Engineering topics

Crutchfield, James P.

Publications and source records attributed to Crutchfield, James P..

4 records

DOE OSTI2024

On principles of emergent organization

After more than a century of concerted effort, physics still lacks basic principles of spontaneous organization. To appreciate why, we first state the problem, outline historical approaches, and survey the present state of the physics of self-organization. This frames the particular challenges arising from mathematical intractability and the resulting need for computational approaches, as well as those arising from a chronic failure to define structure. Then an overview of two modern mathematical formulations of organization—intrinsic computation and evolution operators—lays out a way to overcome these challenges. Together, the vantage point they afford shows how to account for the emergence of structured states via a statistical mechanics of systems arbitrarily far from equilibrium. The result is a constructive path forward to principles of organization that builds on mathematical identification of structure.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Complexity-calibrated benchmarks for machine learning reveal when prediction algorithms succeed and mislead

Abstract Recurrent neural networks are used to forecast time series in finance, climate, language, and from many other domains. Reservoir computers are a particularly easily trainable form of recurrent neural network. Recently, a “next-generation” reservoir computer was introduced in which the memory trace involves only a finite number of previous symbols. We explore the inherent limitations of finite-past memory traces in this intriguing proposal. A lower bound from Fano’s inequality shows that, on highly non-Markovian processes generated by large probabilistic state machines, next-generation reservoir computers with reasonably long memory traces have an error probability that is at least $$\sim 60\%$$ ∼ 60 % higher than the minimal attainable error probability in predicting the next observation. More generally, it appears that popular recurrent neural networks fall far short of optimally predicting such complex processes. These results highlight the need for a new generation of optimized recurrent neural network architectures. Alongside this finding, we present concentration-of-measure results for randomly-generated but complex processes. One conclusion is that large probabilistic state machines—specifically, large $$\epsilon$$ ϵ -machines—are key to generating challenging and structurally-unbiased stimuli for ground-truthing recurrent neural network architectures.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1994

Dripping handrails and the quasi-periodic oscillations of the AM Herculis objects

AM Her objects exhibit periodic, quasi-periodic, and aperiodic variability on timescales ranging from seconds to years. Here, we investigate a process for the production of aperiodic and quasi-periodic accretion rate fluctuations. We consider the nonlinear dynamical model known as the dripping handrail (DHR). The DHR, basically a model for certain types of spatially extended systems and loosely based on water condensing on and dripping off a handrail, has recently been used as a model for the quasi-periodic oscillations (QPO) and very low frequency noise of the low-mass X-ray binary Sco X-1. Here, we show that (1) the DHR is a robust QPO generation process in that it leads to QPO production under a wide range of conditions and assumptions; (2) the phenomenology of the DHR is consistent with the observed aperiodic and quasi-periodic varibility of the AM Her QPO source VV Pup over timescales ranging from 16 ms to 20 s; and (3) a single DHR model can produce both broadband QPOs and features with quality Q greater than 20 as observed in several AM Her QPO sources.

Steiman-Cameron, Thomas Y.↗

NASA NTRS1993

The quasi-periodic oscillations and very low frequency noise of Scorpius X-1 as transient chaos - A dripping handrail?

We present evidence that the quasi-periodic oscillations (QPO) and very low frequency noise (VLFN) characteristic of many accretion sources are different aspects of the same physical process. We analyzed a long, high time resolution EXOSAT observation of the low-mass X-ray binary (LMXB) Sco X-1. The X-ray luminosity varies stochastically on time scales from milliseconds to hours. The nature of this variability - as quantified with both power spectrum analysis and a new wavelet technique, the scalegram - agrees well with the dripping handrail accretion model, a simple dynamical system which exhibits transient chaos. In this model both the QPO and VLFN are produced by radiation from blobs with a wide size distribution, resulting from accretion and subsequent diffusion of hot gas, the density of which is limited by an unspecified instability to lie below a threshold.

Scargle, Jeffrey D.↗