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In this paper, we consider high-dimensional stationary processes where a new observation is generated from a compressed version of past observations. The specific evolution is modeled by an encoder-decoder structure. We estimate the…
Lossy compression relies on an autoencoder to transform a point cloud into latent points for storage, leaving the inherent redundancy of latent representations unexplored. To reduce redundancy in latent points, we propose a diffusion-based…
Predictive manipulation has recently gained considerable attention in the Embodied AI community due to its potential to improve robot policy performance by leveraging predicted states. However, generating accurate future visual states of…
Computational fluid dynamics (CFD) is a powerful tool for modeling turbulent flow and is commonly used for urban microclimate simulations. However, traditional CFD methods are computationally intensive, requiring substantial hardware…
In this paper, a novel semantic communication framework empowered by generative artificial intelligence (GAI) is proposed, to enhance the robustness against both channel noise and transmission data distribution shifts. A theoretical…
This paper studies the problem of forecasting general stochastic processes using a path-dependent extension of the Neural Jump ODE (NJ-ODE) framework \citep{herrera2021neural}. While NJ-ODE was the first framework to establish convergence…
Score-based modeling through stochastic differential equations (SDEs) has provided a new perspective on diffusion models, and demonstrated superior performance on continuous data. However, the gradient of the log-likelihood function, i.e.,…
Scientific measurements are often bottlenecked by suboptimal conditions, whether that be noise, incomplete spatial coverage, or limited resolution, rendering accurate field reconstruction a difficult task. We introduce LatentPDE, a latent…
Is a deep learning model capable of understanding systems governed by certain first principle laws by only observing the system's output? Can deep learning learn the underlying physics and honor the physics when making predictions? The…
Diffusion-based representation learning has achieved substantial attention due to its promising capabilities in latent representation and sample generation. Recent studies have employed an auxiliary encoder to identify a corresponding…
Diffusion models, emerging as powerful deep generative tools, excel in various applications. They operate through a two-steps process: introducing noise into training samples and then employing a model to convert random noise into new…
We present a data-driven framework for reachability analysis of nonlinear dynamical systems that requires no explicit model. A denoising diffusion probabilistic model learns the time-evolving state distribution of a dynamical system from…
In this work we study how diffusion-based generative models produce high-dimensional data, such as an image, by implicitly relying on a manifestation of a low-dimensional set of latent abstractions, that guide the generative process. We…
With the advancement of IoT technologies and the rapid expansion of cyber-physical systems, there is increasing interest in distributed state estimation, where multiple sensors collaboratively monitor large-scale dynamic systems. Compared…
We consider the modeling, stability analysis and controller design problems for discrete-time LTI systems with state feedback, when the actuation signal is subject to switching propagation delays, due to e.g. the routing in a multi-hop…
The prediction of time series is a challenging task relevant in such diverse applications as analyzing financial data, forecasting flow dynamics or understanding biological processes. Especially chaotic time series that depend on a long…
Deep learning models have achieved remarkable progress in precipitation prediction. However, they still face significant challenges in accurately capturing spatial details of radar images, particularly in regions of high precipitation…
Modern time series data often display complex nonlinear dependencies along with irregular regime-switching behaviors. These features present technical challenges in modeling, inference, and in offering insightful understanding into the…
Short-term precipitation forecasting remains challenging due to the difficulty in capturing long-term spatiotemporal dependencies. Current deep learning methods fall short in establishing effective dependencies between conditions and…
To generate coherent responses, language models infer unobserved meaning from their input text sequence. One potential explanation for this capability arises from theories of delay embeddings in dynamical systems, which prove that…