arXiv subjects

Nozomi Sugiura

Publications and source records attributed to Nozomi Sugiura.

12 recordsLinked to original sources

arXiv2026

Koopman Analysis of Sea Surface Temperature with a Signature Kernel

We develop a trajectory-based Koopman method for sea surface temperature (SST) that lifts annual SST segments using a signature kernel -- a reproducing kernel Hilbert space (RKHS) kernel that compares paths via iterated-integral features -- and learns the one-year shift operator. By operating on annual trajectory segments rather than instantaneous fields, the method encodes finite-time history, which helps capture memory effects in SST-only evolution. The resulting operator improves out-of-sample multi-year forecast skill relative to a climatology baseline and reveals coherent spectral modes. We implement the approach via kernel extended dynamic mode decomposition (EDMD) on signature-kernel Gram matrices, yielding a single pipeline for forecasting and spectral diagnostics of high-dimensional SST dynamics.

physics.ao-ph↗

arXiv2024

The barycenter in free nilpotent Lie groups and its application to iterated-integrals signatures

We establish the well-definedness of the barycenter (in the sense of Buser and Karcher) for every integrable measure on the free nilpotent Lie group of step $L$ (over $\mathbb{R}^d$). We provide two algorithms for computing it, using methods from Lie theory (namely, the Baker-Campbell-Hausdorff formula) and from the theory of Gröbner bases of modules. Our main motivation stems from measures induced by iterated-integrals signatures, and we calculate the barycenter for the signature of the Brownian motion.

math.RA↗

arXiv2023

Principal Geodesic Analysis applied to climate time series

Principal Geodesic Analysis (PGA) is applied to a climate time series. First, we transform each multidimensional sequence into the path signature. Since the signature lives in a curved space, usual principal component analysis (PCA) is not applicable. Instead, we treat the signature space as a geodesic manifold. By replacing the notion of straight lines with that of geodesics, the domain of PCA can be extended to the curved space. Then, the first principal component is derived as the geodesic that minimizes the unexplained variance in the data. As an application, we computed the leading modes for one-year NINO SST time series, which are divided into segments that represent annual variations of monthly averages. It is interesting that some months in a year reveal characteristic undulations that could indicate the early signs of upcoming El Ninõ events.

physics.data-an↗

arXiv2022

Introduction to the signature method

The sequential data observed in earth science can be regarded as paths in multidimensional space. To read the path effectively, it is useful to convert it into a sequence of numbers called the signature, which can faithfully describe the order of points and nonlinearity in the path. In particular, a linear combination of the terms in a signature can be used to approximate any nonlinear function defined on a set of paths. Thereby, when one learns a set of sequential data with labels attached to it, linear regression can be applied to the pairs of signature and label, which will achieve high performance learning even when the labels are determined by a nonlinear function. By incorporating the signature methods into machine learning and data assimilation utilizing sequential data, it is expected that we can extract information that has previously been overlooked.

physics.geo-ph↗

arXiv2022

Simple El Niño prediction scheme using the signature of climate time series

El Niño is a typical example of a coupled atmosphere--ocean phenomenon, but it is unclear whether it can be described quantitatively by a correlation between relevant climate events. To provide clarity on this issue, we developed a machine learning-based El Niño prediction model that uses the time series of climate indices. By transforming the multidimensional time series into the path signature, the model is able to properly evaluate the order and nonlinearity of climate events, which allowed us to achieve good forecasting skill (mean square error = 0.596 for 6-month prediction). In addition, it is possible to provide information about the sequence of climate events that tend to change the future NINO3.4 sea surface temperatures. In forecasting experiments conducted, changes in the North Pacific Index and several NINO indices were found to be important precursors. The results suggest that El Niño is predictable to some extent based on the correlation of climate events.

physics.ao-ph↗

arXiv2021

Clustering global ocean profiles according to temperature-salinity structure

An unsupervised clustering using a Gaussian mixture model is applied to Argo profiles distributed over the entire ocean. We employ as the coordinate components in feature space the path signature, which is a central notion in rough path theory. This allows us to better identify the oceanic condition at each horizontal point with distinct clusters, than by using conventional temperature and salinity coordinate. To the best of my knowledge, it is the first attempt at clustering almost all of the existing Argo profiles with the full use of measured sequences of temperature, salinity, and pressure. We will also discuss why the path signature is relevant to representing the property of a profile.

physics.geo-ph↗

arXiv2020

Estimating the population mean for a vertical profile of energy dissipation rate

Energy dissipation rates are an important characteristic of turbulence; however, their magnitude in observational profiles can be incorrectly determined owing to their irregular appearance during vertical evolution. By analysing the data obtained from oceanic turbulence measurements, we demonstrate that the vertical sequences of energy dissipation rates exhibit a scaling property. Utilising this property, we propose a method to estimate the population mean for a profile. For scaling in the observed profiles, we demonstrate that our data exhibit a statistical property consistent with that exhibited by the universal multifractal model. Meanwhile, the population mean and its uncertainty can be estimated by inverting the probability distribution obtained by Monte Carlo simulations of a cascade model; to this end, observational constraints from several moments are imposed over each vertical sequence. This approach enables us to determine, to some extent, whether a profile shows an occasionally large mean or whether the population mean itself is large. Thus, it will contribute to the refinement of the regional estimation of the ocean energy budget, where only a small amount of turbulence observation data is available.

physics.geo-ph↗

arXiv2020

Machine learning technique using the signature method for automated quality control of the Argo profiles

A profile from the Argo ocean observation array is a sequence of three-dimensional vectors composed of pressure, salinity, and temperature, appearing as a continuous curve in three-dimensional space. The shape of this curve is faithfully represented by a path signature, which is a collection of all the iterated integrals. Moreover, the product of two terms of the signature of a path can be expressed as the sum of higher-order terms. Thanks to this algebraic property, a nonlinear function of profile shape can always be represented by a weighted linear combination of the iterated integrals, which enables machine learning of a complicated function of the profile shape. In this study, we performed supervised learning for existing Argo data with quality control flags by using the signature method, and demonstrated the estimation performance by cross-validation. Unlike rule-based approaches, which require several complicated and possibly subjective rules, this method is simple and objective in nature because it relies only on past knowledge regarding the shape of profiles. This technique should be critical to realizing automatic quality control for Argo profile data.

physics.geo-ph↗

arXiv2017

The Onsager--Machlup functional for data assimilation

When taking the model error into account in data assimilation, one needs to evaluate the prior distribution represented by the Onsager--Machlup functional. Through numerical experiments, this study clarifies how the prior distribution should be incorporated into cost functions for discrete-time estimation problems. Consistent with previous theoretical studies, the divergence of the drift term is essential in weak-constraint 4D-Var (w4D-Var), but it is not nec essary in Markov chain Monte Carlo with the Euler scheme. Although the former property may cause difficulties when implementing w4D-Var in large systems, this paper proposes a new technique for estimating the divergence term and its derivative.

physics.data-an↗

arXiv2016

Coarse-grained sensitivity for multiscale data assimilation

We show that the effective average action and its gradient are useful for solving multiscale data assimilation problems. We also present a procedure for numerically evaluating the gradient of the effective average action, and demonstrate that the variational problem for slow degrees of freedom can be solved properly using the "effective gradient."

physics.data-an↗

arXiv2015

A framework for interpreting regularized state estimation

Four-dimensional variational data assimilation (4D-Var) on a seasonal-to-interdecadal time scale under the existence of unstable modes can be viewed as an optimization problem of synchronized, coupled chaotic systems. The problem is tackled by adjusting initial conditions to bring all stable modes closer to observations and by using a continuous guide to direct unstable modes toward a reference time series. This interpretation provides a consistent and effective procedure for solving problems of long-term state estimation. By applying this approach to an ocean general circulation model with a parameterized vertical diffusion procedure, it is demonstrated that tangent linear and adjoint models in this framework should have no unstable modes and hence be suitable for tracking persistent signals. This methodology is widely applicable to extend the assimilation period in 4D-Var.

physics.data-an↗

arXiv2015

Synchronization of coupled stick-slip oscillators

A rationale is provided for the emergence of synchronization in a system of coupled oscillators in a stick-slip motion. The single oscillator has a limit cycle in a region of the state space for each parameter set beyond the supercritical Hopf bifurcation. The two-oscillator system that has similar weakly coupled oscillators exhibits synchronization in a parameter range. The synchronization has an anti-phase nature for an identical pair. However, it tends to be more in-phase for a non-identical pair with a rather weak coupling. A system of three identical oscillators (1, 2, and 3) coupled in a line (with two springs k12=k23) exhibits synchronization with two of them (1 and 2 or 2 and 3) being nearly in-phase. These collective behaviours are systematically estimated using the phase reduction method.

nlin.AO↗