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Chaos arises in many complex dynamical systems, from weather to power grids, but is difficult to accurately model using data-driven emulators, including neural operator architectures. For chaotic systems, the inherent sensitivity to initial…
Variational methods have proven to be excellent tools to approximate ground states of complex many body Hamiltonians. Generic tools like neural networks are extremely powerful, but their parameters are not necessarily physically motivated.…
Data assimilation performance can be significantly impacted by biased noise in observations, altering the signal magnitude and introducing fast oscillations or discontinuities when the system lacks smoothness. To mitigate these issues, this…
Data assimilation leads naturally to a Bayesian formulation in which the posterior probability distribution of the system state, given the observations, plays a central conceptual role. The aim of this paper is to use this Bayesian…
The reconstruction from observations of high-dimensional chaotic dynamics such as geophysical flows is hampered by (i) the partial and noisy observations that can realistically be obtained, (ii) the need to learn from long time series of…
Dynamical systems theory has long provided a foundation for understanding evolving phenomena across scientific domains. Yet, the application of this theory to complex real-world systems remains challenging due to issues in mathematical…
Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically…
We propose, analyze, and test a novel continuous data assimilation reduced order model (DA-ROM) for simulating incompressible flows. While ROMs have a long history of success on certain problems with recurring dominant structures, they tend…
The use of data assimilation technique to identify optimal topography is discussed in frames of time-dependent motion governed by non-linear barotropic ocean model. Assimilation of artificially generated data allows to measure the influence…
A novel strategy is proposed to improve the accuracy of state estimation and reconstruction from low-fidelity models and sparse data from sensors. This strategy combines ensemble Data Assimilation (DA) and Machine Learning (ML) tools,…
Constraining a numerical weather prediction (NWP) model with observations via 4D variational (4D-Var) data assimilation is often difficult to implement in practice due to the need to develop and maintain a software-based tangent linear…
Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…
We introduce a response-theoretic framework that recasts parameter calibration of ergodic stochastic differential equations as a fluctuation-dissipation problem. Our central result is that the full Jacobian of any stationary observable with…
Time series of individual subjects have become a common data type in psychological research. These data allow one to estimate models of within-subject dynamics, and thereby avoid the notorious problem of making within-subjects inferences…
We propose an efficient retraining strategy for a parameterized Reduced Order Model (ROM) that attains accuracy comparable to full retraining while requiring only a fraction of the computational time and relying solely on sparse…
We describe a new approach allowing for systematic causal attribution of weather and climate-related events, in near-real time. The method is purposely designed to facilitate its implementation at meteorological centers by relying on data…
This paper proposes a flexible framework for inferring large-scale time-varying and time-lagged correlation networks from multivariate or high-dimensional non-stationary time series with piecewise smooth trends. Built on a novel and unified…
Today's ocean numerical prediction skills depend on the availability of in-situ and remote ocean observations at the time of the predictions only. Because observations are scarce and discontinuous in time and space, numerical models are…
The dynamic mode decomposition (DMD) has become a leading tool for data-driven modeling of dynamical systems, providing a regression framework for fitting linear dynamical models to time-series measurement data. We present a simple…
Data assimilation plays a crucial role in modern weather prediction, providing a systematic way to incorporate observational data into complex dynamical models. The paper addresses continuous data assimilation for a model arising as a…