arXiv subjects

Themistoklis Sapsis

Publications and source records attributed to Themistoklis Sapsis.

At least 19 recordsLinked to original sources

arXiv2026

A Temporal Barrier Framework for Collision Avoidance in Multi-Agent Autonomous Aerial Vehicles

Operating teams of autonomous aircraft in dynamic, uncertain, and potentially adversarial environments requires safety protocols that are reliable yet selective, and allow agents to fly in close proximity while making progress toward mission objectives. We introduce adversarial time-to-collision (aTTC), a risk metric that quantifies, for a given agent, how quickly any surrounding agent could reach it assuming adversarial intent. We embed aTTC into the control barrier function (CBF) framework, defining the barrier directly in time rather than distance or velocity. The resulting aTTC-CBF is inherently anticipatory: agents modulate their own velocity based not on whether a peer is on a collision course, but on how quickly one could reach collision given its dynamical constraints. A differentiable neural-network surrogate makes the aTTC computable in real time within a standard CBF quadratic program. Across long time-horizon simulations of 3D independent-pursuit and formation-flight scenarios, the aTTC-CBF achieves up to twice the waypoint progress at half the collision rate of a higher-order distance-based CBF baseline.

eess.SY↗

arXiv2025

GEN2: A Generative Prediction-Correction Framework for Long-time Emulations of Spatially-Resolved Climate Extremes

Accurately quantifying the increased risks of climate extremes requires generating large ensembles of climate realization across a wide range of emissions scenarios, which is computationally challenging for conventional Earth System Models. We propose GEN2, a generative prediction-correction framework for an efficient and accurate forecast of the extreme event statistics. The prediction step is constructed as a conditional Gaussian emulator, followed by a non-Gaussian machine-learning (ML) correction step. The ML model is trained on pairs of the reference data and the emulated fields nudged towards the reference, to ensure the training is robust to chaos. We first validate the accuracy of our model on historical ERA5 data and then demonstrate the extrapolation capabilities on various future climate change scenarios. When trained on a single realization of one warming scenario, our model accurately predicts the statistics of extreme events in different scenarios, successfully extrapolating beyond the distribution of training data.

physics.comp-ph↗

arXiv2024

A probabilistic framework for learning non-intrusive corrections to long-time climate simulations from short-time training data

Chaotic systems, such as turbulent flows, are ubiquitous in science and engineering. However, their study remains a challenge due to the large range scales, and the strong interaction with other, often not fully understood, physics. As a consequence, the spatiotemporal resolution required for accurate simulation of these systems is typically computationally infeasible, particularly for applications of long-term risk assessment, such as the quantification of extreme weather risk due to climate change. While data-driven modeling offers some promise of alleviating these obstacles, the scarcity of high-quality simulations results in limited available data to train such models, which is often compounded by the lack of stability for long-horizon simulations. As such, the computational, algorithmic, and data restrictions generally imply that the probability of rare extreme events is not accurately captured. In this work we present a general strategy for training neural network models to non-intrusively correct under-resolved long-time simulations of chaotic systems. The approach is based on training a post-processing correction operator on under-resolved simulations nudged towards a high-fidelity reference. This enables us to learn the dynamics of the underlying system directly, which allows us to use very little training data, even when the statistics thereof are far from converged. Additionally, through the use of probabilistic network architectures we are able to leverage the uncertainty due to the limited training data to further improve extrapolation capabilities. We apply our framework to severely under-resolved simulations of quasi-geostrophic flow and demonstrate its ability to accurately predict the anisotropic statistics over time horizons more than 30 times longer than the data seen in training.

cs.LG↗

arXiv2024

Learning Dissipative Chaotic Dynamics with Boundedness Guarantees

Chaotic dynamics, commonly seen in weather systems and fluid turbulence, are characterized by their sensitivity to initial conditions, which makes accurate prediction challenging. Recent approaches have focused on developing data-driven models that attempt to preserve invariant statistics over long horizons since many chaotic systems exhibit dissipative behaviors and ergodicity. Despite the recent progress in such models, they are still often prone to generating unbounded trajectories, leading to invalid statistics evaluation. To address this fundamental challenge, we introduce a modular framework that provides formal guarantees of trajectory boundedness for neural network chaotic dynamics models. Our core contribution is a dissipative projection layer that leverages control-theoretic principles to ensure the learned system is dissipative. Specifically, our framework simultaneously learns a dynamics emulator and an energy-like function, where the latter is used to construct an algebraic dissipative constraint within the projection layer. Furthermore, the learned invariant level set provides an outer estimate for the system's strange attractor, which is known to be difficult to characterize due to its complex geometry. We demonstrate our model's ability to produce bounded long-horizon forecasts that preserve invariant statistics for chaotic dynamical systems, including Lorenz 96 and a reduced-order model of the Kuramoto-Sivashinsky equation.

eess.SY↗

arXiv2024

Sampling low-fidelity outputs for estimation of high-fidelity density and its tails

In a multifidelity setting, data are available under the same conditions from two (or more) sources, e.g. computer codes, one being lower-fidelity but computationally cheaper, and the other higher-fidelity and more expensive. This work studies for which low-fidelity outputs, one should obtain high-fidelity outputs, if the goal is to estimate the probability density function of the latter, especially when it comes to the distribution tails and extremes. It is suggested to approach this problem from the perspective of the importance sampling of low-fidelity outputs according to some proposal distribution, combined with special considerations for the distribution tails based on extreme value theory. The notion of an optimal proposal distribution is introduced and investigated, in both theory and simulations. The approach is motivated and illustrated with an application to estimate the probability density function of record extremes of ship motions, obtained through two computer codes of different fidelities.

stat.ME↗

arXiv2024

A non-intrusive machine learning framework for debiasing long-time coarse resolution climate simulations and quantifying rare events statistics

Due to the rapidly changing climate, the frequency and severity of extreme weather is expected to increase over the coming decades. As fully-resolved climate simulations remain computationally intractable, policy makers must rely on coarse-models to quantify risk for extremes. However, coarse models suffer from inherent bias due to the ignored "sub-grid" scales. We propose a framework to non-intrusively debias coarse-resolution climate predictions using neural-network (NN) correction operators. Previous efforts have attempted to train such operators using loss functions that match statistics. However, this approach falls short with events that have longer return period than that of the training data, since the reference statistics have not converged. Here, the scope is to formulate a learning method that allows for correction of dynamics and quantification of extreme events with longer return period than the training data. The key obstacle is the chaotic nature of the underlying dynamics. To overcome this challenge, we introduce a dynamical systems approach where the correction operator is trained using reference data and a coarse model simulation nudged towards that reference. The method is demonstrated on debiasing an under-resolved quasi-geostrophic model and the Energy Exascale Earth System Model (E3SM). For the former, our method enables the quantification of events that have return period two orders longer than the training data. For the latter, when trained on 8 years of ERA5 data, our approach is able to correct the coarse E3SM output to closely reflect the 36-year ERA5 statistics for all prognostic variables and significantly reduce their spatial biases.

physics.ao-ph↗

arXiv2023

Statistics of extreme events in coarse-scale climate simulations via machine learning correction operators trained on nudged datasets

This work presents a systematic framework for improving the predictions of statistical quantities for turbulent systems, with a focus on correcting climate simulations obtained by coarse-scale models. While high resolution simulations or reanalysis data are available, they cannot be directly used as training datasets to machine learn a correction for the coarse-scale climate model outputs, since chaotic divergence, inherent in the climate dynamics, makes datasets from different resolutions incompatible. To overcome this fundamental limitation we employ coarse-resolution model simulations nudged towards high quality climate realizations, here in the form of ERA5 reanalysis data. The nudging term is sufficiently small to not pollute the coarse-scale dynamics over short time scales, but also sufficiently large to keep the coarse-scale simulations close to the ERA5 trajectory over larger time scales. The result is a compatible pair of the ERA5 trajectory and the weakly nudged coarse-resolution E3SM output that is used as input training data to machine learn a correction operator. Once training is complete, we perform free-running coarse-scale E3SM simulations without nudging and use those as input to the machine-learned correction operator to obtain high-quality (corrected) outputs. The model is applied to atmospheric climate data with the purpose of predicting global and local statistics of various quantities of a time-period of a decade. Using datasets that are not employed for training, we demonstrate that the produced datasets from the ML-corrected coarse E3SM model have statistical properties that closely resemble the observations. Furthermore, the corrected coarse-scale E3SM output for the frequency of occurrence of extreme events, such as tropical cyclones and atmospheric rivers are presented. We present thorough comparisons and discuss limitations of the approach.

physics.ao-ph↗

arXiv2023

Harnessing the instability mechanisms in airfoil flow for the data-driven forecasting of extreme events

This work addresses the data-driven forecasting of extreme events in the airfoil flow. These events may be seen as examples of the kind of unsteady and intermittent dynamics relevant to the flow around airfoils and wings in a variety of laboratory and real-world applications. W investigate the instability mechanisms at the heart of these extreme events, and how knowledge thereof may be harnessed for efficient data driven forecasting. Through a wavelet and spectral analysis of the flow we find that the extreme events arise due to the instability of a specific frequency component distinct from the vortex shedding mode. During these events this extreme event manifold draws energy from the energetically dominant vortex shedding flow and undergoes an abrupt energy transfer from small to large scales. We also investigate the spatial dependence of the temporal correlation and mutual information between the surface pressure and the aerodynamic forces, with the aim of identifying regions of the airfoil amenable to sparse sensing and the efficient forecasting of extremes. Building on previous work, we show that relying solely on the mutual information for optimal sensor placement fails to improve model prediction over uniform or random sensor placement. However, we show that by isolating the extreme event frequency component offline through a wavelet transform we are able to circumvent the requirement for a recursive long-short term memory (LSTM) network -- resulting in a significant reduction in computational complexity over the previous state of the art. Using the wavelet pre-processed data in conjunction with an extreme event-tailored loss function we find that our model is capable of forecasting extreme events using only three pressure sensors. Furthermore, we find our model to be robust to sensor location -- showing promise for the use of our model in dynamically varying applications.

physics.flu-dyn↗

arXiv2022

A Multi-Scale Deep Learning Framework for Projecting Weather Extremes

Weather extremes are a major societal and economic hazard, claiming thousands of lives and causing billions of dollars in damage every year. Under climate change, their impact and intensity are expected to worsen significantly. Unfortunately, general circulation models (GCMs), which are currently the primary tool for climate projections, cannot characterize weather extremes accurately. To address this, we present a multi-resolution deep-learning framework that, firstly, corrects a GCM's biases by matching low-order and tail statistics of its output with observations at coarse scales; and secondly, increases the level of detail of the debiased GCM output by reconstructing the finer scales as a function of the coarse scales. We use the proposed framework to generate statistically realistic realizations of the climate over Western Europe from a simple GCM corrected using observational atmospheric reanalysis. We also discuss implications for probabilistic risk assessment of natural disasters in a changing climate.

cs.LG↗

arXiv2022

Anisotropic Particles Focusing Effect in Complex Flows

Finite size effects can lead neutrally buoyant particles to exhibit different dynamics than tracer particles, and can alter their transport properties in fluid flows. Here we investigate the effect of the particle's shape on their dispersion in 2-dimensional complex flows. Combining numerical simulations with laboratory experiments, we show that particles with isotropic and anisotropic shapes exhibit different Lagrangian coherent structures, resulting in distinct dispersion phenomena within a given flow field. Experiments with rod shaped particles show a focusing effect in the vicinity of vortex cores. We present a simple model that describes the dynamics of neutrally buoyant ellipsoidal particles in two-dimensional flow and show that particle aspect ratio and orientation dependent forces can generate clustering phenomena in vortices.

physics.flu-dyn↗

arXiv2022

Generative stochastic modeling of strongly nonlinear flows with non-Gaussian statistics

Strongly nonlinear flows, which commonly arise in geophysical and engineering turbulence, are characterized by persistent and intermittent energy transfer between various spatial and temporal scales. These systems are difficult to model and analyze due to combination of high dimensionality and uncertainty, and there has been much interest in obtaining reduced models, in the form of stochastic closures, that can replicate their non-Gaussian statistics in many dimensions. Here, we propose a data-driven framework to model stationary chaotic dynamical systems through nonlinear transformations and a set of decoupled stochastic differential equations (SDEs). Specifically, we use optimal transport to find a transformation from the distribution of time-series data to a multiplicative reference probability measure such as the standard normal distribution. Then we find the set of decoupled SDEs that admit the reference measure as the invariant measure, and also closely match the spectrum of the transformed data. As such, this framework represents the chaotic time series as the evolution of a stochastic system observed through the lens of a nonlinear map. We demonstrate the application of this framework in Lorenz-96 system, a 10-dimensional model of high-Reynolds cavity flow, and reanalysis climate data. These examples show that SDE models generated by this framework can reproduce the non-Gaussian statistics of systems with moderate dimensions (e.g. 10 and more), and predict super-Gaussian tails that are not readily available from little training data. These findings suggest that this class of models provide an efficient hypothesis space for learning strongly nonlinear flows from small amounts of data.

math.DS↗

arXiv2021

Output-weighted and relative entropy loss functions for deep learning precursors of extreme events

Many scientific and engineering problems require accurate models of dynamical systems with rare and extreme events. Such problems present a challenging task for data-driven modelling, with many naive machine learning methods failing to predict or accurately quantify such events. One cause for this difficulty is that systems with extreme events, by definition, yield imbalanced datasets and that standard loss functions easily ignore rare events. That is, metrics for goodness of fit used to train models are not designed to ensure accuracy on rare events. This work seeks to improve the performance of regression models for extreme events by considering loss functions designed to highlight outliers. We propose a novel loss function, the adjusted output weighted loss, and extend the applicability of relative entropy based loss functions to systems with low dimensional output. The proposed functions are tested using several cases of dynamical systems exhibiting extreme events and shown to significantly improve accuracy in predictions of extreme events.

cs.LG↗

arXiv2021

Output-Weighted Sampling for Multi-Armed Bandits with Extreme Payoffs

We present a new type of acquisition functions for online decision making in multi-armed and contextual bandit problems with extreme payoffs. Specifically, we model the payoff function as a Gaussian process and formulate a novel type of upper confidence bound (UCB) acquisition function that guides exploration towards the bandits that are deemed most relevant according to the variability of the observed rewards. This is achieved by computing a tractable likelihood ratio that quantifies the importance of the output relative to the inputs and essentially acts as an \textit{attention mechanism} that promotes exploration of extreme rewards. We demonstrate the benefits of the proposed methodology across several synthetic benchmarks, as well as a realistic example involving noisy sensor network data. Finally, we provide a JAX library for efficient bandit optimization using Gaussian processes.

cs.LG↗

arXiv2021

Learning Optimal Parametric Hydrodynamic Database for Vortex-Induced Crossflow Vibration Prediction

The Vortex-induced vibration (VIV) prediction of long flexible cylindrical structures relies on the accuracy of the hydrodynamic database constructed via rigid cylinder forced vibration experiments. However, to create a comprehensive hydrodynamic database with tens of input parameters including vibration amplitudes and frequencies and Reynolds number, surface roughness and so forth is technically challenging and virtually impossible due to the large number of experiments required. The current work presents an alternative approach to approximate the crossflow (CF) hydrodynamic coefficient database in a carefully chosen parameterized form. The learning of the parameters is posed as a constraint optimization, where the objective function is constructed based on the error between the experimental response and theoretical prediction assuming energy balance between fluid and structure. Such a method yields the optimal estimation of the CF parametric hydrodynamic database and produces the VIV response prediction based on the updated hydrodynamic database. The method then was tested on several experiments, including freely-mounted rigid cylinder in large Reynolds number with combined crossflow and inline vibrations and large-scale flexible cylinder test in the Norwegian Deepwater Program, and the result is shown to robustly and significantly reduce the error in predicting cylinder VIVs.

physics.flu-dyn↗

arXiv2021

Output-Weighted Optimal Sampling for Bayesian Experimental Design and Uncertainty Quantification

We introduce a class of acquisition functions for sample selection that leads to faster convergence in applications related to Bayesian experimental design and uncertainty quantification. The approach follows the paradigm of active learning, whereby existing samples of a black-box function are utilized to optimize the next most informative sample. The proposed method aims to take advantage of the fact that some input directions of the black-box function have a larger impact on the output than others, which is important especially for systems exhibiting rare and extreme events. The acquisition functions introduced in this work leverage the properties of the likelihood ratio, a quantity that acts as a probabilistic sampling weight and guides the active-learning algorithm towards regions of the input space that are deemed most relevant. We demonstrate superiority of the proposed approach in the uncertainty quantification of a hydrological system as well as the probabilistic quantification of rare events in dynamical systems and the identification of their precursors.

stat.ML↗

arXiv2021

Informative Path Planning for Extreme Anomaly Detection in Environment Exploration and Monitoring

An unmanned autonomous vehicle (UAV) is sent on a mission to explore and reconstruct an unknown environment from a series of measurements collected by Bayesian optimization. The success of the mission is judged by the UAV's ability to faithfully reconstruct any anomalous features present in the environment, with emphasis on the extremes (e.g., extreme topographic depressions or abnormal chemical concentrations). We show that the criteria commonly used for determining which locations the UAV should visit are ill-suited for this task. We introduce a number of novel criteria that guide the UAV towards regions of strong anomalies by leveraging previously collected information in a mathematically elegant and computationally tractable manner. We demonstrate superiority of the proposed approach in several applications, including reconstruction of seafloor topography from real-world bathymetry data, as well as tracking of dynamic anomalies. A particularly attractive property of our approach is its ability to overcome adversarial conditions, that is, situations in which prior beliefs about the locations of the extremes are imprecise or erroneous.

stat.ML↗

arXiv2020

Bayesian Optimization with Output-Weighted Optimal Sampling

In Bayesian optimization, accounting for the importance of the output relative to the input is a crucial yet challenging exercise, as it can considerably improve the final result but often involves inaccurate and cumbersome entropy estimations. We approach the problem from the perspective of importance-sampling theory, and advocate the use of the likelihood ratio to guide the search algorithm towards regions of the input space where the objective function to be minimized assumes abnormally small values. The likelihood ratio acts as a sampling weight and can be computed at each iteration without severely deteriorating the overall efficiency of the algorithm. In particular, it can be approximated in a way that makes the approach tractable in high dimensions. The "likelihood-weighted" acquisition functions introduced in this work are found to outperform their unweighted counterparts in a number of applications.

cs.LG↗

arXiv2020

Strong solutions for the Alber equation and stability of unidirectional wave spectra

The Alber equation is a moment equation for the nonlinear Schrödinger equation, formally used in ocean engineering to investigate the stability of stationary and homogeneous sea states in terms of their power spectra. In this work we present the first well-posedness theory for the Alber equation with the help of an appropriate equivalent reformulation. Moreover, we show linear Landau damping in the sense that, under a stability condition on the homogeneous background, any inhomogeneities disperse and decay in time. The proof exploits novel $L^2$ space-time estimates to control the inhomogeneity and our result applies to any regular initial data (without a mean-zero restriction). Finally, the sufficient condition for stability is resolved, and the physical implications for ocean waves are discussed. Using a standard reference dataset (the "North Atlantic Scatter Diagram") it is found that the vast majority of sea states are stable, but modulationally unstable sea states do appear, with likelihood $O(1/1000);$ these would be the prime breeding ground for rogue waves.

math-ph↗