arXiv subjects

Brian Hunt

Publications and source records attributed to Brian Hunt.

12 recordsLinked to original sources

arXiv2025

Tailored Forecasting from Short Time Series via Meta-learning

Machine learning models can effectively forecast dynamical systems from time-series data, but they typically require large amounts of past data, making forecasting particularly challenging for systems with limited history. To overcome this, we introduce Meta-learning for Tailored Forecasting using Related Time Series (METAFORS), which generalizes knowledge across systems to enable forecasting in data-limited scenarios. By learning from a library of models trained on longer time series from potentially related systems, METAFORS builds and initializes a model tailored to short time-series data from the system of interest. Using a reservoir computing implementation and testing on simulated chaotic systems, we demonstrate that METAFORS can reliably predict both short-term dynamics and long-term statistics without requiring contextual labels. We see this even when test and related systems exhibit substantially different behaviors, highlighting METAFORS' strengths in data-limited scenarios.

cs.LG↗

arXiv2024

Prediction Beyond the Medium Range with an Atmosphere-Ocean Model that Combines Physics-based Modeling and Machine Learning

This paper explores the potential of a hybrid modeling approach that combines machine learning (ML) with conventional physics-based modeling for weather prediction beyond the medium range. It extends the work of Arcomano et al. (2022), which tested the approach for short- and medium-range weather prediction, and the work of Arcomano et al. (2023), which investigated its potential for climate modeling. The hybrid model used for the forecast experiments of the paper is based on the low-resolution, simplified parameterization atmospheric general circulation model SPEEDY. In addition to the hybridized prognostic variables of SPEEDY, the model has three purely ML-based prognostic variables: the 6h cumulative precipitation, the sea surface temperature, and the heat content of the top 300m deep layer of the ocean (a new addition compared to the model used in Arcomano et al., 2023). The model has skill in predicting the El Nino cycle and its global teleconnections with precipitation for 3-7 months depending on the season. The model captures equatorial variability of the precipitation associated with Kelvin and Rossby waves and MJO. Predictions of the precipitation in the equatorial region have skill for 15 days in the East Pacific and 11.5 days in the West Pacific. Though the model has low spatial resolution, for these tasks it has prediction skill comparable to what has been published for high-resolution, purely physics-based, conventional, operational forecast models.

physics.ao-ph↗

arXiv2020

Combining Machine Learning with Knowledge-Based Modeling for Scalable Forecasting and Subgrid-Scale Closure of Large, Complex, Spatiotemporal Systems

We consider the commonly encountered situation (e.g., in weather forecasting) where the goal is to predict the time evolution of a large, spatiotemporally chaotic dynamical system when we have access to both time series data of previous system states and an imperfect model of the full system dynamics. Specifically, we attempt to utilize machine learning as the essential tool for integrating the use of past data into predictions. In order to facilitate scalability to the common scenario of interest where the spatiotemporally chaotic system is very large and complex, we propose combining two approaches:(i) a parallel machine learning prediction scheme; and (ii) a hybrid technique, for a composite prediction system composed of a knowledge-based component and a machine-learning-based component. We demonstrate that not only can this method combining (i) and (ii) be scaled to give excellent performance for very large systems, but also that the length of time series data needed to train our multiple, parallel machine learning components is dramatically less than that necessary without parallelization. Furthermore, considering cases where computational realization of the knowledge-based component does not resolve subgrid-scale processes, our scheme is able to use training data to incorporate the effect of the unresolved short-scale dynamics upon the resolved longer-scale dynamics ("subgrid-scale closure").

cs.LG↗

arXiv2019

The Recurrent Processing Unit: Hardware for High Speed Machine Learning

Machine learning applications are computationally demanding and power intensive. Hardware acceleration of these software tools is a natural step being explored using various technologies. A recurrent processing unit (RPU) is fast and power-efficient hardware for machine learning under development at the University of Maryland. It is comprised of a recurrent neural network and a trainable output vector as a hardware implementation of a reservoir computer. The reservoir is currently realized on both Xilinx 7-series and Ultrascale+ ZYNQ SoCs using an autonomous Boolean network for processing and a Python-based software API. The RPU is capable of classifying up to 40M MNIST images per second with the reservoir consuming under 261mW of power. Using an array of 2048 unclocked gates with roughly 100pS transition times, we achieve about 20 TOPS and 75 TOPS/W.

cs.ET↗

arXiv2019

Separation of Chaotic Signals by Reservoir Computing

We demonstrate the utility of machine learning in the separation of superimposed chaotic signals using a technique called Reservoir Computing. We assume no knowledge of the dynamical equations that produce the signals, and require only training data consisting of finite time samples of the component signals. We test our method on signals that are formed as linear combinations of signals from two Lorenz systems with different parameters. Comparing our nonlinear method with the optimal linear solution to the separation problem, the Wiener filter, we find that our method significantly outperforms the Wiener filter in all the scenarios we study. Furthermore, this difference is particularly striking when the component signals have similar frequency spectra. Indeed, our method works well when the component frequency spectra are indistinguishable - a case where a Wiener filter performs essentially no separation.

eess.SP↗

arXiv2018

Hybrid Forecasting of Chaotic Processes: Using Machine Learning in Conjunction with a Knowledge-Based Model

A model-based approach to forecasting chaotic dynamical systems utilizes knowledge of the physical processes governing the dynamics to build an approximate mathematical model of the system. In contrast, machine learning techniques have demonstrated promising results for forecasting chaotic systems purely from past time series measurements of system state variables (training data), without prior knowledge of the system dynamics. The motivation for this paper is the potential of machine learning for filling in the gaps in our underlying mechanistic knowledge that cause widely-used knowledge-based models to be inaccurate. Thus we here propose a general method that leverages the advantages of these two approaches by combining a knowledge-based model and a machine learning technique to build a hybrid forecasting scheme. Potential applications for such an approach are numerous (e.g., improving weather forecasting). We demonstrate and test the utility of this approach using a particular illustrative version of a machine learning known as reservoir computing, and we apply the resulting hybrid forecaster to a low-dimensional chaotic system, as well as to a high-dimensional spatiotemporal chaotic system. These tests yield extremely promising results in that our hybrid technique is able to accurately predict for a much longer period of time than either its machine-learning component or its model-based component alone.

cs.LG↗

arXiv2008

Synchronization in networks of networks: the onset of coherent collective behavior in systems of interacting populations of heterogeneous oscillators

The onset of synchronization in networks of networks is investigated. Specifically, we consider networks of interacting phase oscillators in which the set of oscillators is composed of several distinct populations. The oscillators in a given population are heterogeneous in that their natural frequencies are drawn from a given distribution, and each population has its own such distribution. The coupling among the oscillators is global, however, we permit the coupling strengths between the members of different populations to be separately specified. We determine the critical condition for the onset of coherent collective behavior, and develop the illustrative case in which the oscillator frequencies are drawn from a set of (possibly different) Cauchy-Lorentz distributions. One motivation is drawn from neurobiology, in which the collective dynamics of several interacting populations of oscillators (such as excitatory and inhibitory neurons and glia) are of interest.

math.DS↗

arXiv2007

Estimating the State of Large Spatiotemporally Chaotic Systems

Data assimilation refers to the process of obtaining an estimate of a system's state using a model for the system's time evolution and a time series of measurements that are possibly noisy and incomplete. However, for practical reasons, the high dimensionality of large spatiotemporally chaotic systems prevents the use of classical data assimilation techniques. Here, via numerical computations on the paradigmatic example of large aspect ratio Rayleigh-Benard convection, we demonstrate the applicability of a recently developed data assimilation method designed to circumvent this difficulty. In addition, we describe extensions of the algorithm for estimating unknown system parameters. Our results suggest the potential usefulness of our data assimilation technique to a broad class of situations in which there is spatiotemporally chaotic behavior.

nlin.CD↗

arXiv2004

Two Models for the Study of Congested Internet Connections

In this paper, we introduce two deterministic models aimed at capturing the dynamics of congested Internet connections. The first model is a continuous-time model that combines a system of differential equations with a sudden change in one of the state variables. The second model is a discrete-time model with a time step that arises naturally from the system. Results from these models show good agreement with the well-known ns network simulator, better than the results of a previous, similar model. This is due in large part to the use of the sudden change to reflect the impact of lost data packets. We also discuss the potential use of this model in network traffic state estimation.

cs.NI↗

arXiv2002

Fractal Properties of Robust Strange Nonchaotic Attractors in Maps of Two or More Dimensions

We consider the existence of robust strange nonchaotic attractors (SNA's) in a simple class of quasiperiodically forced systems. Rigorous results are presented demonstrating that the resulting attractors are strange in the sense that their box-counting dimension is N+1 while their information dimension is N. We also show how these properties are manifested in numerical experiments.

nlin.CD↗

arXiv2002

Evolving Networks with Multi-species Nodes and Spread in the Number of Initial Links

We consider models for growing networks incorporating two effects not previously considered: (i) different species of nodes, with each species having different properties (such as different attachment probabilities to other node species); and (ii) when a new node is born, its number of links to old nodes is random with a given probability distribution. Our numerical simulations show good agreement with analytic solutions. As an application of our model, we investigate the movie-actor network with movies considered as nodes and actors as links.

physics.data-an↗

arXiv2000

A stretched exponential bound on the rate of growth of the number of periodic points for prevalent diffeomorphisms

Let M be a compact manifold of dimension at least 2, Diff^r(M) be the space of C^r diffeomorphisms of M. Define for any diffeomorphism f in Diff^r(M) number of isolated periodic points of period n by P_n(f)=# {isolated x in M: f^n(x)=x}. Artin--Mazur proved that for a dense set of diffeomorphisms the number of periodic points P_n(f) growth at most exponentially fast in n. The author proved that there is an open set N \subset Diff^r(M) such that for a Baire generic set of diffeomorphisms the number of periodic points P_n(f) growth arbitrarily fast. Arnold posed a problem: Prove that diffeomorphisms with at most exponential growth of the number of periodic points in period have probability one. In this paper we annonce and exhibit key ingredients for a partial solution to Arnold's problem: we prove that for any epsilon>0 with probability one the number of periodic points is bounded by a streched exponential estimate P_n(f)<exp(Cn^{1+epsilon}).

math.DS↗