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

Diffusion-based generative models have demonstrated exceptional performance, yet their iterative sampling procedures remain computationally expensive. A prominent strategy to mitigate this cost is distillation, with offline distillation…

In this work, we develop reduced order models (ROMs) to predict solutions to a multiscale kinetic transport equation with a diffusion limit under the parametric setting. When the underlying scattering effect is not sufficiently strong, the…

It has been recognized that the data generated by the denoising diffusion probabilistic model (DDPM) improves adversarial training. After two years of rapid development in diffusion models, a question naturally arises: can better diffusion…

Stochastic reaction-diffusion processes may be presented in terms of integrable quantum chains and can be used to describe various biological and chemical systems. Exploiting the integrability of the models one finds in some cases good…

In the paper, we consider the problem of robust approximation of transfer Koopman and Perron-Frobenius (P-F) operators from noisy time series data. In most applications, the time-series data obtained from simulation or experiment is…

The vulnerability of the high-performance machine learning models implies a security risk in applications with real-world consequences. Research on adversarial attacks is beneficial in guiding the development of machine learning models on…

Achievement of solutions in Navier-Stokes equation is one of challenging quests, especially for its closure problem. For achievement of particular solutions, there are variety of numerical simulations including Direct Numerical Simulation…

This study presents a collection of purely data-driven workflows for constructing reduced-order models (ROMs) for distributed dynamical systems. The ROMs we focus on, are data-assisted models inspired by, and templated upon, the theory of…

In this study, the numerical solutions of reaction-diffusion systems are investigated via the trigonometric quintic B-spline nite element collocation method. These equations appear in various disciplines in order to describe certain…

Diffusion models have gained significant attention for high-fidelity image generation. Our work investigates the potential of exploiting diffusion models for adversarial robustness in image classification and object detection. Adversarial…

Seismic data processing involves techniques to deal with undesired effects that occur during acquisition and pre-processing. These effects mainly comprise coherent artefacts such as multiples, non-coherent signals such as electrical noise,…

Deep learning is revolutionizing weather forecasting, with new data-driven models achieving accuracy on par with operational physical models for medium-term predictions. However, these models often lack interpretability, making their…

One of the key challenges that Reinforcement Learning (RL) faces is its limited capability to adapt to a change of data distribution caused by uncertainties. This challenge arises especially in RL systems using deep neural networks as…

In this paper we propose a Bayesian method as a numerical way to correct and stabilise projection-based reduced order models (ROM) in computational fluid dynamics problems. The approach is of hybrid type, and consists of the classical…

Inverse design refers to the problem of optimizing the input of an objective function in order to enact a target outcome. For many real-world engineering problems, the objective function takes the form of a simulator that predicts how the…

In this article we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear…

The use of dissipation for the controlled creation of nontrivial quantum many-body correlated states is of much fundamental and practical interest. What is the result of imposing number conservation, which, in closed system, gives rise to…

In this paper, we propose a non-parametric method for state estimation of high-dimensional nonlinear stochastic dynamical systems, which evolve according to gradient flows with isotropic diffusion. We combine diffusion maps, a manifold…

Nonlinear parametric inverse problems appear in many applications. Here, we focus on diffuse optical tomography (DOT) in medical imaging to recover unknown images of interest, such as cancerous tissue in a given medium, using a mathematical…

Denoising diffusion probabilistic models (DDPMs) are a recent family of generative models that achieve state-of-the-art results. In order to obtain class-conditional generation, it was suggested to guide the diffusion process by gradients…