification. Using Project Brainwave by Microsoft to accelerate the ResNet-50 image classification model, we achieve average inference times of 60 (10) milliseconds with our experimental physics software framework using Brainwave as a cloud (edge or on-premises) service, representing an improvement by a factor of approximately 30 (175) in model inference latency over traditional CPU inference in current experimental hardware. A single FPGA service accessed by many CPUs achieves a throughput of 600--700 inferences per second using an image batch of one, comparable to large batch-size GPU throughput and significantly better than small batch-size GPU throughput. Deployed as an edge or cloud service for the particle physics computing model, coprocessor accelerators can have a higher duty cycle and are potentially much more cost-effective.
In statistical data assimilation (SDA) and supervised machine learning (ML), we wish to transfer information from observations to a model of the processes underlying those observations. For SDA, the model consists of a set of differential equations that describe the dynamics of a physical system. For ML, the model is usually constructed using other strategies. In this paper, we develop a systematic formulation based on Monte Carlo sampling to achieve such information transfer. Following the derivation of an appropriate target distribution, we present the formulation based on the standard Metropolis-Hasting (MH) procedure and the Hamiltonian Monte Carlo (HMC) method for performing the high dimensional integrals that appear. To the extensive literature on MH and HMC, we add (1) an annealing method using a hyperparameter that governs the precision of the model to identify and explore the highest probability regions of phase space dominating those integrals, and (2) a strategy for initializing the state space search. The efficacy of the proposed formulation is demonstrated using a nonlinear dynamical model with chaotic solutions widely used in geophysics.
texttt{GooStats} is a software framework that provides a flexible environment and common tools to implement multi-variate statistical analysis. The framework is built upon the texttt{CERN ROOT}, texttt{MINUIT} and texttt{GooFit} packages. Running a multi-variate analysis in parallel on graphics processing units yields a huge boost in performance and opens new possibilities. The design and benchmark of texttt{GooStats} are presented in this article along with illustration of its application to statistical problems.
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