Related papers: Overcoming the Curse of Dimensionality: Structural…

Pairwise Causal Discovery is the task of determining causal, anticausal, confounded or independence relationships from pairs of variables. Over the last few years, this challenging task has promoted not only the discovery of novel machine…

High-dimensional spatio-temporal dynamics can often be encoded in a low-dimensional subspace. Engineering applications for modeling, characterization, design, and control of such large-scale systems often rely on dimensionality reduction to…

Reconstructing PDE-governed fields from sparse and irregular measurements is challenging due to their ill-posed nature. Deterministic surrogates are trained on dense fields that struggle with limited measurements and uncertainty…

Understanding brain dynamics and functions critically depends on knowledge of the network connectivity among neurons. However, the complexity of brain structural connectivity, coupled with continuous modifications driven by synaptic…

This paper presents StrADiff, a Structured Source-Wise Adaptive Diffusion Framework for unsupervised blind source separation under linear and nonlinear mixing. The framework treats each latent dimension as a source branch and assigns to it…

We introduce Prior-Informed Flow Matching (PIFM), a conditional flow model for graph reconstruction. Reconstructing graphs from partial observations remains a key challenge; classical embedding methods often lack global consistency, while…

In image restoration, single-step discriminative mappings often lack fine details via expectation learning, whereas generative paradigms suffer from inefficient multi-step sampling and noise-residual coupling. To address this dilemma, we…

Unsupervised Reinforcement Learning from Internal Feedback (RLIF) has emerged as a promising paradigm for eliciting the latent capabilities of Large Language Models (LLMs) without external supervision. However, current methods rely on…

Deep Implicit Functions (DIFs) represent 3D geometry with continuous signed distance functions learned through deep neural nets. Recently DIFs-based methods have been proposed to handle shape reconstruction and dense point correspondences…

We introduce Coupled Flow Matching (CPFM), a framework that integrates controllable dimensionality reduction and high-fidelity reconstruction. CPFM learns coupled continuous flows for both the high-dimensional data x and the low-dimensional…

Over the past few years, deep learning methods have proved to be of great interest for the computational fluid dynamics community, especially when used as surrogate models, either for flow reconstruction, turbulence modeling, or for the…

Artificial intelligence, particularly the subfield of machine learning, has seen a paradigm shift towards data-driven models that learn from and adapt to data. This has resulted in unprecedented advancements in various domains such as…

Inferring network topology from dynamical observations is a fundamental problem pervading research on complex systems. Here, we present a simple, direct method to infer the structural connection topology of a network, given an observation…

Physics-Informed Neural Networks (PINNs) offer a powerful paradigm for flow reconstruction, seamlessly integrating sparse velocity measurements with the governing Navier-Stokes equations to recover complete velocity and latent pressure…

Physical dynamic networks most commonly consist of interconnections of physical components that can be described by diffusive couplings. These diffusive couplings imply that the cause-effect relationships in the interconnections are…

Predicting the evolution of a large system of units using its structure of interaction is a fundamental problem in complex system theory. And so is the problem of reconstructing the structure of interaction from temporal observations. Here,…

Functional connectivity estimates are highly sensitive to analysis choices and can be dominated by noise when the number of sampled time points is small relative to network dimensionality. This issue is particularly acute in fMRI, where…

Time-delay embedding is a powerful technique for reconstructing the state space of nonlinear time series. However, the fidelity of reconstruction relies on the assumption that the time-delay map is an embedding, which is implicitly…

Engineered infrastructure systems pose inverse problems in which hidden states, unknown parameters, and subsystem couplings must be inferred from sparse and noisy measurements. These problems are difficult because physical subsystems are…

Dynamic functional connectivity (dFC) is ubiquitously observed in the brain, but why functional networks should remain dynamic even at rest is unclear. We asked whether temporal reconfiguration becomes advantageous when keeping a functional…