arXiv subjects

Adriano Gualandi

Publications and source records attributed to Adriano Gualandi.

5 recordsLinked to original sources

arXiv2024

Spatio-temporal Dynamical Indices for Complex Systems

Complex systems span multiple spatial and temporal scales, making their dynamics challenging to understand and predict. This challenge is especially daunting when one wants to study localized and/or rare events. Advances in dynamical systems theory, including the development of state-dependent dynamical indices, namely local dimension and persistence, have provided powerful tools for studying these phenomena. However, existing applications of such indices rely on a predefined and fixed spatial domain, that provides a single scalar quantity for the entire region of interest. This aspect prevents understanding the spatially localized dynamical behavior of the system. In this work, we introduce Spatio-temporal Dynamical Indices (SDIs), that leverage the existing framework of state-dependent local dimension and persistence. SDIs are obtained via a sliding window approach, enabling the exploration of space-dependent properties in spatio-temporal data. As an example, we show that, through this framework, we are able to reconcile previously different perspectives on European summertime heatwaves. This result showcases the importance of accounting for spatial scales when performing scale-dependent dynamical analyses.

physics.ao-ph↗

arXiv2024

Time-Lagged Recurrence: a data-driven method to estimate the predictability of dynamical systems

Nonlinear dynamical systems are ubiquitous in nature and they are hard to forecast. Not only they may be sensitive to small perturbations in their initial conditions, but they are often composed of processes acting at multiple scales. Classical approaches based on the Lyapunov spectrum rely on the knowledge of the dynamic forward operator, or of a data-derived approximation of it. This operator is typically unknown, or the data are too noisy to derive its faithful representation. Here we propose a new data-driven approach to analyze the local predictability of dynamical systems. This method, based on the concept of recurrence, is closely linked to the well-established framework of local dynamical indices. When applied to both idealized systems and real-world datasets arising from large-scale atmospheric fields, our new approach proves its effectiveness in estimating local predictability. Additionally, we discuss its relationship with other local dynamical indices, and how it reveals the scale-dependent nature of predictability. Furthermore, we explore its link to information theory, its extension that includes a weighting strategy, and its real-time application. We believe these aspects collectively demonstrate its potential as a powerful diagnostic tool for complex systems.

nlin.CD↗

arXiv2024

PILA: Physics-Informed Low Rank Augmentation for Interpretable Earth Observation

Physically meaningful representations are essential for Earth Observation (EO), yet existing physical models are often simplified and incomplete. This leads to discrepancies between simulation and observations that hinder reliable forward model inversion. Common approaches to EO inversion either ignored this incompleteness or relied on case-specific preprocessing. More recent methods use physics-informed autoencoders but depend on auxiliary variables that are difficult to interpret and multiple regularizers that are difficult to balance. We propose Physics-Informed Low-Rank Augmentation (PILA), a framework that augments incomplete physical models using a learnable low-rank residual to improve flexibility, while remaining close to the governing physics. We evaluate PILA on two EO inverse problems involving diverse physical processes: forest radiative transfer inversion from optical remote sensing; and volcanic deformation inversion from Global Navigation Satellite Systems (GNSS) displacement data. Across different domains, PILA yields more accurate and interpretable physical variables. For forest spectral inversion, it improves the separation of tree species and, compared to ground measurements, reduces prediction errors by 40-71\% relative to the state-of-the-art. For volcanic deformation, PILA's recovery of variables captures a major inflation event at the Akutan volcano in 2008, and estimates source depth, volume change, and displacement patterns that are consistent with prior studies that however required substantial additional preprocessing. Finally, we analyse the effects of model rank, observability, and physical priors, and suggest that PILA may offer an effective general pathway for inverting incomplete physical models even beyond the domain of Earth Observation. The code is available at https://github.com/yihshe/PILA.git.

cs.LG↗

arXiv2023

A Hybrid Two-level MCMC Framework to Accelerate Posterior Mean Estimation with Deep Learning Surrogates for Bayesian Inverse Problems

Bayesian inverse problems arise in various scientific and engineering domains, and solving them can be computationally demanding. This is especially the case for problems governed by partial differential equations, where the repeated evaluation of the forward operator is extremely expensive. Recent advances in Deep Learning (DL)-based surrogate models have shown promising potential to accelerate the solution of such problems. However, despite their ability to learn from complex data, DL-based surrogate models generally cannot match the accuracy of high-fidelity numerical models, which limits their practical applicability. We propose a novel hybrid two-level Markov Chain Monte Carlo (MCMC) method that combines the strengths of DL-based surrogate models and high-fidelity numerical solvers to {compute the posterior mean of Quantities of Interest (QoI) in} Bayesian inverse problems governed by partial differential equations. The intuition is to leverage the evaluation speed of a DL-based surrogate model as the base chain, and correct its errors using a limited number of high-fidelity numerical model evaluations in a correction chain; hence its name hybrid two-level MCMC method. Through a detailed theoretical analysis, we show that our approach can achieve the same accuracy as a pure numerical MCMC method while requiring only a small fraction of the computational cost. The theoretical analysis is further supported by several numerical experiments, namely a Poisson, a non-linear reaction-diffusion, and a Navier-Stokes equation. The proposed hybrid framework can be generalized to other approaches such as the ensemble Kalman filter and sequential Monte Carlo methods.

math.NA↗

arXiv2022

Stochastic Chaos and Predictability in Laboratory Earthquakes

Laboratory earthquakes exhibit characteristics of a low dimensional random attractor with a dimension similar to that of natural slow earthquakes. A model of stochastic differential equations based on rate and state-dependent friction explains the laboratory observations. We study the transition from stable sliding to stickslip events and find that aperiodic behavior can be explained by small perturbations in the stress state. Friction's nonlinear nature amplifies small scale perturbations, reducing the predictability of the otherwise periodic macroscopic dynamics.

nlin.CD↗