arXiv subjects

Yannis G. Kevrekidis

Publications and source records attributed to Yannis G. Kevrekidis.

8 recordsLinked to original sources

arXiv2026

Mechanism-Aware Ensemble Conditioning for Data-Limited Emulation of Extreme Events

Extreme events in chaotic systems are difficult to learn from short trajectories because they are controlled by transient finite-time instability rather than by frequently observed bulk dynamics. We propose a mechanism-aware conditioning plug-in framework that turns a nudged coarse ensemble into a non-intrusive sensor of local instability geometry. In the small-noise regime, the ensemble covariance aggregates the same finite-time deformation kernels that govern local instability, providing a Jacobian-free proxy for the local amplification structure around a synchronized coarse trajectory. A small FiLM module injects statistics of this ensemble geometry into an otherwise unchanged backbone while leaving the coarse simulator unchanged. We demonstrate this interface in two distinct pipelines: a Transformer-style residual-attention corrector for a controlled low-dimensional chaotic system and a probabilistic recurrent STORN corrector for topographic two-layer quasi-geostrophic (QG) flow. In the low-dimensional benchmark, ensemble covariance directions co-activate with OTD modes and FiLM conditioning improves 99th-percentile exceedance-frequency errors over an identical no-context Transformer baseline. In QG, a fixed ensemble-conditioned FiLM-STORN model trained on only $50$ time units substantially improves long-horizon rare-event statistics in the data-limited regime, including density-tail errors, exceedance frequencies, and spatial exceedance-area distributions relative to an unconditioned STORN trained on the same data; on averaged high-threshold exceedance diagnostics, it also outperforms the baseline STORN trained with $20$ times more high-resolution data. These results show that local instability geometry is not merely interpretable post hoc, but an actionable conditioning signal for data-efficient rare-event emulation.

cs.LG↗

arXiv2026

The Right Space for Dynamics: Numerics with Diffeomorphism Equivariance

Among many (equivalent, via invertible transformations) representations of the evolution of a dynamical system, which one is to be preferred? Here we show how the use of infinite-dimensional Lie group theory (and its numerical implementation) allows us to single out one representation, by selecting an element of the group of diffeomorphisms acting on the dynamical system. We present and discuss several types of ``phase conditions" defining the selected representation, and illustrate their computational implementation. Study of dynamics modulo diffeomorphisms ``liberates" mathematical modeling of physical phenomena from a user's preferred coordinates, and spontaneously selects a ``right latent space" for the system.

math.DS↗

arXiv2026

Conformal Disentanglement and Latent-Space Curation: A Neural Framework for Perspective Synthesis, Differentiation and Targeted Generation

Many scientific and engineering problems involve observing a common phenomenon through multiple heterogeneous sensors or measurement modalities. Such observations typically contain both information shared across sensors, reflecting the underlying system, and sensor-specific or extraneous components arising from measurement processes or environmental effects. Disentangling these contributions is essential when sensor-independent observations are unavailable. We propose a neural autoencoder framework that explicitly separates shared and sensor-specific latent variables from multi-sensor data. The architecture enforces geometric independence between latent components through structural constraints and orthogonality-based regularization, yielding interpretable and disentangled representations. Building on this representation, we then introduce a latent-space generative methodology in which generative models are tuned/"restricted" on selected disentangled latent subspaces; we then constructively combine disentangled observed latent variables to conditionally synthesize new samples via trained decoders. This enables consistent data generation with prescribed shared (or sensor-specific) characteristics. It also supports cross-sensor inference by consistently sampling distributions over plausible measurements in unobserved modalities. We demonstrate the approach on several computational examples, showing effective disentanglement, targeted data generation, and modality imputation in heterogeneous sensing settings.

cs.LG↗

arXiv2025

Towards Coordinate- and Dimension-Agnostic Machine Learning for Partial Differential Equations

The machine learning methods for data-driven identification of partial differential equations (PDEs) are typically defined for a given number of spatial dimensions and a choice of coordinates the data have been collected in. This dependence prevents the learned evolution equation from generalizing to other spaces. In this work, we reformulate the problem in terms of coordinate- and dimension-independent representations, paving the way toward what we call ``spatially liberated" PDE learning. To this end, we employ a machine learning approach to predict the evolution of scalar field systems expressed in the formalism of exterior calculus, which is coordinate-free and immediately generalizes to arbitrary dimensions by construction. We demonstrate the performance of this approach in the FitzHugh-Nagumo and Barkley reaction-diffusion models, as well as the Patlak-Keller-Segel model informed by in-situ chemotactic bacteria observations. We provide extensive numerical experiments that demonstrate that our approach allows for seamless transitions across various spatial contexts. We show that the field dynamics learned in one space can be used to make accurate predictions in other spaces with different dimensions, coordinate systems, boundary conditions, and curvatures.

cs.LG↗

arXiv2025

Thinner Latent Spaces: Detecting Dimension and Imposing Invariance with Conformal Autoencoders

Conformal Autoencoders are a neural network architecture that imposes orthogonality conditions between the gradients of latent variables to obtain disentangled representations of data. In this work we show that orthogonality relations within the latent layer of the network can be leveraged to infer the intrinsic dimensionality of nonlinear manifold data sets (locally characterized by the dimension of their tangent space), while simultaneously computing encoding and decoding (embedding) maps. We outline the relevant theory relying on differential geometry, and describe the corresponding gradient-descent optimization algorithm. The method is applied to several data sets and we highlight its applicability, advantages, and shortcomings. In addition, we demonstrate that the same computational technology can be used to build coordinate invariance to local group actions when defined only on a (reduced) submanifold of the embedding space.

cs.LG↗

arXiv2025

Data-Driven, ML-assisted Approaches to Problem Well-Posedness

Classically, to solve differential equation problems, it is necessary to specify sufficient initial and/or boundary conditions so as to allow the existence of a unique solution. Well-posedness of differential equation problems thus involves studying the existence and uniqueness of solutions, and their dependence to such pre-specified conditions. However, in part due to mathematical necessity, these conditions are usually specified "to arbitrary precision" only on (appropriate portions of) the boundary of the space-time domain. This does not mirror how data acquisition is performed in realistic situations, where one may observe entire "patches" of solution data at arbitrary space-time locations; alternatively one might have access to more than one solutions stemming from the same differential operator. In our short work, we demonstrate how standard tools from machine and manifold learning can be used to infer, in a data driven manner, certain well-posedness features of differential equation problems, for initial/boundary condition combinations under which rigorous existence/uniqueness theorems are not known. Our study naturally combines a data assimilation perspective with an operator-learning one.

cs.LG↗

arXiv2024

Social Physics of Bacteria: Avoidance of an Information Black Hole

Social physics explores responses to information exchange in a social network, and can be mapped down to bacterial collective signaling. Here, we explore how social inter-bacterial communication includes coordination of response to communication loss, as opposed to solitary searching for food, with collective response emergence at the population level. We present a 2-dimensional enclosed microfluidic environment that utilizes concentric rings of funnel ratchets, which direct motile E.coli bacteria towards a sole exit hole, an information ``black hole'', passage into the black hole irreversibly sweeps the bacteria away via hydrodynamic flow. We show that the spatiotemporal evolution of entropy production reveals how bacteria avoid crossing the hydrodynamic black hole information horizon.

physics.bio-ph↗

arXiv2003

Apparent hysteresis in a driven system with self-organized drag

Interaction between extended defects and impurities lies at the heart of many physical phenomena in materials science. Here we revisit the ubiquitous problem of the driven motion of an extended defect in a field of mobile impurities, which self-organize to cause drag on the defect. Under a wide range of external conditions (e.g. drive), the defect undergoes a transition from slow to fast motion. This transition is commonly hysteretic: the defect either moves slow or fast, depending on the initial condition. We explore such hysteresis via a kinetic Monte Carlo spin simulation combined with computational coarse-graining. Obtaining bifurcation diagrams (stable and unstable branches), we map behavior regimes in parameter space. Estimating fast-slow switching times, we determine whether a simulation or experiment will exhibit hysteresis depending on observation conditions. We believe our approach is applicable to quantifying hysteresis in a wide range of physical contexts.

cond-mat↗