Related papers: Deep Adversarial Koopman Model for Reaction-Diffus…

Non-adversarial robustness, also known as natural robustness, is a property of deep learning models that enables them to maintain performance even when faced with distribution shifts caused by natural variations in data. However, achieving…

The Koopman operator has recently garnered much attention for its value in dynamical systems analysis and data-driven model discovery. However, its application has been hindered by the computational complexity of extended dynamic mode…

A learning method is proposed for Koopman operator-based models with the goal of improving closed-loop control behavior. A neural network-based approach is used to discover a space of observables in which nonlinear dynamics is linearly…

Typical generative diffusion models rely on a Gaussian diffusion process for training the backward transformations, which can then be used to generate samples from Gaussian noise. However, real world data often takes place in discrete-state…

Temporal distributional shifts, with underlying dynamics changing over time, frequently occur in real-world time series and pose a fundamental challenge for deep neural networks (DNNs). In this paper, we propose a novel deep sequence model…

Koopman operator theory has emerged as a powerful tool for system identification, particularly for approximating nonlinear time-invariant systems (NTIS). This paper considers a network of agents with limited observation capabilities that…

Synthetic data generation has become an emerging tool to help improve the adversarial robustness in classification tasks since robust learning requires a significantly larger amount of training samples compared with standard classification…

Aerial manipulators undergo rapid, configuration-dependent changes in inertial coupling forces and aerodynamic forces, making accurate dynamics modeling a core challenge for reliable control. Analytical models lose fidelity under these…

This paper proposes a new method to propagate uncertainties undergoing nonlinear dynamics using the Koopman Operator (KO). Probability density functions are propagated directly using the Koopman approximation of the solution flow of the…

Recent breakthroughs in the field of deep learning have led to advancements in a broad spectrum of tasks in computer vision, audio processing, natural language processing and other areas. In most instances where these tasks are deployed in…

Neural Networks (NNs) have been identified as a potentially powerful tool in the study of complex dynamical systems. A good example is the NN differential equation (DE) solver, which provides closed form, differentiable, functional…

Developing large-scale distributed methods that are robust to the presence of adversarial or corrupted workers is an important part of making such methods practical for real-world problems. Here, we propose an iterative approach that is…

We study an autocatalytic reaction-diffusion scheme, the Gray-Scott model, when the mixing processes do not homogenize the reactants. Starting from the master equation, we derive the resulting coupled, nonlinear, stochastic partial…

This paper proposes a novel reaction-diffusion system approximation tailored for singular diffusion problems, typified by the fast diffusion equation. While such approximation methods have been successfully applied to degenerate parabolic…

Reaction-Diffusion systems arise in diverse areas of science and engineering. Due to the peculiar characteristics of such equations, analytic solutions are usually not available and numerical methods are the main tools for approximating the…

We study here the random diffusion model. This is a continuum model for a conserved scalar density field $\phi$ driven by diffusive dynamics. The interesting feature of the dynamics is that the {\it bare} diffusion coefficient $D$ is…

Diffusion-based models have achieved notable empirical successes in reinforcement learning (RL) due to their expressiveness in modeling complex distributions. Despite existing methods being promising, the key challenge of extending existing…

The conditional diffusion model (CDM) enhances the standard diffusion model by providing more control, improving the quality and relevance of the outputs, and making the model adaptable to a wider range of complex tasks. However, inaccurate…

Inverse problems exist in many disciplines of science and engineering. In computer vision, for example, tasks such as inpainting, deblurring, and super resolution can be effectively modeled as inverse problems. Recently, denoising diffusion…

Conventional meta-atom designs rely heavily on researchers' prior knowledge and trial-and-error searches using full-wave simulations, resulting in time-consuming and inefficient processes. Inverse design methods based on optimization…